1.
Domenico Fetti
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Domenico Fetti was an Italian Baroque painter, active mainly in Rome, Mantua and Venice. He then worked in Mantua from 1613 to 1622, patronized by the Cardinal, later Duke Ferdinando I Gonzaga. In the Ducal Palace, he painted the Miracle of the Loaves and Fishes. Into this mix, in the 1620s–30s, three "foreigners"—Fetti and his younger contemporaries Bernardo Strozzi and Jan Lys—breathed the first influences of Roman Baroque style. They adapted it to Caravaggio-influenced monumentality. In Venice, where he remained despite pleas from the Duke to return to Mantua, Fetti changed his style: his formalized painting style became more colorful. In addition, he devoted attention to smaller cabinet pieces that adapt genre imaging to religious stories. His group of paintings entitled Parables, which represent New Testament scenes, are at the Dresden Gemäldegalerie. He influenced Leonaert Bramer. His painting style appears to have been influenced by Rubens. He would likely have continued to find excellent patronage in Venice had he not died there in 1623 or 1624. Jan Lys, eight years younger, but who had arrived in Venice nearly contemporaneously, died during the plague of 1629–30. Subsequently, Fetti's style would influence the Venetians Pietro della Vecchia and Sebastiano Mazzone. His pupils in Mantua were Francesco Bernardi and Dionisio Guerri. Fetti's works include: The Good Samaritan Melancholy Emperor Domitian Eve and Laboring Adam Angel in the Garden Jacob's Dream Portrait of an Actor Wittkower, Rudolf.
Domenico Fetti
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Melanconia (Accademia, Venice)
Domenico Fetti
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Portrait of a Man with a Sheet of Music (Getty Museum)
Domenico Fetti
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Portrait of an Actor (c. 1621–1622)
Domenico Fetti
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Ideal Portrait of Gonzaga (c. 1620)
2.
Syracuse, Sicily
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Syracuse is a historic city in Sicily, the capital of the province of Syracuse. The city is notable for its rich Greek history, culture, amphitheatres, as the birthplace of the preeminent mathematician and engineer Archimedes. This 2,700-year-old city played a key role in ancient times, when it was one of the major powers of the Mediterranean world. Syracuse is located beside the Ionian Sea. The city became a very powerful city-state. Syracuse was exerted influence over the entirety of Magna Graecia, of which it was the most important city. Described as "the greatest Greek city and the most beautiful of them all", it equaled Athens in size during the fifth century BC. It later became part of the Roman Republic and Byzantine Empire. After this Palermo overtook it as the capital of the Kingdom of Sicily. Eventually the kingdom would be united with the Kingdom of Naples to form the Two Sicilies until the Italian unification of 1860. In the modern day, the city is listed by UNESCO along with the Necropolis of Pantalica. In the city itself has a population of around 125,000 people. The inhabitants are known as Siracusans. Syracuse is mentioned at 28:12 as Paul stayed there. The saint of the city is Saint Lucy; she was born in Syracuse and her feast day, Saint Lucy's Day, is celebrated on 13 December.
Syracuse, Sicily
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Ortygia island, where Syracuse was founded in ancient Greek times. Mount Etna is visible in the distance.
Syracuse, Sicily
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A Syracusan tetradrachm (c. 415–405 BC), sporting Arethusa and a quadriga.
Syracuse, Sicily
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Decadrachme from Sicile struck at Syracuse and sign d'Évainète
Syracuse, Sicily
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The siege of Syracuse in a 17th-century engraving.
3.
Magna Graecia
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Most notably the Roman poet Ovid referred in his poem Fasti. According to Strabo Great Greece started already at the time of the Tojan War and lasted for several centuries. Also during that period, Greek colonies were established in places widely separated as the eastern coast of the Black Sea, Massalia. They included settlements in Sicily and the southern part of the Italian Peninsula. The Romans called the area of Sicily and the foot of Italy Magna Graecia since it was so densely inhabited by the Greeks. The ancient geographers differed on whether the term included Sicily or merely Apulia and Calabria: Strabo being the most prominent advocate of the wider definitions. With colonization, Greek culture was exported in its dialects of the Ancient Greek language, its traditions of the independent polis. An original Hellenic civilization soon developed, later interacting with the native Italic civilisations. Many of the Hellenic cities became very powerful, like Neapolis, Syracuse, Acragas Paestum and Sybaris. Other cities in Magna Graecia included others. Following the Pyrrhic War in the 3rd century BC, Magna Graecia was absorbed into the Roman Republic. A remarkable example of the influence is the Griko-speaking minority that still exists today in the Italian regions of Calabria and Apulia. Some scholars, such as Gerhard Rohlfs, argue that the origins of Griko may ultimately be traced to the colonies of Magna Graecia. One example is the Griko people, some of whom still maintain their Greek language and customs. For example, Greeks re-entered the region by the Ottoman Empire.
Magna Graecia
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Cities of Magna Graecia and other Greek settlements in Italy (in red)
Magna Graecia
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Northwestern
Magna Graecia
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Greek temples of Paestum, Campania
Magna Graecia
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Mosaic from Caulonia, Calabria
4.
Mathematics
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Mathematics is the study of topics such as quantity, structure, space, change. There is a range of views among philosophers as to the exact scope and definition of mathematics. Mathematicians use them to formulate new conjectures. Mathematicians resolve the falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of logic, mathematics developed from counting, calculation, measurement, the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Galileo Galilei said, "The universe can not become familiar with the characters in which it is written. Without these, one is wandering about in a dark labyrinth." Carl Friedrich Gauss referred as "the Queen of the Sciences". Benjamin Peirce called mathematics "the science that draws necessary conclusions". David Hilbert said of mathematics: "We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules.
Mathematics
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Euclid (holding calipers), Greek mathematician, 3rd century BC, as imagined by Raphael in this detail from The School of Athens.
Mathematics
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Greek mathematician Pythagoras (c. 570 – c. 495 BC), commonly credited with discovering the Pythagorean theorem
Mathematics
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Leonardo Fibonacci, the Italian mathematician who established the Hindu–Arabic numeral system to the Western World
Mathematics
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Carl Friedrich Gauss, known as the prince of mathematicians
5.
Physics
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One of the main goal of physics is to understand how the universe behaves. Physics is one of perhaps the oldest through its inclusion of astronomy. The boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms of other sciences while opening new avenues of research in areas such as philosophy. Physics also makes significant contributions through advances in new technologies that arise from theoretical breakthroughs. The United Nations named the World Year of Physics. Astronomy is the oldest of the natural sciences. The planets were often a target of worship, believed to represent their gods. While the explanations for these phenomena were often unscientific and lacking in evidence, these early observations laid the foundation for later astronomy. In the book, he was also the first to delved further into the way the eye itself works. Fellow polymaths, from Robert Grosseteste and Leonardo da Vinci to René Descartes, Johannes Kepler and Isaac Newton, were in his debt. Indeed, the influence of Ibn al-Haytham's Optics ranks alongside that of Newton's work of the same title, published 700 years later. The translation of The Book of Optics had a huge impact on Europe. From it, later European scholars were able to build the same devices as what Ibn Al Haytham understand the way light works. From this, important things as eyeglasses, magnifying glasses, telescopes, cameras were developed.
Physics
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Further information: Outline of physics
Physics
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Ancient Egyptian astronomy is evident in monuments like the ceiling of Senemut's tomb from the Eighteenth Dynasty of Egypt.
Physics
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Sir Isaac Newton (1643–1727), whose laws of motion and universal gravitation were major milestones in classical physics
Physics
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Albert Einstein (1879–1955), whose work on the photoelectric effect and the theory of relativity led to a revolution in 20th century physics
6.
Engineering
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The term Engineering is derived from ingeniare, meaning "to contrive, devise". Engineering has existed as humans devised fundamental inventions such as lever, wheel, pulley. Each of these inventions is essentially consistent with the modern definition of engineering. The engineering is derived from the engineer, which itself dates back to 1390 when an engine'er originally referred to "a constructor of military engines." In this context, now obsolete, an "engine" referred to a military machine, i.e. a mechanical contraption used in war. Notable examples of the obsolete usage which have survived to the present day are military engineering corps, e.g. the U.S. Army Corps of Engineers. The word "engine" itself is of even older origin, ultimately deriving from the Latin ingenium, meaning "innate quality, especially mental power, hence a clever invention." The earliest civil engineer known by name is Imhotep. Ancient Greece developed machines in both civilian and military domains. The mechanical inventions of Archimedes are examples of early mechanical engineering. In the Middle Ages, the trebuchet was developed. The first engine was built by Thomas Savery. The development of this device gave rise to the Industrial Revolution in the coming decades, allowing for the beginnings of mass production. Similarly, in addition to military and civil engineering, the fields then known as the mechanic arts became incorporated into engineering. The inventions of the Scottish engineer James Watt gave rise to mechanical engineering.
Engineering
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The steam engine, a major driver in the Industrial Revolution, underscores the importance of engineering in modern history. This beam engine is on display in the Technical University of Madrid.
Engineering
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Relief map of the Citadel of Lille, designed in 1668 by Vauban, the foremost military engineer of his age.
Engineering
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The Ancient Romans built aqueducts to bring a steady supply of clean fresh water to cities and towns in the empire.
Engineering
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The International Space Station represents a modern engineering challenge from many disciplines.
7.
Astronomy
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Astronomy is a natural science that studies celestial objects and phenomena. It applies mathematics, chemistry, in an effort to explain the origin of those objects and phenomena and their evolution. The objects of interest include planets, moons, stars, comets; while the phenomena include supernovae explosions, gamma ray bursts, cosmic microwave background radiation. More generally all astronomical phenomena that originate outside Earth's atmosphere is within the perview of astronomy. Physical cosmology, is concerned with the study of the Universe as a whole. Astronomy is the oldest of the natural sciences. The early civilizations in recorded history, such as Greeks, Indians, Egyptians, Nubians, Iranians, Chinese, Maya performed methodical observations of the night sky. During the 20th century, the field of professional astronomy split into theoretical branches. Observational astronomy is focused on acquiring data from observations of astronomical objects, then analyzed using basic principles of physics. Theoretical astronomy is oriented toward the development of computer or analytical models to describe astronomical phenomena. The two fields complement each other, with theoretical astronomy seeking to explain the observational observations being used to confirm theoretical results. Astronomy is one of the few sciences where amateurs can still play an active role, especially in the observation of transient phenomena. Amateur astronomers have contributed to many important astronomical discoveries, such as finding new comets. Astronomy means "law of the stars". Astronomy should not be confused with the belief system which claims that human affairs are correlated with the positions of celestial objects.
Astronomy
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A star -forming region in the Large Magellanic Cloud, an irregular galaxy.
Astronomy
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A giant Hubble mosaic of the Crab Nebula, a supernova remnant
Astronomy
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19th century Sydney Observatory, Australia (1873)
Astronomy
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19th century Quito Astronomical Observatory is located 12 minutes south of the Equator in Quito, Ecuador.
8.
Invention
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An invention is a unique or novel device, method, composition or process. The process is a process within an overall engineering and product development process. It may be an improvement for creating an object or a result. An invention that achieves a completely unique result may be a radical breakthrough. Such works are novel and not obvious to others skilled in the same field. An inventor may be taking a big step in failure. Some inventions can be patented. A patent legally legally recognizes that a claimed invention is actually an invention. The process of obtaining a patent is often expensive. Another meaning of invention is cultural invention, an innovative set of social behaviours adopted by people and passed on to others. The Institute for Social Inventions collected such ideas in magazines and books. Invention is also an important component of design creativity. Inventions often extend the boundaries of human knowledge, capability. Brainstorming also can spark new ideas for an invention. Creative processes are frequently used by engineers, designers, architects and scientists.
Invention
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' BUILD YOUR OWN TELEVISION RECEIVER.' Science and Invention magazine cover, November 1928
Invention
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Alessandro Volta with the first electrical battery. Volta is recognized as one of the most influential inventors of all time.
Invention
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Thomas Edison with phonograph. Edison is considered one of the most prolific inventors in history, holding 1,093 U.S. patents in his name.
Invention
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A rare 1884 photo showing the experimental recording of voice patterns by a photographic process at the Alexander Graham Bell Laboratory in Washington, D.C. Many of their experimental designs panned out in failure.
9.
Archimedes' principle
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Archimedes' principle is a law of physics fundamental to fluid mechanics. It was formulated by Archimedes of Syracuse. Practically, the Archimedes' principle allows the buoyancy of an object fully immersed in a liquid to be calculated. The downward force on the object is simply its weight. The buoyant force on the object is that stated by Archimedes' principle, above. Thus the upward force on the object is the difference between the buoyant force and its weight. Consider a cube immersed with its sides parallel to the direction of gravity. The fluid will exert a normal force on each face, therefore only the forces on the bottom faces will contribute to buoyancy. The difference between the bottom and the top face is directly proportional to the height. The weight of the object in the fluid is reduced, because of the force acting on it, called upthrust. Thus, among completely submerged objects with equal masses, objects with greater volume have greater buoyancy. Suppose a rock's weight is measured as 10 newtons when suspended with gravity acting on it. Suppose that when the rock is lowered into water, it displaces water of weight 3 newtons. Buoyancy reduces the apparent weight of objects that have sunk completely to the floor. It is generally easier to lift an object up through the water than it is to pull it out of the water.
Archimedes' principle
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Diving medicine:
Archimedes' principle
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Continuum mechanics
10.
Archimedes' screw
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Water is pumped by turning a screw-shaped surface inside a pipe. The pump is commonly attributed to Archimedes on the occasion of his visit to Egypt. This tradition may reflect only that the apparatus was introduced in Archimedes's lifetime by unknown Greek engineers. Some writers have suggested the device may have been in use in Assyria some 350 years earlier. The Archimedes screw consists of a screw inside a hollow pipe. The screw is turned usually by manual labour. As the shaft turns, the bottom end scoops up a volume of water. This water is then pushed up the tube by the rotating helicoid until finally it pours out from the top of the tube. If water into the next lower one, it will be transferred upwards by the next segment of the screw. In some designs, they both rotate together, instead of the screw turning within a stationary casing. A screw could be cast as a single piece in bronze. Some researchers have postulated this as being the device used to irrigate the Hanging Gardens of one of the Seven Wonders of the Ancient World. A triple helix was built of wood strips around a heavy wooden pole. It was used for draining land, underneath other places in the creation of polders. Archimedes screws are used in treatment plants because they cope well with varying rates of flow and with suspended solids.
Archimedes' screw
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An Archimedes screw in Huseby south of Växjö Sweden
Archimedes' screw
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Archimedes screw
Archimedes' screw
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Roman screw used to dewater mines in Spain
Archimedes' screw
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Modern Archimedes screws which have replaced some of the windmills used to drain the polders at Kinderdijk in the Netherlands
11.
Fluid statics
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Fluid statics or hydrostatics is the branch of fluid mechanics that studies incompressible fluids at rest. Hydrostatics are categorized as a part of the fluid statics, the study of all fluids, incompressible or not, at rest. Hydrostatics is fundamental to the engineering of equipment for storing, using fluids. It is also relevant to meteorology, to medicine, many other fields. Some principles of hydrostatics have been known by the builders of boats, cisterns, aqueducts and fountains. It was used as a tool. The height of this pipe is the same as the line carved into the interior of the cup. The cup may be filled without any fluid passing into the pipe in the center of the cup. However, when the amount of fluid exceeds this line, fluid will overflow into the pipe in the center of the cup. Due to the drag that molecules exert on one another, the cup will be emptied. Heron's fountain is a device invented by Heron of Alexandria that consists of a jet of fluid being fed by a reservoir of fluid. The device consisted of two containers arranged one above the other. Several cannula connecting the various vessels. Trapped air inside the vessels induces a jet of water out of a nozzle, emptying all water from the intermediate reservoir. Pascal made contributions in both hydrostatics and hydrodynamics.
Fluid statics
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Table of Hydraulics and Hydrostatics, from the 1728 Cyclopædia
Fluid statics
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Diving medicine:
12.
Lever
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A lever is a machine consisting of a beam or rigid rod pivoted at a fixed hinge, or fulcrum. A lever is a rigid body capable of rotating on a point on itself. On the basis of the location of fulcrum, effort, the lever is divided into three types. It is one of the six simple machines identified by Renaissance scientists. A lever amplifies an force to provide a greater output force, said to provide leverage. The ratio of the force to the input force is the mechanical advantage of the lever. The word "lever" entered English about 1300 from Old French, in which the word was levier. This sprang from the stem of the verb lever, meaning "to raise". The verb, in turn, goes back to itself from the adjective levis, meaning "light". The word's primary origin is the Proto-Indo-European stem legwh - "easy" or "nimble", among other things. The PIE stem also gave rise to the English word "light". The earliest remaining writings regarding levers were provided by Archimedes. The distance required to do this might be exemplified in astronomical terms to the Circinus galaxy - about 9 million light years. It is assumed that in ancient Egypt, constructors used the lever to uplift obelisks weighing more than 100 tons. A lever is a beam connected to ground by a pivot, called a fulcrum.
Lever
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Levers can be used to exert a large force over a small distance at one end by exerting only a small force over a greater distance at the other.
Lever
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A lever in balance
Lever
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This is an engraving from Mechanics Magazine published in London in 1824.
13.
Archimedes' use of infinitesimals
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The Method of Mechanical Theorems, also referred to as The Method, is one of the major surviving works of Archimedes of Syracuse. In 1906 was rediscovered in the celebrated Archimedes Palimpsest. In these treatises, he proves the same theorems by exhaustion, finding upper lower bounds which both converge to the answer required. Nevertheless, the mechanical method was what he used to discover the relations for which he later gave rigorous proofs. His idea is to use the law of the lever to determine the areas of figures from the known center of mass of other figures. The simplest example in modern language is the area of the parabola. The idea is to mechanically balance the parabola with a certain triangle, made of the same material. The parabola is the region in the x-y plane between the x-axis and = x2 as x varies from 0 to 1. The triangle is the region in the line y = x, also as x varies from 0 to 1. Slice the parabola and triangle into vertical slices, one for each value of x. Imagine that the x-axis is a lever, with a fulcrum at x = 0. Since each pair of slices balances, moving the whole parabola to x = 1 would balance the whole triangle. The center of mass of a triangle can be easily found by the following method, also due to Archimedes. So the center of mass of a triangle must be at the point of the medians. For the triangle in question, one median is the line y = x/2, while a second median is the line y = 1 − x.
Archimedes' use of infinitesimals
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Contents
14.
Neusis construction
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The neusis is a geometric construction method, used in antiquity by Greek mathematicians. That is, one end of the element has to lie on the other end on m, while the line element is "inclined" towards P. A neusis construction might be performed by means of a'neusis ruler': a marked ruler, rotatable around the point P. A second marking on the ruler indicates the distance a from the origin. The yellow eye is moved along l, until the blue eye coincides with m. The position of the element thus found is shown in the figure as a blue bar. Line m the line. Length a is called the diastema. Neuseis have been important because they sometimes provide a means to solve geometric problems that are not solvable by means of compass and straightedge alone. Examples are the construction of a regular heptagon, nonagon, or tridecagon. Mathematicians such as Archimedes of Alexandria freely used neuseis; Sir Isaac Newton also used neusis constructions. Nevertheless, gradually the technique dropped out of use. T. L. Heath, the historian of mathematics, has suggested that the Greek mathematician Oenopides was the first to put compass-and-straightedge constructions above neuseis. Hundred years after him Euclid too shunned neuseis in The Elements. The next attack on the neusis came when, from the fourth century BC, Plato's idealism gained ground.
Neusis construction
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Neusis trisection of an angle θ > 135° to find φ = θ /3, using only the length of the ruler. The radius of the arc is equal to the length of the ruler. For angles θ < 135° the same construction applies, but with P extended beyond AB.
Neusis construction
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Neusis construction
15.
Greek language
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It is an independent branch of the Indo-European family of languages, native to Greece, western and northeastern Asia Minor, southern Italy, Albania and Cyprus. Greek has the longest documented history of any living language, spanning 34 centuries of written records. The alphabet was in turn the basis of the Latin, Cyrillic, Armenian, Coptic, Gothic and many other writing systems. Together with the Latin traditions of the Roman world, the study of the Greek texts and society of antiquity constitutes the discipline of Classics. During antiquity, it was a widely spoken franca in the Mediterranean world and beyond. Greek would eventually develop into Medieval Greek. The language is spoken by at least million people today in Greece, Cyprus, Italy, Albania, Turkey, the Greek diaspora. Greek roots are often used to coin new words for other languages; Greek and Latin are the predominant sources of scientific vocabulary. It has been spoken since around the 3rd millennium BC, or possibly earlier. Among the Indo-European languages, its date of earliest written attestation is matched only by the now extinct Anatolian languages. The Greek language is conventionally assumed last ancestor of all known varieties of Greek. The unity of Proto-Greek would have ended as Hellenic migrants entered the Greek peninsula sometime in the Bronze Age. Mycenaean Greek: the language of the Mycenaean civilisation. Greek is recorded on tablets dating from the 15th century BC onwards. Ancient Greek: in its various dialects, the language of the Archaic and Classical periods of the ancient Greek civilisation.
Greek language
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Idealized portrayal of Homer
Greek language
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regions where Greek is the official language
Greek language
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Greek language road sign, A27 Motorway, Greece
16.
Greeks
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They also form a significant diaspora, with Greek communities established around the world. The cultural centers of the Greeks have included Constantinople at various periods. Most ethnic Greeks live nowadays within the borders of Cyprus. The Greek genocide and exchange between Greece and Turkey nearly ended the three millennia-old Greek presence in Asia Minor. Most Greeks are officially registered as members of the Greek Orthodox Church. The Greeks speak the Greek language, which forms its unique branch within the Indo-European family of languages, the Hellenic. They are part of a group of pre-modern ethnicities, described by Anthony D. Smith as an "archetypal people". Both migrations occur at incisive periods, the Doric at the Bronze Age collapse. The Mycenaeans quickly penetrated the Aegean Sea and, by the 15th BC, had reached Rhodes, Crete, Cyprus and the shores of Asia Minor. Around 1200 BC, another Greek-speaking people, followed from Epirus. The Greeks of classical antiquity idealized the Mycenaean period as a glorious era of heroes, closeness of the gods and material wealth. The ethnogenesis of the Greek nation is linked in the 8th century BC. The works of Homer and Hesiod were written in the 8th BC, becoming the basis of the national religion, ethos, history and mythology. The Oracle of Apollo at Delphi was established in this period. The classical period of Greek civilization covers a time spanning from the 5th century BC to the death of Alexander the Great, in 323 BC.
Greeks
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Hoplites fighting. Detail from an Attic black-figure hydria, ca. 560 BC–550 BC. Louvre, Paris.
Greeks
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A reconstruction of the 3rd millennium BC "Proto-Greek area", according to Bulgarian linguist Vladimir Georgiev.
Greeks
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Bust of Cleopatra VII. Altes Museum, Berlin.
Greeks
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Statues of Saints Cyril and Methodius, missionaries of Christianity among the Slavic peoples, on the Holy Trinity Column in Olomouc, Czech Republic.
17.
Greek mathematics
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Greek mathematicians were united by language. Greek mathematics of the period following Alexander the Great is sometimes called Hellenistic mathematics. The word "mathematics" itself derives from the ancient Greek μάθημα, meaning "subject of instruction". The origin of Greek mathematics is not well documented. The earliest advanced civilizations in Greece and in Europe were the Minoan and later Mycenaean civilization, both of which flourished during the 2nd millennium BC. While these civilizations were capable of advanced engineering, including four-story palaces with beehive tombs, they left behind no mathematical documents. Though no direct evidence is available, it is generally thought that the neighboring Babylonian and Egyptian civilizations had an influence on the younger Greek tradition. Historians traditionally place the beginning of Greek mathematics proper to the age of Thales of Miletus. Despite this, it is generally agreed that Thales is the first of the seven wise men of Greece. Thales' theorem and theorem are attributed to Thales. It is for this reason that Thales is often hailed as the true mathematician. Thales is also thought to be the earliest known man in history to whom specific mathematical discoveries have been attributed. Another important figure in the development of Greek mathematics is Pythagoras of Samos. Like Thales, Pythagoras also traveled to Egypt and Babylon, then under the rule of Nebuchadnezzar, but settled in Croton, Magna Graecia. And since in antiquity it was customary to give all credit to the master, Pythagoras himself was given credit for the discoveries made by his order.
Greek mathematics
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Statue of Euclid in the Oxford University Museum of Natural History
Greek mathematics
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An illustration of Euclid 's proof of the Pythagorean Theorem
Greek mathematics
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The Antikythera mechanism, an ancient mechanical calculator.
18.
Inventor
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An invention is a unique or novel device, method, composition or process. The process is a process within an overall engineering and product process. It may be an improvement for creating a result. An invention that achieves a completely unique function or result may be a radical breakthrough. Such works are novel and not obvious to others skilled in the same field. An inventor may be taking a big step in success or failure. Some inventions can be patented. A patent legally protects the intellectual property rights of the inventor and legally recognizes that a claimed invention is actually an invention. The rules and requirements for patenting an invention vary from country to country and the process of obtaining a patent is often expensive. Another meaning of invention is cultural invention, an innovative set of social behaviours passed on to others. The Institute for Social Inventions collected such ideas in books. Invention is also an important component of creativity. Inventions often extend the boundaries of human capability. Brainstorming also can spark new ideas for an invention. Creative processes are frequently used by engineers, designers, scientists.
Inventor
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' BUILD YOUR OWN TELEVISION RECEIVER.' Science and Invention magazine cover, November 1928
Inventor
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Alessandro Volta with the first electrical battery. Volta is recognized as one of the most influential inventors of all time.
Inventor
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Thomas Edison with phonograph. Edison is considered one of the most prolific inventors in history, holding 1,093 U.S. patents in his name.
Inventor
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A rare 1884 photo showing the experimental recording of voice patterns by a photographic process at the Alexander Graham Bell Laboratory in Washington, D.C. Many of their experimental designs panned out in failure.
19.
Scientist
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A scientist is a person engaging in a systematic activity to acquire knowledge that describes and predicts the natural world. In a more restricted sense, a scientist may refer to an individual who uses the scientific method. The person may be an expert in one or more areas of science. The scientist was coined by the theologian, philosopher and man of science William Whewell. This article focuses on the more restricted use of the word. Scientists perform research toward a more comprehensive understanding including physical, mathematical and social realms. Philosophy is a distinct activity, not generally considered science. Philosophers aim to provide a comprehensive understanding of intangible aspects of experience that can not be physically measured. When science is done with a goal toward practical utility, it is called applied science. An applied scientist rather is conducting research with the aim of developing new technologies and practical methods. When science is done with an inclusion of intangible aspects of reality it is called natural philosophy. Technology have continually modified human existence through the engineering process. As a profession the scientist of today is widely recognized. Jurisprudence and mathematics are often grouped with the sciences. Some of the greatest physicists have also been creative lawyers.
Scientist
Scientist
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Chemical scientists in a laboratory of the University of La Rioja
Scientist
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"No one in the history of civilization has shaped our understanding of science and natural philosophy more than the great Greek philosopher and scientist Aristotle (384-322 BC), who exerted a profound and pervasive influence for more than two thousand years" —Gary B. Ferngren
Scientist
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Alessandro Volta, the inventor of the electrical battery and discoverer of methane, is widely regarded as one of the greatest scientists in history.
20.
Classical antiquity
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It is the period in which Roman society flourished and wielded great influence throughout Europe, North Africa and Southwestern Asia. It ends at the close of Late Antiquity blending into the Early Middle Ages. Such a wide sampling of territory covers many disparate cultures and periods. The earliest period of classical antiquity takes place before the background of gradual re-appearance of historical sources following the Bronze collapse. The 7th centuries BC are still largely proto-historical, with the earliest Greek alphabetic inscriptions appearing in the first half of the 8th century. In the same period falls the traditional date for the establishment of the Ancient Olympic Games, in 776 BC. The Phoenicians originally expanded by the 8th century dominating trade in the Mediterranean. The Etruscans had established political control in the region by the 7th century BC, forming the aristocratic and monarchial elite. According to legend, Rome was founded BC by twin descendants of the Trojan prince Aeneas, Romulus and Remus. The final king of Rome was Tarquinius Superbus. As the son-in-law of Servius Tullius, Superbus was of Etruscan birth. It was during his reign that the Etruscans reached their apex of power. Superbus destroyed all the Sabine shrines and altars from the Tarpeian Rock, enraging the people of Rome. Lucius Junius Brutus, summoned the Senate and had Superbus and the monarchy expelled from Rome in 510 BC. After Superbus' expulsion, the Senate voted to never again allow the rule of a king and reformed Rome in 509 BC.
Classical antiquity
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The Parthenon is one of the most iconic symbols of the classical era, exemplifying ancient Greek culture
21.
Calculus
–
It has two major branches, integral calculus; these two branches are related to each other by the fundamental theorem of calculus. Both branches make use of the fundamental notions of infinite series to a well-defined limit. Generally, modern calculus is considered to have been developed by Isaac Newton and Gottfried Leibniz. Calculus has widespread uses in science, engineering and economics. Calculus is a part of modern education. A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of limits, broadly called mathematical analysis. Calculus has historically been called "the calculus of infinitesimals", or "infinitesimal calculus". Calculus is also used for naming theories of computation, such as propositional calculus, calculus of variations, lambda calculus, process calculus. The method of exhaustion was later reinvented by Liu Hui in the 3rd century AD in order to find the area of a circle. In the 5th AD, Zu Chongzhi established a method that would later be called Cavalieri's principle to find the volume of a sphere. Indian mathematicians gave a semi-rigorous method of differentiation of some trigonometric functions. In the Middle East, Alhazen derived a formula for the sum of fourth powers. The infinitesimal quantities he introduced were disreputable at first. The formal study of calculus brought together Cavalieri's infinitesimals with the calculus of finite differences developed at around the same time. Pierre de Fermat, claiming that he borrowed from Diophantus, introduced the concept of adequality, which represented equality up to an infinitesimal term.
Calculus
–
Isaac Newton developed the use of calculus in his laws of motion and gravitation.
Calculus
–
Gottfried Wilhelm Leibniz was the first to publish his results on the development of calculus.
Calculus
–
Maria Gaetana Agnesi
Calculus
–
The logarithmic spiral of the Nautilus shell is a classical image used to depict the growth and change related to calculus
22.
Mathematical analysis
–
Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, analytic functions. These theories are usually studied in the context of real and complex functions. Analysis evolved from calculus, which involves the elementary techniques of analysis. Many of its ideas can be traced back to earlier mathematicians. Early results in analysis were implicitly present in the early days of Greek mathematics. For instance, an infinite sum is implicit in Zeno's paradox of the dichotomy. The explicit use of infinitesimals appears in Archimedes' The Method of a work rediscovered in the 20th century. In Asia, the Chinese mathematician Liu Hui used the method of exhaustion in the 3rd century AD to find the area of a circle. Zu Chongzhi established a method that would later be called Cavalieri's principle to find the volume of a sphere in the 5th century. The Indian mathematician Bhāskara II used what is now known as Rolle's theorem in the 12th century. His followers at the Kerala school of mathematics further expanded his works, up to the 16th century. The modern foundations of mathematical analysis were established in 17th century Europe. During this period, techniques were applied to approximate discrete problems by continuous ones. In the 18th century, Euler introduced the notion of mathematical function. Instead, Cauchy formulated calculus in terms of geometric infinitesimals.
Mathematical analysis
–
A strange attractor arising from a differential equation. Differential equations are an important area of mathematical analysis with many applications to science and engineering.
23.
Method of exhaustion
–
If the sequence is correctly constructed, the difference in area between the containing shape will become arbitrarily small as n becomes large. The method of exhaustion typically required a form of proof by contradiction, known as reductio absurdum. This amounts to finding an area of a region by first comparing it to the area of a second region. The idea originated in the 5th century BC with Antiphon, although it is not entirely clear how well he understood it. The theory was made rigorous a few decades later by Eudoxus of Cnidus, who used it to calculate volumes. It was later reinvented by Liu Hui in the 3rd century AD in order to find the area of a circle. The first use of the term was by Grégoire de Saint-Vincent in Opus geometricum quadraturae circuli et sectionum. The method of exhaustion is seen to the methods of calculus. Euclid used the method of exhaustion to prove the following six propositions of his Elements. 2 The area of a circle is proportional to the square of its radius. 5 The volumes of two tetrahedra of the same height are proportional to the areas of their triangular bases. 10 The volume of a cone is a third of the volume of the corresponding cylinder which has the same base and height. 11 The volume of a cone of the same height is proportional to the area of the base. 18 The volume of a sphere is proportional to the cube of its diameter. The Method of Mechanical Theorems The Quadrature of the Parabola Trapezoidal rule
Method of exhaustion
–
Grégoire de Saint-Vincent
24.
Geometry
–
Geometry is a branch of mathematics concerned with questions of shape, size, relative position of figures, the properties of space. A mathematician who works in the field of geometry is called a geometer. Geometry arose independently in a number of early cultures for dealing with lengths, areas, volumes. Geometry began to see elements of mathematical science emerging in the West as early as the 6th century BC. By the 3rd BC, geometry was put into an axiomatic form by Euclid, whose treatment, Euclid's Elements, set a standard for many centuries to follow. Geometry arose independently with texts providing rules for geometric constructions appearing as early as the 3rd century BC. Islamic scientists expanded on them during the Middle Ages. By the 17th century, geometry had been put on a solid analytic footing by mathematicians such as René Descartes and Pierre de Fermat. Since then, into modern times, geometry has expanded into non-Euclidean geometry and manifolds, describing spaces that lie beyond the normal range of human experience. While geometry has evolved significantly throughout the years, there are some general concepts that are less fundamental to geometry. These include the concepts of points, lines, planes, surfaces, curves, as well as the more advanced notions of manifolds and topology or metric. Contemporary geometry has many subfields: Euclidean geometry is geometry in its classical sense. The educational curriculum of the majority of nations includes the study of points, lines, planes, angles, triangles, congruence, similarity, solid figures, circles, analytic geometry. Euclidean geometry also has applications in computer science, various branches of modern mathematics. Differential geometry uses techniques of linear algebra to study problems in geometry.
Geometry
–
Visual checking of the Pythagorean theorem for the (3, 4, 5) triangle as in the Chou Pei Suan Ching 500–200 BC.
Geometry
–
An illustration of Desargues' theorem, an important result in Euclidean and projective geometry
Geometry
–
Geometry lessons in the 20th century
Geometry
–
A European and an Arab practicing geometry in the 15th century.
25.
Theorem
–
A theorem is a logical consequence of the axioms. The proof of a mathematical theorem is a logical argument for the statement given in accord with the rules of a deductive system. The proof of a theorem is often interpreted as justification of the truth of the statement. Mathematical theorems are conditional statements. In this case, the proof deduces the conclusion from conditions called premises. However, the conditional could be interpreted differently depending on the meanings assigned to the derivation rules and the conditional symbol. In some cases, a picture alone may be sufficient to prove a theorem. Because theorems lie at the core of mathematics, they are also central to its aesthetics. Theorems are often described as being "trivial", or "difficult", or "deep", or even "beautiful". Its proof may involve surprising and subtle connections between disparate areas of mathematics. Fermat's Last Theorem is a particularly well-known example of such a theorem. Logically, many theorems are of the form of an conditional: if A, then B. Such a theorem does not assert B, only that B is a necessary consequence of A. In this case A is called B the conclusion. To be proved, a theorem must be expressible as a formal statement.
Theorem
–
A planar map with five colors such that no two regions with the same color meet. It can actually be colored in this way with only four colors. The four color theorem states that such colorings are possible for any planar map, but every known proof involves a computational search that is too long to check by hand.
26.
Area
–
Area is the quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane. Surface area is its analog on the two-dimensional surface of a three-dimensional object. It is the two-dimensional analog of the volume of a solid. The area of a shape can be measured by comparing the shape to squares of a fixed size. A shape with an area of three square metres would have the same area as three such squares. In mathematics, the area of any other shape or surface is a dimensionless real number. There are well-known formulas for the areas of simple shapes such as triangles, rectangles, circles. Using these formulas, the area of any polygon can be found by dividing the polygon into triangles. For shapes with curved boundary, calculus is usually required to compute the area. Indeed, the problem of determining the area of plane figures was a major motivation for the historical development of calculus. For a solid shape such as a sphere, cylinder, the area of its boundary surface is called the surface area. Area plays an important role in modern mathematics. In analysis, the area of a subset of the plane is defined using Lebesgue measure, though not every subset is measurable. In general, area in higher mathematics is seen as a special case of volume for two-dimensional regions. It can be proved that such a function exists.
Area
–
A square metre quadrat made of PVC pipe.
Area
–
The combined area of these three shapes is approximately 15.57 squares.
27.
Circle
–
A circle is a simple closed shape in Euclidean geometry. The distance between any of the centre is called the radius. A circle is a closed curve which divides the plane into two regions: an interior and an exterior. The bounding line is called the point, its centre. Annulus: the ring-shaped object, the region bounded by two concentric circles. Arc: any connected part of the circle. Centre: the point equidistant from the points on the circle. Chord: a line segment whose endpoints lie on the circle. Circumference: the length of one circuit along the circle, or the distance around the circle. It is twice the radius. Disc: the region of the plane bounded by a circle. Lens: the intersection of two discs. Passant: a coplanar straight line that does not touch the circle. Sector: a region bounded by two radii and an arc lying between the radii. Segment: a region, not containing the centre, bounded by a chord and an arc lying between the chord's endpoints.
Circle
–
The compass in this 13th-century manuscript is a symbol of God's act of Creation. Notice also the circular shape of the halo
Circle
–
A circle with circumference (C) in black, diameter (D) in cyan, radius (R) in red, and centre (O) in magenta.
Circle
–
Circular piece of silk with Mongol images
Circle
–
Circles in an old Arabic astronomical drawing.
28.
Surface area
–
The surface area of a solid object is a measure of the total area that the surface of the object occupies. Smooth surfaces, such as a sphere, are assigned area using their representation as parametric surfaces. This definition of area is based on methods of infinitesimal calculus and involves partial derivatives and double integration. A general definition of area was sought by Henri Lebesgue and Hermann Minkowski at the turn of the twentieth century. Their work led to the development of geometric theory, which studies various notions of surface area for irregular objects of any dimension. An important example is the Minkowski content of a surface. While the areas of simple surfaces have been known since antiquity, a rigorous mathematical definition of area requires a great deal of care. This should provide S ↦ A which assigns a positive real number to a certain class of surfaces that satisfies several natural requirements. The most fundamental property of the area is its additivity: the area of the whole is the sum of the areas of the parts. Surface areas of polygonal shapes must agree with their geometrically defined area. This means that area is invariant under the group of Euclidean motions. These properties uniquely characterize area for a wide class of geometric surfaces called piecewise smooth. The area of the whole surface is then obtained by adding together the areas of the pieces, using additivity of area. The main formula can be specialized to different classes of surfaces, giving = f and surfaces of revolution. It was demonstrated by Hermann Schwarz that already for the cylinder, different choices of approximating flat surfaces can lead to limiting values of the area.
Surface area
–
The inner membrane of the mitochondrion has a large surface area due to infoldings, allowing higher rates of cellular respiration (electron micrograph).
Surface area
–
A sphere of radius has surface area
29.
Volume
–
Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance or shape occupies or contains. Volume is often quantified numerically using the cubic metre. Three mathematical shapes are also assigned volumes. Circular shapes can be easily calculated using arithmetic formulas. Volumes of a complicated shape can be calculated by integral calculus if a formula exists for the shape's boundary. Two-dimensional shapes are assigned zero volume in the three-dimensional space. The volume of a solid can be determined by fluid displacement. Displacement of liquid can also be used to determine the volume of a gas. The combined volume of two substances is usually greater than the volume of one of the substances. However, sometimes one substance dissolves in the combined volume is not additive. In geometry, volume is expressed by means of the volume form, is an important global Riemannian invariant. In thermodynamics, volume is a conjugate variable to pressure. Any unit of length gives a corresponding unit of volume: the volume of a cube whose sides have the given length. For example, a cubic centimetre is the volume of a cube whose sides are one centimetre in length. In the International System of Units, the standard unit of volume is the cubic metre.
Volume
–
A measuring cup can be used to measure volumes of liquids. This cup measures volume in units of cups, fluid ounces, and millilitres.
30.
Sphere
–
A sphere is a perfectly round geometrical object in three-dimensional space, the surface of a completely round ball. The given point is the center of the mathematical ball. While outside mathematics the terms "sphere" and "ball" are sometimes used interchangeably, in mathematics a distinction is made between the ball. The sphere share the same radius, diameter, center. The area of a sphere is: A = 4 π r 2. The total volume is the summation of all shell volumes: V ≈ ∑ A ⋅ r. In the limit as δr approaches zero this equation becomes: V = ∫ 0 r A d r ′. Substitute V: 4 3 π r 3 = ∫ 0 r A d r ′. Differentiating both sides of this equation with respect to r yields A as a function of r: 4 π r 2 = A. Which is generally abbreviated as: A = 4 π r 2. Alternatively, the element on the sphere is given in spherical coordinates by dA = r2 sin θ dθ dφ. For more generality, see element. Archimedes first derived this formula, which shows that the volume inside a sphere is 2/3 that of a circumscribed cylinder. The total volume is the summation of all incremental volumes: V ≈ ∑ π y 2 ⋅ δ x. In the limit as δx approaches zero this equation becomes: V = ∫ − r r π y 2 d x.
Sphere
–
Circumscribed cylinder to a sphere
Sphere
–
A two-dimensional perspective projection of a sphere
Sphere
Sphere
–
Deck of playing cards illustrating engineering instruments, England, 1702. King of spades: Spheres
31.
Parabola
–
It fits any of several superficially different mathematical descriptions which can all be proved to define curves of exactly the same shape. One description of a parabola involves a line. The focus does not lie on the directrix. The parabola is the locus of points in that plane that are equidistant from the focus. A third description is algebraic. A parabola is a graph of a quadratic function, y = x2, for example. The perpendicular to the directrix and passing through the focus is called the "axis of symmetry". The point on the parabola that intersects the axis of symmetry is the point where the parabola is most sharply curved. The distance between the focus, measured along the axis of symmetry, is the "focal length". The "latus rectum" is the chord of the parabola which passes through the focus. Parabolas can open up, down, right, or in some other arbitrary direction. Any parabola can be rescaled to fit exactly on any other parabola --, all parabolas are geometrically similar. Conversely, light that originates from a source at the focus is reflected into a parallel beam, leaving the parabola parallel to the axis of symmetry. The same effects occur with other forms of energy. This reflective property is the basis of practical uses of parabolas.
Parabola
–
Parabolic compass designed by Leonardo da Vinci
Parabola
–
Part of a parabola (blue), with various features (other colours). The complete parabola has no endpoints. In this orientation, it extends infinitely to the left, right, and upward.
Parabola
–
A bouncing ball captured with a stroboscopic flash at 25 images per second. Note that the ball becomes significantly non-spherical after each bounce, especially after the first. That, along with spin and air resistance, causes the curve swept out to deviate slightly from the expected perfect parabola.
Parabola
–
Parabolic trajectories of water in a fountain.
32.
Pi
–
The number π is a mathematical constant, the ratio of a circle's circumference to its diameter, commonly approximated as 3.14159. It has been represented by the Greek letter "π" since the mid-18th century, though it is also sometimes spelled out as "pi". Being an irrational number, π cannot be expressed exactly as a fraction. Still, fractions such as other rational numbers are commonly used to approximate π. The digits appear to be randomly distributed. Also, π is a transcendental number – a number, not the root of any non-zero polynomial having rational coefficients. This transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with straightedge. Ancient civilizations needed the value of π to be computed accurately for practical reasons. It was calculated to seven digits, using geometrical techniques, to about five in Indian mathematics in the 5th century AD. However, the extensive calculations involved have been used to test high-precision multiplication algorithms. Because its definition relates to the circle, π is found in many formulae in geometry, especially those concerning circles, ellipses or spheres. It is also found in cosmology, mechanics and electromagnetism. Attempts to memorize the value of π with increasing precision have led to records of over 70,000 digits. In English, π is pronounced as "pie". In mathematical use, the lowercase π is distinguished from its capital counterpart Π, which denotes a product of a sequence.
Pi
–
The constant π is represented in this mosaic outside the Mathematics Building at the Technical University of Berlin.
Pi
–
The circumference of a circle is slightly more than three times as long as its diameter. The exact ratio is called π.
Pi
–
Archimedes developed the polygonal approach to approximating π.
Pi
–
Isaac Newton used infinite series to compute π to 15 digits, later writing "I am ashamed to tell you to how many figures I carried these computations".
33.
Archimedes spiral
–
The Archimedean spiral is a spiral named after the 3rd century BC Greek mathematician Archimedes. Equivalently, in polar coordinates it can be described by the equation r = a + b θ with real numbers a and b. Changing the parameter a will turn the spiral, while b controls the distance between successive turnings. Archimedes described such a spiral On Spirals. The Archimedean spiral has one for θ > 0 and one for θ < 0. The two arms are smoothly connected at the origin. Only one arm is shown on the accompanying graph. Taking the image of this arm across the y-axis will yield the other arm. Some sources describe the Archimedean spiral as a spiral with a "constant distance" between successive turns. This is somewhat misleading. Sometimes the term spiral is used for the more general group of spirals r = a + b θ 1 / c. The normal Archimedean spiral occurs when c = 1. Other spirals falling into this group include the hyperbolic spiral, the lituus. Virtually all static spirals appearing in nature are logarithmic spirals, not Archimedean ones. Dynamic spirals are Archimedean.
Archimedes spiral
–
Three 360° turnings of one arm of an Archimedean spiral
34.
Exponentiation
–
Exponentiation is a mathematical operation, written as bn, involving two numbers, the base b and the exponent n. The exponent is usually shown as a superscript to the right of the base. The exponent −1 of b, or 1 / b, is called the reciprocal of b. The definition of exponentiation can be extended to allow any real or complex exponent. Exponentiation by integer exponents can also be defined for a wide variety of algebraic structures, including matrices. The term power was used by the Greek mathematician Euclid for the square of a line. Archimedes discovered and proved the law of exponents, 10a 10b = 10a+b, necessary to manipulate powers of 10. In the late 16th century, Jost Bürgi used Roman numerals for exponents. Nicolas Chuquet used a form of exponential notation in the 15th century, later used by Henricus Grammateus and Michael Stifel in the 16th century. The word "exponent" was coined in 1544 by Michael Stifel. Samuel Jeake introduced the term indices in 1696. In the 16th century Robert Recorde used the terms square, cube, second sursolid, zenzizenzizenzic. Biquadrate has been used to refer to the fourth power as well. Some mathematicians used exponents only for powers greater than two, preferring to represent squares as repeated multiplication. Thus they would write polynomials, for example, as ax + bxx + cx3 + d.
Exponentiation
–
Graphs of y = b x for various bases b: base 10 (green), base e (red), base 2 (blue), and base 1 / 2 (cyan). Each curve passes through the point (0, 1) because any nonzero number raised to the power of 0 is 1. At x = 1, the value of y equals the base because any number raised to the power of 1 is the number itself.
35.
Statics
–
The application of Newton's second law to a system gives: F = m a. Where bold font indicates a vector that has magnitude and direction. F is the total of the forces acting on the system, a is the acceleration of the system. The magnitude of the acceleration will be inversely proportional to the mass. The assumption of static equilibrium of a = 0 leads to: F = 0. The summation of forces, one of which might be unknown, allows that unknown to be found. Likewise the application of the assumption of zero acceleration to the summation of moments acting on the system leads to: M = I α = 0. The summation of moments, one of which might be unknown, allows that unknown to be found. These two equations together, can be applied to solve for as many as two loads acting on the system. From Newton's first law, this implies that the net force and torque on every part of the system is zero. See statically determinate. A scalar is a quantity which only has a magnitude, such as temperature. A vector has a direction. Vectors are added using the triangle law. Vectors contain components in orthogonal bases.
Statics
–
Example of a beam in static equilibrium. The sum of force and moment is zero.
36.
Machine
–
Gary Dell'Abate, also known as Baba Booey, is an American radio producer, has been the executive producer of The Howard Stern Show since 1984. They Call Me Baba Booey, was released on November 2, 2010. ` Abate was born and raised in Uniondale, New York, on Long Island. He comes from a Italian-American family. Salvatore Dell ` Abate, was an ice cream salesman, while his mother sold cooking items such as frying pans at the local supermarket. He interned at several radio stations including WLIR. While interning with a traffic reporter on WNBC, he came into contact with Howard Stern. ` Abate was originally hired for $350 a week, with duties including getting Stern's lunch and scheduling guests for the show. In the course of discussing a Quick Draw McGraw cel he might purchase, he misstated the name of McGraw's sidekick Baba Looey as Baba Booey. Speaking at the end of the show, Dell ` Abate said, "I think we've taken this as far as it will go." Howard Stern replied, "Gary, we've only scratched the surface of this." ` Abate remains Baba Booey to this day. Eventually he titled his autobiography They Call Baba Booey. Dell'Abate later recalled that when he watched the cartoon as a child, Quick Draw would often call Baba Looey "Baba Boy," usually in frantic moments. Quick Draw's drawn-out pronunciation of "boy" often sounded like "booey," which led Dell'Abate to think that the character's name was actually "Baba Booey."
Machine
–
Gary Dell'Abate
Machine
37.
Block and tackle
–
The pulleys are assembled together to form blocks and then blocks are paired so that one is fixed and one moves with the load. The rope is threaded, or rove, through the pulleys to provide mechanical advantage that amplifies that force applied to the rope. Hero of Alexandria described cranes formed from assemblies of pulleys in the first century. Illustrated versions of Hero's "book on raising heavy weights" show early block and tackle systems. A block is a set of pulleys or "sheaves" mounted on a single axle. An assembly of blocks with a rope threaded through the pulleys is called tackle. A system amplifies the tension force in the rope to lift heavy loads. They are common on boats and sailing ships, where tasks are often performed manually. Its mechanical advantage is the number of parts of the rope that act on the load. The mechanical advantage of a tackle dictates how much easier it is to haul or lift the load. Consider the set of pulleys that form the moving block and the parts of the rope that support this block. This means the input force on the rope is FA=FB/n. Thus, the block and tackle reduces the input force by the factor n. Ideal mechanical advantage correlates directly with velocity ratio. The velocity ratio of a tackle is the ratio between the velocity of the hauling line to that of the hauled load.
Block and tackle
–
A gun tackle has a single pulley in both the fixed and moving blocks with 2 rope parts (n) supporting the load (F B) of 100N. The mechanical advantage is 2, requiring a force of only 50N to lift the load.
Block and tackle
–
Contents
Block and tackle
–
A double tackle has two pulleys in both the fixed and moving blocks with four rope parts (n) supporting the load (F B) of 100N. The mechanical advantage is 4, requiring a force of only 25N to lift the load.
38.
Roman Republic
–
It was during this period that Rome's control expanded to hegemony over the entire Mediterranean world. By the following century, it included Spain, what is now southern France. Two centuries after that, towards the end of the 1st century BC, it included much of the eastern Mediterranean. The exact date of transition can be a matter of interpretation. Roman government was headed by two consuls, advised by a senate composed of appointed magistrates. Many of Rome's legislative structures can still be observed throughout Europe and much of the world in modern nation states and international organizations. The exact causes and motivations during the republic are subject to wide debate. While they can be seen as motivated by outright imperialism, historians typically take a much more nuanced view. They argue that Rome's expansion was driven by the new contingencies that these decisions created. It was also less able to defend itself against its non-Roman enemies, which made attack by these enemies more likely. It was, therefore, more likely to seek an alliance of protection with Rome. This growing coalition moved Rome closer to confrontation with major powers. The result was more alliance-seeking, on the part of both the Roman confederacy and city-states seeking membership within that confederacy. This shift mainly took place in parts such as the southern Italian towns that sided with Hannibal. In contrast, Roman expansion into Spain and Gaul occurred as a mix of military occupation.
Roman Republic
–
Route of Pyrrhus of Epirus
Roman Republic
–
Roman consul accompanied by two lictors
Roman Republic
–
Gaius Gracchus, tribune of the people, presiding over the Plebeian Council
Roman Republic
–
A Roman denarius struck in 56 BC showing on one side the bust of the Goddess Diana, and on the reverse the Roman general Lucius Cornelius Sulla is offered an olive branch by his ally Bocchus I as the captive Jugurtha kneels beside Sulla with his hands bound.
39.
Cicero
–
Marcus Tullius Cicero was a Roman philosopher, politician, lawyer, orator, political theorist, consul, constitutionalist. Cicero is considered one of Rome's greatest orators and prose stylists. He created a Latin philosophical vocabulary distinguishing himself as a translator and philosopher. Though he was an accomplished successful lawyer, he believed his political career was his most important achievement. Following Julius Caesar's death, he became an enemy of Mark Antony in the ensuing struggle, attacking him in a series of speeches. His severed hands and head were then, as a final revenge of Mark Antony, displayed in the Roman Forum. Petrarch's rediscovery of Cicero's letters is often credited for initiating the 14th-century Renaissance in public affairs, classical Roman culture. He was born in 106 BC in a hill town 100 kilometers southeast of Rome. His father possessed good connections in Rome. However, being a semi-invalid, Cicero studied extensively to compensate. Cicero's brother Quintus wrote in a letter that she was a thrifty housewife. Personal surname, comes from the Latin for chickpea, cicer. Plutarch explains that the name was originally given to one of Cicero's ancestors who had a cleft in the tip of his nose resembling a chickpea. However, it is more likely that Cicero's ancestors prospered through the sale of chickpeas. Romans often chose personal surnames: the famous family names of Fabius, Lentulus, Piso come from the Latin names of beans, lentils, peas.
Cicero
–
A first century AD bust of Cicero in the Capitoline Museums, Rome
Cicero
–
The Young Cicero Reading by Vincenzo Foppa (fresco, 1464), now at the Wallace Collection
Cicero
–
Cicero Denounces Catiline, fresco by Cesare Maccari, 1882–88
Cicero
–
Cicero's death (France, 15th century)
40.
Cylinder (geometry)
–
It is one of the most basic curvilinear geometric shapes. If the ends are open, it is called an open cylinder. If the ends are closed by flat surfaces it is called a solid cylinder. The volume of such a cylinder have been known since deep antiquity. The area of the side is also known as L. An open cylinder therefore has surface area L = 2πrh. The area of a closed cylinder is made up the sum of all three components: top, bottom and side. Its area is A = 2πr2 + 2πrh = 2πr = πd = L +2 B, where d is the diameter. For a given volume, the closed cylinder with the smallest area has h = 2r. Equivalently, for a given area, the closed cylinder with the largest volume has h = 2r, i.e. the cylinder fits snugly in a cube. Cylindric sections are the intersections of cylinders with planes. For a circular cylinder, there are four possibilities. A tangent to the cylinder meets the cylinder in a single straight line segment. Moved to itself, the plane either does not intersect the cylinder or intersects it in two parallel line segments. All other planes intersect the cylinder in an ellipse or, when they are perpendicular to the axis of the cylinder, in a circle.
Cylinder (geometry)
–
Tycho Brahe Planetarium building, Copenhagen, its roof being an example of a cylindric section
Cylinder (geometry)
–
A right circular cylinder with radius r and height h.
Cylinder (geometry)
–
In projective geometry, a cylinder is simply a cone whose apex is at infinity, which corresponds visually to a cylinder in perspective appearing to be a cone towards the sky.
41.
Alexandria
–
Its low elevation on the Nile delta makes it highly vulnerable to rising sea levels. It is Egypt's largest seaport, serving approximately 80 % of Egypt's exports. Alexandria is an important industrial center from Suez. It is also an important destination. It was founded by Alexander the Great. It was the second most powerful city of the ancient world after Rome. It was founded by Alexander the Great in April 331 BC as Ἀλεξάνδρεια. Alexander's chief architect for the project was Dinocrates. It was intended to be the link between Greece and the rich Nile valley. It was the cultural center of the ancient world for some time. Its museum attracted many of the greatest scholars, including Greeks, Jews and Syrians. The city was later lost its significance. Just east of Alexandria, there was in ancient times marshland and several islands. As early as the 7th century BC, there existed important port cities of Canopus and Heracleion. The latter was recently rediscovered under water.
Alexandria
–
Alexandria Ἀλεξάνδρεια
Alexandria
Alexandria
–
Residential neighborhood in Alexandria
Alexandria
–
Fishing in Alexandria
42.
Isidore of Miletus
–
He also created the comprehensive compilation of Archimedes' works. Isidore is also renowned for producing the comprehensive compilation of Archimedes' work, one copy of which survived to the present. Emperor Justinian I appointed his architects to rebuild the Hagia Sophia following his victory over protesters within the city of his Roman Empire, Constantinople. The Blues and the Greens, opposed each other in the chariot races at the Hippodrome and often resorted to violence. During the Nika Riot, more than thousand people died. The Hagia Sophia was quickly repaired. Isidore the Younger, introduced the new dome design that can be viewed in the Hagia Sophia in present-day Istanbul, Turkey. After a great earthquake in 989 ruined the dome of Hagia Sophia, the Byzantine officials summoned Trdat the Architect to Byzantium to organize repairs. The restored dome was completed by 994. Cakmak, AS; Taylor, RM; Durukal, E. "The Structural Configuration of the First Dome of Justinian's Hagia Sophia: An Investigation Based on Structural and Literary Analysis". Soil Earthquake Engineering. 29. Krautheimer, Richard. Early Christian and Byzantine Architecture.
Isidore of Miletus
–
Interior panorama of the Hagia Sophia, the patriarchal basilica designed by Isidore. The influence of Archimedes' solid geometry works, which Isidore was the first to compile, is evident.
43.
Byzantine
–
During most of its existence, the empire was the most powerful economic, cultural, military force in Europe. Several signal events from the 4th to 6th centuries mark the period of transition during which the Roman Empire's Greek East and Latin West divided. Constantine I reorganised the empire, made Constantinople the new capital, legalised Christianity. Under Theodosius I, Christianity became the Empire's official state religion and other religious practices were proscribed. Finally, under the reign of Heraclius, the Empire's military and administration were restructured and adopted Greek for official use instead of Latin. The borders of the Empire evolved significantly over its existence, as it went through several cycles of decline and recovery. During the reign of Maurice, the Empire's eastern frontier was expanded and the north stabilised. In a matter of years the Empire lost its richest provinces, Egypt and Syria, to the Arabs. This battle opened the way for the Turks to settle in Anatolia as a homeland. The Empire recovered again during the Komnenian restoration, such that by the 12th century Constantinople was the largest and wealthiest European city. Its remaining territories were progressively annexed by the Ottomans over the 15th century. The Fall of Constantinople to the Ottoman Empire in 1453 finally ended the Byzantine Empire. The term comes from "Byzantium", the name of the city of Constantinople before it became Constantine's capital. This older name of the city would rarely be used from this point onward except in historical or poetic contexts. However, it was not until the mid-19th century that the term came into general use in the Western world.
Byzantine
–
Tremissis with the image of Justinian the Great (r. 527–565) (see Byzantine insignia)
Byzantine
–
Byzantine lamellar armour klivanium (Κλιβάνιον) - a predecessor of Ottoman krug mirror armour
Byzantine
–
The Baptism of Constantine painted by Raphael 's pupils (1520–1524, fresco, Vatican City, Apostolic Palace); Eusebius of Caesarea records that (as was common among converts of early Christianity) Constantine delayed receiving baptism until shortly before his death
Byzantine
–
Restored section of the Theodosian Walls.
44.
Middle Ages
–
In the history of Europe, the Middle Ages or medieval period lasted from the 5th to the 15th century. It merged into the Age of Discovery. The Middle Ages is the middle period of the three traditional divisions of Western history: classical antiquity, the medieval period, the modern period. The medieval period is itself subdivided into Late Middle Ages. Counterurbanisation, movement of peoples, which had begun in Late Antiquity, continued in the Early Middle Ages. The large-scale movements including Germanic peoples, formed new kingdoms in what remained of the Western Roman Empire. Although there were substantial changes in society and political structures, the break with classical antiquity was not complete. The Byzantine Empire remained a major power. In the West, most kingdoms incorporated the few extant Roman institutions. Monasteries were founded as campaigns to Christianise pagan Europe continued. The Franks, under the Carolingian dynasty, briefly established the Carolingian Empire during 9th century. The Crusades, first preached in 1095, were military attempts by Western European Christians to regain control of the Holy Land from Muslims. Kings became the heads of centralised nation states, reducing crime and violence but making the ideal of a unified Christendom more distant. Intellectual life was marked by a philosophy that emphasised joining faith by the founding of universities. Controversy, the Western Schism within the Catholic Church paralleled the interstate conflict, peasant revolts that occurred in the kingdoms.
Middle Ages
–
The Cross of Mathilde, a crux gemmata made for Mathilde, Abbess of Essen (973–1011), who is shown kneeling before the Virgin and Child in the enamel plaque. The body of Christ is slightly later. Probably made in Cologne or Essen, the cross demonstrates several medieval techniques: cast figurative sculpture, filigree, enamelling, gem polishing and setting, and the reuse of Classical cameos and engraved gems.
Middle Ages
–
A late Roman statue depicting the four Tetrarchs, now in Venice
Middle Ages
–
Coin of Theodoric
Middle Ages
–
Mosaic showing Justinian with the bishop of Ravenna, bodyguards, and courtiers
45.
Renaissance
–
This new thinking became manifest in art, politics, literature. Early examples were the development of perspective in oil painting and the recycled knowledge of how to make concrete. The Renaissance first began in Florence, in the 14th century. Major centres were Italian city-states such as Venice, Genoa, Milan, Bologna, finally Rome during the Renaissance Papacy. The word Renaissance, literally meaning "Rebirth" in French, first appeared in English in the 1830s. The word also occurs in Jules Michelet's 1855 work, Histoire de France. The word Renaissance has also been extended to other historical and cultural movements, such as the Carolingian Renaissance and the Renaissance of the 12th century. The Renaissance was a cultural movement that profoundly affected intellectual life in the modern period. Renaissance scholars searched in art. However, a subtle shift took place in the way that intellectuals approached religion, reflected in many other areas of cultural life. Political philosophers, most famously Niccolò Machiavelli, sought to describe political life as it really was, to understand it rationally. Others see more general competition between artists and polymaths such as Brunelleschi, Ghiberti, Donatello, Masaccio for artistic commissions as sparking the creativity of the Renaissance. Yet it remains much debated why the Renaissance began in Italy, why it began when it did. Accordingly, several theories have been put forward to explain its origins. During the Renaissance, money and art went hand in hand.
Renaissance
–
David, by Michelangelo (Accademia di Belle Arti, Florence) is a masterpiece of Renaissance and world art.
Renaissance
–
Renaissance
Renaissance
–
Leonardo da Vinci 's Vitruvian Man (c. 1490) shows clearly the effect writers of Antiquity had on Renaissance thinkers. Based on the specifications in Vitruvius ' De architectura (1st century BC), Leonardo tried to draw the perfectly proportioned man.
Renaissance
–
Portrait of a young woman (c. 1480-85) (Simonetta Vespucci) by Sandro Botticelli
46.
Archimedes Palimpsest
–
It was overwritten with a Christian religious text by 13th-century monks. A copy of this text was made around 950 AD, again in the Byzantine Empire, by an anonymous scribe. This medieval Byzantine manuscript then traveled to Jerusalem, likely sometime after the Crusader sack of Constantinople in 1204. There, in 1229, the original Archimedes codex was washed, with at least six other parchment manuscripts, including one with works of Hypereides. The palimpsest remained near Jerusalem through at least the 16th century at the isolated Greek Orthodox monastery of Mar Saba. At some point before 1840 the palimpsest was brought back by the Greek Orthodox Patriarchate of Jerusalem to their library in Constantinople. In 1899 the Greek scholar Papadopoulos-Kerameus produced a catalog of the library's manuscripts and included a transcription of several lines of the partially visible underlying text. Upon seeing these lines Johan Heiberg, the world's authority on Archimedes, realized that the work was by Archimedes. When Heiberg studied the palimpsest in Constantinople in 1906, he confirmed that the palimpsest included works by Archimedes thought to have been lost. Shortly thereafter Archimedes' Greek text was translated into English by T. L. Heath. Before that it was not widely known among mathematicians, physicists or historians. The manuscript was still in the Greek Orthodox Patriarchate of Jerusalem's library in Constantinople in 1920. Sometime between 1930 the palimpsest was acquired by a "traveler to the Orient who lived in Paris." Stored secretly for years in Marie's cellar the palimpsest suffered damage from water and mold. These gold leaf portraits nearly obliterated the text underneath them, x-ray fluorescence imaging at Stanford would later be required to reveal it.
Archimedes Palimpsest
–
A typical page from the Archimedes Palimpsest. The text of the prayer book is seen from top to bottom, the original Archimedes manuscript is seen as fainter text below it running from left to right
Archimedes Palimpsest
–
Discovery reported in the New York Times on July 16, 1907
Archimedes Palimpsest
–
After imaging a page from the palimpsest, the original Archimedes text is now seen clearly
Archimedes Palimpsest
–
Ostomachion is a dissection puzzle in the Archimedes Palimpsest (shown after Suter from a different source; this version must be stretched to twice the width to conform to the Palimpsest)
47.
Colonies in antiquity
–
Colonies in antiquity were city-states founded from a mother-city, not from a territory-at-large. Bonds between its metropolis remained often close, took specific forms. However, unlike in the period of European colonialism during the late modern era, ancient colonies were usually sovereign and self-governing from their inception. An Egyptian colony, stationed in southern Canaan dates to slightly before the First Dynasty. Narmer had Egyptian pottery exported back to Egypt, from regions such as Arad, En Besor, Rafiah, Tel ʿErani. Shipbuilding was known to the ancient Egyptians perhaps earlier. The Archaeological Institute of America reports that the earliest dated ship -- dating to 3000 BC -- may have possibly belonged to Pharaoh Aha. Egypt at its height controlled Crete across the Mediterranean Sea. The Phoenicians were the major power in the Mediterranean in the early part of the first millennium BC. They established colonies as far west as modern Spain, at Gadir. From Gadir the Phoenicians controlled access to Britain. The Carthaginians later founded their own colony in the southeast of Spain, Carthago Nova, eventually conquered by Rome. But in most cases the motivation was to further the wealth of the mother-city. Colonies were established in Ionia and Thrace early as the 8th century BC. There were two similar types of one known as an ἀποικία - apoikia and the other as an ἐμπορίov - emporion.
Colonies in antiquity
–
The Mediterranean in ca. the 6th century BC. Phoenician cities are labelled in yellow, Greek cities in red, and other cities in grey.
Colonies in antiquity
–
Map showing the Augustus "roman coloniae" in north Africa
48.
Southern Italy
–
It generally coincides with Sardinia. Southern Italy carries a unique legacy of culture. It features major tourist attractions, such as the Palace of Caserta, the Amalfi Coast, Pompeii and other archaeological sites. There are also many ancient Greek cities such as Sybaris, which were founded several centuries before the start of the Roman Republic. These same subdivisions are at the bottom of the Italian constituencies for the European Parliament. The Mezzogiorno first came into use in the 18th century and is an Italian rendition of meridies. It eventually came into vogue after the Italian unification. In a similar manner, Southern France is colloquially known as le Midi. Southern Italy forms the lower part of the Italian "boot", containing the ankle, the toe, the heel, along with the island of Sicily. It is an arm of the Ionian Sea. On the eastern coast is the Adriatic Sea, leading into the rest of the Mediterranean through the Strait of Otranto. Along the northern coast of the Salernitan Gulf and on the south of the Sorrentine Peninsula runs the Amalfi Coast. Off the tip of the peninsula is the isle of Capri. The largest city of Southern Italy is a name from the Greek that it has historically maintained for millennia. Bari, Taranto, Reggio Calabria, Salerno are the next largest cities in the area.
Southern Italy
–
Satellite image of Southern Italy
Southern Italy
–
Greek temple of Hera, Selinunte, Sicily.
Southern Italy
–
Castel del Monte, built by Frederick II between 1240 and 1250 in Andria, Apulia.
Southern Italy
–
Castel Nuovo, Naples: initiated by the Anjou, it was heavily altered as it served as Spanish headquarters until the 18th century.
49.
Byzantine Greeks
–
Throughout the Middle Ages, the Byzantine Greeks are referred to as "Byzantines" and "Byzantine Greeks" in modern historiography. The terms "Byzantine Empire" and "Byzantine Greeks" were first coined by British historian George Finlay. These peasants lived within three kinds of settlements: the proasteion or estate. Soldiers among the Byzantine Greeks were at trained on an annual basis. As the Byzantine Empire entered the 11th century, more of the soldiers within the army were either professional mercenaries. Success came easily to Greek merchants, who enjoyed a very strong position in international trade. Despite the challenges posed by Italian merchants, they held their own throughout the latter half of the Byzantine Empire's existence. The language of the Byzantine Greeks since the age of Constantine had been Greek, although Latin was the language of the administration. From the reign of Emperor Heraclius, Greek also replaced Latin in administration. Over time, the relationship between the West, particularly with Latin Europe, deteriorated. However, the Byzantine Empire continued the unbroken line of succession of the Roman emperors. During most of the Middle Ages, the Byzantine Greeks self-identified as a term which in the Greek language had become synonymous with Christian Greeks. The ancient name Hellenes was revived as an ethnonym in the Middle Byzantine period. "Byzantine Greeks" is an exonym applied by later historians like Hieronymus Wolf; the "Byzantines" continued to call themselves Romaioi in their language. Most historians agree that the defining features of their civilization were: 1) Greek language, culture, literature, science, 2) Roman law and tradition, 3) Christian faith.
Byzantine Greeks
–
Byzantine culture
Byzantine Greeks
–
The double-headed eagle, emblem of the Palaiologos dynasty.
Byzantine Greeks
–
Soldier wearing the lamellar klivanion cuirass and a straight spathion sword.
Byzantine Greeks
–
A page of 5th or 6th century Iliad like the one a grammarian might possess.
50.
John Tzetzes
–
John Tzetzes was a Byzantine poet and grammarian, known to have lived at Constantinople during the 12th century. His most important work is the Chiliades. Tzetzes was Greek on his mother's side. Tzetzes was described as vain, violently attacked his fellow grammarians. Owing to a lack of written material, he was obliged to trust to his memory; therefore caution has to be exercised in reading his work. However, he made a great contribution to the furtherance of the study of ancient Greek literature. The whole production suffers from an unnecessary display of the total number of authors quoted being more than 400. The author subsequently brought out a revised edition with marginal notes in verse. Tzetzes supplemented Homer's Iliad by a work that continues the tale to the Achaeans' return home. In the Antehomerica, Tzetzes recalled the events taking place before Homer's Iliad. All three are currently available in English translations. For the other works of Tzetzes see J. A. Fabricius, Bibliotheca graeca, Karl Krumbacher, Geschichte der byz. Litt.; monograph by G. Hart, "De Tzetzarum nomine, vitis, scriptis," in Jahn's Jahrbucher für classische Philologie. Supplementband xii. This article incorporates text from a publication now in the public domain: Chisholm, ed..
John Tzetzes
–
16th-century manuscript of Hesiod 's Theogony with commentaries by John Tzetze
51.
Astronomer
–
An astronomer is a scientist in the field of astronomy who concentrates their studies on a specific question or field outside of the scope of Earth. Examples of fields astronomers work on include: planetary science, solar astronomy, the formation of galaxies. There are also related but distinct subjects like cosmology which studies the Universe as a whole. Astronomers usually fit into two types: Observational astronomers make direct observations of planets, stars and galaxies, analyse the data. Theoretical astronomers create and investigate models of things that cannot be observed. They use this data to create simulations to theorize how celestial bodies work. There are further subcategories inside these two main branches of astronomy such as cosmology. That distinction the terms "astronomer" and "astrophysicist" are interchangeable. Professional astronomers are highly educated individuals who typically are employed by research universities. The number of professional astronomers in the United States is actually quite small. The American Astronomical Society, the major organization of professional astronomers in North America, has approximately 7,000 members. This number includes scientists from other fields such as engineering, whose research interests are closely related to astronomy. The International Astronomical Union comprises almost 10,145 members from 70 different countries who are involved in astronomical research at the Ph.D. level and beyond. Before CCDs, photographic plates were a common method of observation. Modern astronomers spend relatively little time at telescopes usually just a few weeks per year.
Astronomer
–
The Astronomer by Johannes Vermeer
Astronomer
–
Galileo is often referred to as the Father of modern astronomy
Astronomer
–
Guy Consolmagno (Vatikan observatory), analyzing a meteorite, 2014
Astronomer
–
Emily Lakdawalla at the Planetary Conference 2013
52.
Plutarch
–
Plutarch was a Greek biographer and essayist, known primarily for his Parallel Lives and Moralia. He is classified as a Middle Platonist. Plutarch's surviving works were intended for both Greek and Roman readers. His family was wealthy. The name of Plutarch's grandfather was Lamprias, as he attested in his Life of Antony. Timon and Lamprias, are frequently mentioned in his essays and dialogues, wherein Timon in particular is spoken of in the most affectionate terms. Rualdus, in his 1624 Life of Plutarchus, recovered the name of Plutarch's wife, Timoxena, from internal evidence afforded by his writings. Interestingly, he hinted in that letter of consolation. The exact number of his sons is not certain, although Autobulus and second Plutarch, are often mentioned. This is nowhere definitely stated. Plutarch studied mathematics and philosophy at the Academy of Athens from 66 to 67. At some point, Plutarch took up Roman citizenship. He was initiated into the mysteries of the Greek god Apollo. At his estate, guests from all over the empire congregated for serious conversation, presided over by Plutarch in his marble chair. The 78 essays and other works which have survived are now known collectively as the Moralia.
Plutarch
–
Ruins of the Temple of Apollo at Delphi, where Plutarch served as one of the priests responsible for interpreting the predictions of the oracle.
Plutarch
–
Parallel Lives, Amyot translation, 1565
Plutarch
–
Plutarch's bust at Chaeronea, his home town.
Plutarch
–
A page from the 1470 Ulrich Han printing of Plutarch's Parallel Lives.
53.
Parallel Lives
Parallel Lives
–
Parallel Lives
54.
Hiero II of Syracuse
–
He was a former general of Pyrrhus of Epirus and an important figure of the First Punic War. On the departure of Pyrrhus from Sicily the Syracusan army and citizens appointed him commander of the troops. He strengthened his position by marrying the daughter of Leptines, the leading citizen. They were finally defeated in a pitched battle near Mylae by Hiero, only prevented from capturing Messana by Carthaginian interference. His grateful countrymen then made him king. In 264 BC he again returned to the attack, the Mamertines called in the aid of Rome. He asked Archimedes to find out if all the gold had been used, as had been agreed. Vitruvius concludes this story by stating that Archimedes' method successfully detected the goldsmith's fraud; he had taken some of the gold and substituted silver instead. A picture of the prosperity of Syracuse during his rule is given in the sixteenth idyll of Theocritus, his favourite poet. The German historian Alexander von Stauffenberg was habilitated in 1931 for his work about Hiero II. This article incorporates text from a publication now in the public domain: ed.. "article name needed". Encyclopædia Britannica. Cambridge University Press.
Hiero II of Syracuse
–
Coin of Hiero II of Syracuse
Hiero II of Syracuse
–
Zeus' sacrificial altar built by Hiëro II in Syracuse
Hiero II of Syracuse
–
Image of Philistis (left), the wife of Hiero II, from a coin.
55.
Ancient Egypt
–
It is one of six civilizations to arise independently. Egyptian civilization coalesced around 3150 BC with the political unification of Upper and Lower Egypt under the first pharaoh Narmer. In the aftermath of Alexander one of his generals, Ptolemy Soter, established himself as the new ruler of Egypt. This Greek Ptolemaic Kingdom ruled Egypt until 30 BC, when, under Cleopatra, it became a Roman province. The success of Egyptian civilization came partly from its ability to adapt to the conditions of the Nile River valley for agriculture. The predictable flooding and controlled irrigation of the fertile valley produced surplus crops, which supported social development and culture. Egypt left a lasting legacy. Its antiquities carried off to far corners of the world. Its monumental ruins have inspired the imaginations of writers for centuries. The Nile has been the lifeline of its region for much of human history. Nomadic human hunter-gatherers began living in the Nile valley through the end of the Middle Pleistocene some 120,000 years ago. In Predynastic and Early Dynastic times, the Egyptian climate was much less arid than it is today. Large regions of Egypt were traversed by herds of grazing ungulates. The Nile region supported large populations of waterfowl. This is also the period when many animals were first domesticated.
Ancient Egypt
–
The Great Sphinx and the pyramids of Giza are among the most recognizable symbols of the civilization of ancient Egypt.
Ancient Egypt
–
A typical Naqada II jar decorated with gazelles. (Predynastic Period)
Ancient Egypt
–
The Narmer Palette depicts the unification of the Two Lands.
56.
Eratosthenes
–
Eratosthenes of Cyrene was a Greek mathematician, geographer, poet, astronomer, music theorist. He was a man of learning, becoming the chief librarian at the Library of Alexandria. He invented the discipline of geography, including the terminology used today. His calculation was remarkably accurate. He was also the first to calculate the tilt of the Earth's axis. Additionally, Eratosthenes invented the day. Eratosthenes created the first map of the world, incorporating meridians based on the geographic knowledge of his era. Eratosthenes was the founder of scientific chronology; he endeavored to revise the dates of the political events from the conquest of Troy. In theory, Eratosthenes introduced the sieve of an efficient method of identifying prime numbers. He was a figure of influence in many fields. According to an entry in the Suda, his critics scorned him, calling Beta because he always came in all his endeavors. Eratosthenes yearned to understand the complexities of the entire world. The son of Aglaos, Eratosthenes was born in 276 BC in Cyrene. Under the economy prospered based largely on the export of horses and silphium, a plant used for rich medicine. Cyrene became a place of cultivation, where knowledge blossomed.
Eratosthenes
–
19th-century reconstruction of Eratosthenes' map of the known world, c. 194 BC
Eratosthenes
–
Eratosthenes
Eratosthenes
–
The Burning of the Library at Alexandria in 391 AD, an illustration from "Hutchinsons History of the Nations", c. 1910
57.
Second Punic War
–
The two states fought three major wars over the course of their existence. They are called the "Punic Wars" because Rome's name for Carthaginians was Poeni, derived from Poenici, a reference by Phoenician settlers. In the following year, Hannibal's army defeated the Romans again, this time at Cannae. In consequence of these defeats, many Roman allies went over to Carthage, prolonging the war in Italy for over a decade. Against Hannibal's skill on the battlefield, the Romans deployed the Fabian strategy. A sideshow of this war was the indecisive First Macedonian War in the Ionian Sea. The pleas fell on deaf ears. Many of the Saguntians chose to commit suicide rather than face subjugation by the Carthaginians. Before the war, Hasdrubal the Fair had made a treaty. Hannibal departed along the coast in late spring of 218 BC. At the Ebro, he subdued the tribes from there to the Pyrenees within weeks, but with severe losses. At the Pyrenees, he left a detachment of 11,000 Iberian troops, who showed reluctance to leave their homeland, as a garrison for the newly conquered region. Hannibal reportedly entered Gaul with 9,000 cavalry. He took his army by an inland route, avoiding the Roman allies along the coast. In the meantime, a Roman fleet with an force was underway to northern Iberia.
Second Punic War
–
Iberian warrior from bas-relief c. 200 BC. The warrior is armed with a falcata and an oval shield. National Archaeological Museum of Spain, Madrid
Second Punic War
–
Western Mediterranean, 218 BC. Italian cities and Celtic tribes that joined Hannibal after the invasion of Italy are depicted in blue.
Second Punic War
–
Iberian falcata, 4th/3rd century BC. This weapon, a scythe-shaped sword, was unique to Iberia [citation needed]. By its inherent weight distribution, it could deliver blows as powerful as an axe. National Archaeological Museum of Spain, Madrid
Second Punic War
–
Detail of frieze showing the equipment of a soldier in the manipular Roman legion (left). Note mail armour, oval shield and helmet with plume (probably horsehair). The soldier in the centre is an officer (bronze cuirass, mantle), prob. a tribunus militum. From an altar built by Gnaeus Domitius Ahenobarbus, consul in 122 BC. Musée du Louvre, Paris
58.
Marcus Claudius Marcellus
–
Furthermore, he is noted for having conquered the fortified city of Syracuse in a protracted siege during which the famous inventor, was killed. Marcus Claudius Marcellus died in 208 BC leaving behind a legacy of military conquests and a reinvigorated Roman legend of the spolia opima. Little is known of Marcus Claudius Marcellus' early years to his military expeditions. The fullest account of Marcellus' life was written by a Greek biographer in the time of the Roman Empire. According to Plutarch, Marcellus was raised with the purpose of entering military service. Marcellus’ general education may have been lacking. In his youth, Marcellus quickly distinguished himself as an ambitious warrior, known for his skill in hand-to-hand combat. He is noted to having saved the life of Otacilius, when the two were surrounded by enemy soldiers in Italy. As a young man in the Roman army, Marcellus was praised by his superiors for his valor. In 226 BC, he was elected to the position of curule aedile in the Roman Republic. The position of curule aedile was quite prestigious for a man like Marcellus. An aedile was an enforcer of public order. This is generally the first position one might take in seeking a political career. Around the same time that he became an aedile, Marcellus was also awarded the position of augur, which Plutarch describes as being an interpreter of omens. By about the age of 40, Marcellus had already become public official.
Marcus Claudius Marcellus
–
Drawing of Marcus Claudius Marcellus in Universal Historical Dictionary by George Crabb
59.
Siege
–
A siege is a military blockade of a city or fortress with the intent of conquering by attrition or assault. This derives from sedere, Latin for "to sit". Siege warfare is a form of low-intensity conflict characterized by one party holding a strong, static defensive position. Consequently, an opportunity for negotiation between combatants is not uncommon, as fluctuating advantage can encourage diplomacy. A siege occurs when an attacker encounters a city or fortress that refuses to surrender. Failing a military outcome, sieges can often be decided by starvation, disease, which can afflict either the attacker or defender. This form of siege, though, can take many months or even years, depending upon the size of the stores of food the fortified position holds. Siege machinery was also a tradition of the Greco-Roman world. During the early modern period, siege warfare dominated the conduct of war in Europe. Leonardo da Vinci gained as much of his renown as from his artwork. Medieval campaigns were generally designed around a succession of sieges. In the Napoleonic era, increasing use of ever more powerful cannon reduced the value of fortifications. In the 20th century, the significance of the classical siege declined. With the advent of mobile warfare, a fortified stronghold is no longer as decisive as it once was. Modern sieges are more commonly the result of smaller hostage, extreme resisting arrest situations.
Siege
–
Picture of the siege of Rancagua during the Chilean War of Independence
Siege
–
The Egyptian siege of Dapur in the 13th century BC, from Ramesseum, Thebes
Siege
–
Depiction of various siege machines in the mid-16th century.
Siege
–
Medieval trebuchets could sling about two projectiles per hour at enemy positions.
60.
Mathematical diagram
–
These are named after Jean-Robert Argand, although they were first described by mathematician Caspar Wessel. Argand diagrams are frequently used to plot the positions of the zeroes of a function in the complex plane. The concept of the complex plane allows a geometric interpretation of complex numbers. Under addition, they add like vectors. In particular, multiplication by a complex number of modulus 1 acts as a rotation. The name "butterfly" comes from the shape of the data-flow diagram in the radix-2 case, as described below. The same structure can also be found in the Viterbi algorithm, used for finding the most likely sequence of hidden states. This diagram resembles a butterfly as in the Morpho butterfly shown for comparison), hence the name. Commutative diagrams play the role in theory that equations play in algebra. A Hasse diagram is a simple picture of a finite partially ordered set, forming a drawing of the partial order's transitive reduction. In this case, we say y covers y is an immediate successor of x. In a Hasse diagram, it is required that the curves be drawn so that each meets exactly two vertices: its two endpoints. This is often done by creating a break in the strand going underneath. If by following the diagram the alternately crosses itself "over" and "under", then the diagram represents a particularly well-studied class of knot, alternating knots. The Venn diagram is constructed with a collection of closed curves drawn in the plane.
Mathematical diagram
–
Euclid's Elements, ms. from Lüneburg, A.D. 1200
61.
Hekatonkheires
–
Their name derives from the Greek ἑκατόν and χείρ, "each of them having a hundred hands and fifty heads". Hesiod's Theogony reports that the three Hecatoncheires became the guards of the gates of Tartarus. The Hundred-Handed-Ones are "giants" of great storms and hurricanes. Other accounts make Briareos one of the assailants of Olympus. After his defeat, he was buried under Mount Aetna. According to Hesiod, the Hecatoncheires were children of Gaia and Uranus. They played no known part in cult. They were: Briareos "Strong", also called Aegaeon, spelled in Latin as "Briareus." Kottos "Strike, punch". Gyges or Gyes, possibly "Limb" or "Curved." Soon after they were born, their father Uranus threw them into the depths of Tartarus because he saw them as hideous monsters. During the War of the Titans, the Hecatoncheires fought against the Titans, throwing rocks as big as mountains, one hundred at a time, overwhelming them. After this, the Hecatoncheires became the guards of Tartarus. Briareos became the son-in-law of Poseidon, who gave him "Kymopoliea his daughter to wed." In Ovid's Metamorphoses and in Philostratus' Life of Apollonius of Tyana he is a marine deity.
Hekatonkheires
–
Etching by Tommaso Piroli after a drawing of John Flaxman.
62.
Benjamin West
–
Benjamin West PRA was an Anglo-American painter of historical scenes around and after the time of the American War of Independence and the Seven Years' War. He was the second president of the Royal Academy in London, serving from 1806 to 1820. He was offered a knighthood by the British Crown, but declined it, believing that he should instead be made a peer. He said that "Art is the representation of human beauty, ideally perfect in design, noble in attitude." The family later moved to Pennsylvania, where his father was the proprietor of the Square Tavern, still standing in that town. Benjamin West was an autodidact; even when president of the Royal Academy, could scarcely spell". From 1746 to 1759, West worked mostly painting portraits. His resulting composition, which significantly differs from the source, has been called "the most interesting painting produced in colonial America". During this time West met John Wollaston, a famous painter who had immigrated from London. West was a close friend of Benjamin Franklin, whose portrait he painted. Franklin was the godfather of Benjamin. In common with many artists lovers of the fine arts at that time he conducted a Grand Tour. West expanded his repertoire from the originals. In Rome he met a number of neo-classical artists including German-born Anton Rafael Mengs, Scottish Gavin Hamilton, Austrian Angelica Kauffman. In August 1763, West arrived in England, on what he initially intended as a visit on his way back to America.
Benjamin West
–
External video
Benjamin West
–
Self Portrait of Benjamin West, ca. 1763
Benjamin West
–
Benjamin Franklin Drawing Electricity from the Sky c. 1816 at the Philadelphia Museum of Art
Benjamin West
–
Self-Portrait (National Portrait Gallery in Washington, D.C.)
63.
Latin
–
Latin is a classical language belonging to the Italic branch of the Indo-European languages. The Latin alphabet is derived from Greek alphabets. Latin was originally spoken in the Italian Peninsula. Through the power of the Roman Republic, it became the dominant language, initially in Italy and subsequently throughout the Roman Empire. Vulgar Latin developed such as Italian, Portuguese, Spanish, French, Romanian. Latin, Italian and French have contributed many words to the English language. Ancient Greek roots are used in theology, biology, medicine. By the late Roman Republic, Old Latin had been standardised into Classical Latin. Vulgar Latin was the colloquial form attested in inscriptions and the works of comic playwrights like Plautus and Terence. Later, Early Modern Latin and Modern Latin evolved. Latin was used until well into the 18th century, when it began to be supplanted by vernaculars. Ecclesiastical Latin remains the Roman Rite of the Catholic Church. Many students, scholars and members of the Catholic clergy speak Latin fluently. It is taught around the world. The language has been passed down through various forms.
Latin
–
Latin inscription, in the Colosseum
Latin
–
Julius Caesar 's Commentarii de Bello Gallico is one of the most famous classical Latin texts of the Golden Age of Latin. The unvarnished, journalistic style of this patrician general has long been taught as a model of the urbane Latin officially spoken and written in the floruit of the Roman republic.
Latin
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A multi-volume Latin dictionary in the University Library of Graz
Latin
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Latin and Ancient Greek Language - Culture - Linguistics at Duke University in 2014.
64.
Valerius Maximus
–
Valerius Maximus was a Latin writer and author of a collection of historical anecdotes. He worked during the reign of Tiberius. He has been represented as a mean flatterer of the same type as Martial. But, if the references to the imperial administration are carefully scanned, they will be seen to be extravagant neither in kind nor in number. The few allusions to Augustus hardly pass beyond the conventional style of the writer's day. The only passage which can fairly be called fulsome is the violently rhetorical tirade against Sejanus. The style of Valerius's writings seems to indicate that he was a professional rhetorician. According to the manuscripts, its title is Factorum ac memorabilium libri IX, "Nine Books of Memorable Deeds and Sayings." Each section has an appendix consisting of extracts from the annals of other peoples, principally the Greeks. The author's chief sources are Cicero, Livy, Sallust and Pompeius Trogus, especially the first two. And even on the historical side we owe something to Valerius. He is also a typical example of a literary period often criticised for poor writers. In Valerius are all the rhetorical tendencies of the age. Simple statement is avoided and novelty pursued at any price. Like other schoolbooks it was epitomated.
Valerius Maximus
–
Page from an incunable of Valerius Maximus, Facta et dicta memorabilia, printed in red and black by Peter Schöffer (Mainz, 1471)
Valerius Maximus
–
Simon de Hesdin presents his translation of Valerius Maximus' 'Facta et dicta memorabilia' to Charles V, king of France
65.
Quaestor
–
A quaestor was a public official in Ancient Rome. The position served different functions depending on the period. In the Roman Kingdom, parricidii were appointed by the king to handle murders. In the Roman Republic, quaestors were elected officials that supervised the state treasury and conducted audits. It was the lowest ranking position in the cursus honorum. In modern usage in Italy and Romania, a quaestor is a ranking officer on the force. In some organizations, a quaestor is the officer that oversees its finances, similar to a treasurer in other organizations. The earliest quaestors were quaestores parricidii, an office dating back to the Kingdom of Rome. Quaestores parricidii were chosen to investigate capital crimes, may have been appointed as needed rather than holding a permanent position. In the Roman Republic, quaestors were elected officials who supervised financial affairs of the state, its officers. The quaestors tasked with financial supervision were also called quaestores aerarii, because they oversaw the aerarium in the Temple of Saturn. The earliest origins of the office is obscure, but by about 420 BCE there were four quaestors elected each year by the Comitia Tributa. After 267 BCE, the number was expanded to ten. Once elected as quaestor, a Roman man earned the right to sit in the Senate and began progressing through the cursus honorum. Quaestors were also given a fasces and were entitled to one lictor.
Quaestor
–
Ancient Rome
66.
Sicily
–
Sicily is the largest island in the Mediterranean Sea. It constitutes an autonomous Region of Italy, along with surrounding minor islands, officially referred to as Regione Siciliana. Sicily is located in the central Mediterranean Sea, south of the Italian Peninsula, from which it is separated by the narrow Strait of Messina. Its most prominent landmark is Mount Etna, the tallest active volcano in Europe, currently 3,329 m high, one of the most active in the world. The island has a typical Mediterranean climate. The earliest archaeological evidence of human activity on the island dates from as early as 12,000 BC. It became part of Italy in 1860 following the Expedition of the Thousand, a revolt led during a plebiscite. Sicily was given special status as an autonomous region after the Italian constitutional referendum of 1946. Sicily has a unique culture, especially to the arts, music, literature, cuisine, architecture. It is also Selinunte. Sicily has a roughly triangular shape, earning the Trinacria. The total area of the island is 25,711 km2, while the Autonomous Region of Sicily has an area of 27,708 km2. The terrain of inland Sicily is mostly hilly and is intensively cultivated wherever possible. Along the northern coast, the mountain ranges of Madonie, 2,000 m, Nebrodi, 1,800 m, Peloritani, 1,300 m, are an extension of the mainland Apennines. The cone of Mount Etna dominates the eastern coast.
Sicily
–
Mount Etna rising over suburbs of Catania
Sicily
–
Sicily Sicilia
Sicily
–
Sicilian landscape
Sicily
–
Location of the Salso
67.
Polybius
–
Polybius was a Greek historian of the Hellenistic period noted for his work, The Histories, which covered the period of 264–146 BC in detail. Polybius was born around 200 BC in Megalopolis, Arcadia, when it was an active member of the Achaean League. Lycortas, was a land-owning politician and member of the governing class who became strategos of the Achaean League. Consequently, Polybius was able to observe first hand the political and military affairs of Megalopolis. He developed an interest in horse riding and hunting, diversions that later commended him to his Roman captors. In either 169 BC or 170 BC, Polybius was elected hipparchus, an event which often presaged election to the annual strategia. His early political career was devoted largely towards maintaining the independence of Megalopolis. Polybius’ father, Lycortas, was a prominent advocate of neutrality during the Roman war against Perseus of Macedonia. Polybius remained on cordial terms with his former pupil Scipio Aemilianus and was among the members of the Scipionic Circle. Polybius remained a counselor to Scipio when he defeated the Carthaginians in the Third Punic War. Following the destruction of Carthage, Polybius likely journeyed along the Atlantic coast of Africa, as well as Spain. After the destruction of Corinth in the same year, Polybius returned to Greece, making use of his Roman connections to lighten the conditions there. Polybius was charged with the difficult task of organizing the new form of government in the Greek cities, in this office he gained great recognition. He apparently interviewed veterans to clarify details of the events he was recording and was similarly given access to archival material. Little is known of Polybius' later life; he most likely accompanied Scipio to Spain, acting as his military advisor during the Numantine War.
Polybius
–
The Stele of Polybius, possible representation of the man
Polybius
–
Marcus Tullius Cicero
Polybius
–
Montesquieu
68.
Livy
–
Livy and Augustus's wife, Livia, were from the same clan in different locations, although not related by blood. Livy was born in northern Italy, now modern Padua. There is a debate about the year of Titus Livius' birth, more likely 59 BC. At the time of his birth, his city of Patavium was the second wealthiest on the Italian peninsula. Patavium was a part of the province of Cisalpine Gaul at the time. Livy's teen years were during a time that coincided with the civil wars that were occurring throughout the Roman world. The wealthier citizens of Patavium went into hiding. Therefore, the other residents of Patavium did not end up supporting Marcus Antonius in his campaign for control over Rome. On, Asinius Pollio made a jibe at Livy's "patavinity", saying that Livy's Latin showed certain "provincialisms" frowned on at Rome. During his time in Rome, he held any other governmental position. His elementary mistakes in military matters show that he was never a soldier. However, he was educated in rhetoric. It seems that Livy means to live an independent life. He devoted a large part of his life to his writings, which he was able to do because of his financial freedom. He was not heard of to engage in declamation, a common pastime.
Livy
–
Bust of Caesar Augustus from the Musei Capitolini, Rome
Livy
–
Titus Livius (fictitious portrait)
69.
Mass
–
In physics, mass is a property of a physical body. It is the measure of an object's resistance to acceleration when a force is applied. It also determines the strength of its gravitational attraction to other bodies. In the theory of relativity a related concept is the mass -- content of a system. The SI unit of mass is the kilogram. It would still have the same mass. This is because weight is a force, while mass is the property that determines the strength of this force. In Newtonian physics, mass can be generalized in an object. However, at very high speeds, special relativity postulates that energy is an additional source of mass. Thus, all forms of energy resist acceleration by a force and have gravitational attraction. In addition, "matter" thus can not be precisely measured. There are distinct phenomena which can be used to measure mass. Gravitational mass measures the gravitational force exerted by an object. Passive gravitational mass measures the gravitational force exerted on an object in a gravitational field. Mass–energy measures the total amount of energy contained within a body, using E = mc2.
Mass
–
Depiction of early balance scales in the Papyrus of Hunefer (dated to the 19th dynasty, ca. 1285 BC). The scene shows Anubis weighing the heart of Hunefer.
Mass
–
The kilogram is one of the seven SI base units and one of three which is defined ad hoc (i.e. without reference to another base unit).
Mass
–
Galileo Galilei (1636)
Mass
–
Distance traveled by a freely falling ball is proportional to the square of the elapsed time
70.
Vitruvius
–
By his own description Vitruvius served as an artilleryman, the third class of arms in the military offices. He probably served as a senior officer of artillery in charge of doctores ballistarum and libratores who actually operated the machines. Little is known about Vitruvius' life. Most inferences about him are extracted from his only surviving work De Architectura. Even his first name Marcus and his cognomen Pollio are uncertain. Cetius Faventinus writes of "Vitruvius Polio aliique auctores"; this can be read as "others" or, less likely, as "others". Neither association, however, is borne out by De Architectura, nor by the little, known of Mamurra. A praefect architectus armamentarius of the group. He is mentioned in Pliny the Elder's table of contents for Naturalis Historia, in the heading for mosaic techniques. Frontinus refers to "Vitruvius the architect" in his late 1st-century work De aquaeductu. These names vary depending on the edition of De architectura. Publius Minidius is also written as Publius Numidicus and Publius Numidius, speculated as the same Publius Numisius inscribed on the Roman Theatre at Heraclea. As an army engineer he specialized in the construction of ballista and scorpio artillery war machines for sieges. It is speculated that Vitruvius served with Caesar's chief engineer Lucius Cornelius Balbus. The locations where he served can be reconstructed from, for example, descriptions of the building methods of various "foreign tribes".
Vitruvius
–
A 1684 depiction of Vitruvius (right) presenting De Architectura to Augustus
Vitruvius
–
Vitruvian Man by Leonardo da Vinci, an illustration of the human body inscribed in the circle and the square derived from a passage about geometry and human proportions in Vitruvius' writings
Vitruvius
–
Greek house plan after Vitruvius
Vitruvius
–
Drainage wheel from Rio Tinto mines
71.
Votive crown
–
A votive crown is a votive offering in the form of a crown, normally in precious metals and often adorned with jewels. Especially in the Early Middle Ages, they are of a special form, designed to be suspended by chains at an altar, image. There were pagan votive crowns in the ancient world, although these are essentially known only from literary references. These are now divided between the National Archaeological Museum of Spain in Madrid and the Musée de Cluny in Paris. In the example above, "King Recceswinth offered this". These royal donations signified the submission of the monarchy to God. The Iron Crown of Lombardy was perhaps originally made as a votive crown, although it was later used for the coronation of monarchs including Napoleon I. Instead, he had it suspended by chains over the main altar of Hagia Sophia, upsetting the two ladies. It hung there until Emperor Leo IV coveted it and took it for his own use. Another Byzantine crown, given by Leo VI is now in the Treasury of San Marco, Venice, is decorated with cloisonné enamels. This is now a rare example of a medieval crown that has survived above ground. Statues of the Infant Jesus of Prague type, are among those most commonly crowned. It is now in private hands in the US. Votive crowns have continued to be produced in Catholic countries in modern times. Often such crowns were kept except for special occasions such as relevant feast-days, when they are worn by the statue.
Votive crown
–
Detail of a votive crown from Visigothic Hispania, before 672. Part of the Treasure of Guarrazar. Out of view are chains for suspension above, and a Byzantine pendant cross below. Alternate view.
Votive crown
–
One of many crowned statues of the Virgin Mary carried in the processions of Holy Week in Seville.
72.
Gold
–
Gold is a chemical element with the symbol Au and the atomic number 79. In its purest form, it is a bright, slightly reddish yellow, dense, soft, ductile metal. Chemically, gold is a group 11 element. It is solid under standard conditions. The metal therefore occurs often in free elemental form, as nuggets or grains, in rocks, in alluvial deposits. It occurs in a solid series with the native element silver and also naturally alloyed with copper and palladium. Less commonly, it occurs in minerals as gold compounds, often with tellurium. Gold's atomic number of 79 makes one of the higher atomic number elements that occur naturally in the universe. Because the Earth was molten when it was just formed, almost all of the gold present in the early Earth probably sank into the planetary core. Aqua regia can dissolve it. The acid mixture causes the formation of a soluble anion. Gold also dissolves in alkaline solutions of cyanide, which are used in electroplating. This is not a chemical reaction. Gold is a precious metal used throughout recorded history. A total of 183,600 tonnes of gold is in existence above ground, as of 2014.
Gold
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Gold, 79 Au
Gold
–
Moche gold necklace depicting feline heads. Larco Museum Collection. Lima-Peru
Gold
–
Mirror for the future James Webb Space Telescope coated in gold to reflect infrared light
Gold
–
The world's largest gold bar has a mass of 250 kg. Toi museum, Japan.
73.
Silver
–
Silver is the metallic element with the atomic number 47. Its symbol is Ag, from the Latin argentum, derived from the Greek ὰργὀς, ultimately from a Proto-Indo-European root reconstructed as * h2erǵ -, "grey" or "shining". It exhibits the highest electrical conductivity, thermal conductivity, reflectivity of any metal. Most silver is produced as a byproduct of copper, gold, lead, refining. Silver has long been valued as a precious metal. Its purity is typically measured on a per mille basis; a 94%-pure alloy is described as "0.940 fine". As one of the seven metals of antiquity, silver has had an enduring role in most human cultures. Silver is used as an investment medium. Silver is used industrially in specialized mirrors, window coatings, in catalysis of chemical reactions. Silver compounds are used in photographic film and X-rays. Other silver compounds are used as disinfectants and microbiocides, added to bandages and wound-dressings, catheters, other medical instruments. Silver is similar in its chemical properties to its two vertical neighbours in group 11 of the periodic table, copper and gold. Silver is an extremely soft, ductile and malleable metal, though it is slightly less malleable than gold. Silver crystallizes in a cubic lattice with bulk coordination number 12, where only the single 5s electron is delocalized, similarly to copper and gold. Unlike metals with incomplete d-shells, metallic bonds in silver are relatively weak.
Silver
–
Electrolytically refined silver
Silver
–
Silver 1000 oz t (~31 kg) bullion bar
Silver
–
Cessna 210 equipped with a silver iodide generator for cloud seeding
Silver
–
A Canadian 50 cent piece from 1951, with King George the 6th on the obverse and Canada's (now former) coat of arms on the reverse. It is made of 80% silver and 20% copper.
74.
Density
–
The density, or more precisely, the volumetric mass density, of a substance is its mass per unit volume. The symbol most often used for density is ρ, although the Latin letter D can also be used. For a pure substance the density has the same numerical value as its mass concentration. Different materials usually have different densities, density may be relevant to buoyancy, purity and packaging. Osmium and iridium are the densest known elements at standard conditions for temperature and pressure but certain chemical compounds may be denser. Thus a relative density less than one means that the substance floats in water. The density of a material varies with temperature and pressure. This variation is typically small for solids and liquids but much greater for gases. Increasing the pressure on an object decreases the volume of the object and thus increases its density. Increasing the temperature of a substance decreases its density by increasing its volume. This causes it to rise relative to more dense unheated material. The reciprocal of the density of a substance is occasionally called its specific volume, a term sometimes used in thermodynamics. Density is an intensive property in that increasing the amount of a substance does not increase its density; rather it increases its mass. Upon this discovery, he leapt from his bath and ran naked through the streets shouting, "Eureka! Eureka!"
Density
–
Air density vs. temperature
75.
Eureka (word)
–
Eureka is an interjection used to celebrate a discovery or invention. It is a transliteration of an exclamation attributed to Greek inventor Archimedes. It is closely related to heuristic, which refers to experience-based techniques for discovery. The long vowels in the first two syllables would sound like a double stress to English ears. The initial / h / is preserved such as Finnish, Danish, German. The exclamation'Eureka!' is famously attributed to the ancient Greek scholar Archimedes. He reportedly proclaimed "Eureka! He then realized that the volume of irregular objects could be measured with precision, a previously intractable problem. This story first appeared in written form of two centuries after it supposedly took place. The expression is also the state motto of California, referring to the momentous discovery of gold near Sutter's Mill in 1848. The city of Eureka, California, founded in 1850, uses the California State Seal as its official seal. Eureka was the jumping off point of a smaller rush in nearby Trinity County, California in 1850. It is the largest of towns named for "eureka!". Many places, works of culture, other objects have since been named "Eureka"; see Eureka for a list. "Eureka" was also associated with a gold rush in Ballarat, Victoria, Australia.
Eureka (word)
–
16th-century illustration of Archimedes in the bath, with Hiero's crown at bottom right
76.
Buoyancy
–
In science, buoyancy is an upward force exerted by a fluid that opposes the weight of an immersed object. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus the pressure at the bottom of a column of fluid is greater than at the top of the column. Similarly, the pressure at the bottom of an object submerged in a fluid is greater than at the top of the object. This pressure difference results in a net upwards force on the object. For this reason, an object whose density is greater than that of the fluid in which it is submerged tends to sink. If the object is either less dense than the liquid or is shaped appropriately, the force can keep the object afloat. In a situation of fluid statics, the upward force is equal to the magnitude of the weight of fluid displaced by the body. The center of buoyancy of an object is the centroid of the displaced volume of fluid. Archimedes' principle is named after Archimedes of Syracuse, who first discovered this law in 212 B.C. More tersely: Buoyancy = weight of displaced fluid. The weight of the displaced fluid is directly proportional to the volume of the displaced fluid. Thus, among completely submerged objects with equal masses, objects with greater volume have greater buoyancy. This is also known as upthrust. Suppose a rock's weight is measured as 10 newtons when suspended by a string in a vacuum with gravity acting upon it.
Buoyancy
–
A metallic coin (one British pound coin) floats in mercury due to the buoyancy force upon it and appears to float higher because of the surface tension of the mercury.
Buoyancy
–
The forces at work in buoyancy. Note that the object is floating because the upward force of buoyancy is equal to the downward force of gravity.
77.
Galileo Galilei
–
Galileo Galilei was an Italian polymath: astronomer, physicist, engineer, philosopher, mathematician, he played a major role in the scientific revolution of the seventeenth century. Galileo has been called the "father of the "father of science". Galileo also worked in applied science and technology, inventing an improved military compass and other instruments. Galileo's championing of heliocentrism and Copernicanism was controversial during his lifetime, when most subscribed to either geocentrism or the Tychonic system. He met with opposition from astronomers, who doubted heliocentrism because of the absence of an observed stellar parallax. He was tried by the Inquisition, found "vehemently suspect of heresy", forced to recant. He spent the rest of his life under house arrest. Three of Galileo's five siblings survived infancy. Michelangelo, also became a noted composer although he contributed during Galileo's young adulthood. Michelangelo would occasionally have to support his musical excursions. These financial burdens may have contributed to Galileo's early fire to develop inventions that would bring him additional income. When Galileo Galilei was eight, his family moved to Florence, but he was left with Jacopo Borghini for two years. Galileo then was educated at 35 southeast of Florence. The Italian male given name "Galileo" derives from the Latin "Galilaeus", meaning "of Galilee", a biblically significant region in Northern Israel. The biblical roots of Galileo's name and surname were to become the subject of a famous pun.
Galileo Galilei
–
Portrait of Galileo Galilei by Giusto Sustermans
Galileo Galilei
–
Galileo's beloved elder daughter, Virginia (Sister Maria Celeste), was particularly devoted to her father. She is buried with him in his tomb in the Basilica of Santa Croce, Florence.
Galileo Galilei
–
Galileo Galilei. Portrait by Leoni
Galileo Galilei
–
Cristiano Banti 's 1857 painting Galileo facing the Roman Inquisition
78.
Athenaeus
–
Athenaeus of Naucratis was a Greek rhetorician and grammarian, flourishing about the end of the 2nd and beginning of the 3rd century AD. He was a contemporary of Adrantus. The fifteen volumes Deipnosophistae mostly survives. Both works are lost. The Deipnosophistae, which means "dinner-table philosophers," survives in fifteen books. Otherwise the work seems to be entire. It is an immense store-house of information, chiefly on matters connected with dining, but also containing remarks on music, songs, dances, courtesans, luxury. The conversation extends to enormous length. The guests supposedly quote from memory. Much of it probably comes at second-hand from early scholars. They are all probably fictitious personages, the majority take no part in the conversation. The complete version with the gaps noted above, is preserved in only one manuscript, conventionally referred to as A. The epitomized version of the text is preserved in two manuscripts, conventionally known as C and E. The standard edition of the text is Kaibel's Teubner. The standard numbering is drawn largely from Casaubon.
Athenaeus
–
The Deipnosophistes belongs to the literary tradition inspired by the use of the Greek banquet. Banqueters playing Kottabos while a musician plays the Aulos, decorated by the artist 'Nicias'/'Nikias'
79.
Syracusia
–
Syracusia was a 110 m ancient Greek ship sometimes claimed to be the largest transport ship of antiquity. She only sailed once, to Alexandria in the Ptolemaic Kingdom. Syracusia was built around 240 BC by Archias of Corinth on the orders of Hieron II of Syracuse. The Moschion of Phaselis said that Syracusia could carry a cargo of some 1,600 to 1,800 tons and a capacity of 1942 passengers. She reputedly bore soldiers, as well as a catapult. She sailed once to berth in Alexandria, where she was later given to Ptolemy III Euergetes of Egypt and renamed Alexandria. A discussion of this ship, well as the complete text of Athenaeus is in Casson's Ships and Seamanship in the Ancient World. This may be the first example of proactive technology. Additionally, the top deck featured eight towers, equipped with four fully armed men. On the bow of the ship was a raised platform for fighting, on top of, a giant catapult. Possibly a promenade lined with flowers and tents for use by the passengers. In terms of comfort, Syracusia would be the equivalent of Titanic compared to other ships of the era. Sheer size allowed for the creation of various recreational spaces aboard, including a garden and an indoor bath room with hot water. The lower levels of the ship were reserved on board while the upper levels were for the use of passengers. Ptolemy's son sought to outdo Syracusia.
Syracusia
–
Syracusia as imagined in 1798.
80.
Gymnasium (ancient Greece)
–
The gymnasium in Ancient Greece functioned as a training facility for competitors in public games. It was also a place for socializing and engaging in intellectual pursuits. The name comes from the Ancient Greek term gymnós meaning "naked". Athletes competed nude, a practice, said to encourage aesthetic appreciation of the male body, to be a tribute to the gods. Gymnasia and palestrae were under the patronage of Heracles, in Athens, Theseus. The verb had this meaning because one undressed for exercise. Historically, the gymnasium was used for scholarly and philosophical pursuits. The English noun gymnast, first recorded in 1594, is formed from the Greek γυμναστής, but in Greek this word means "trainer" not "gymnast". The palaistra was the part of the gymnasium devoted to ball games. The gymnasium was formed as a public institution where young men over 18 received training in physical exercises. The gymnastai were trainers of the athletes. The Greek gymnasiums also held discussions on public libraries were nearby. The contests took place in honour of gods, sometimes forming the funeral rites of a deceased chief. A victory in the great religious festivals was counted an honour for the whole state. The regulation of the Athenian gymnasium is attributed by Pausanias to Theseus.
Gymnasium (ancient Greece)
–
Pompeii gymnasium, from the top of the stadium wall.
Gymnasium (ancient Greece)
–
A hermaic sculpture of an old man, thought to be the master of a gymnasium. He held a long stick in his right hand. Ai Khanoum, Afghanistan, 2nd century BC.
81.
Aphrodite
–
Aphrodite is the Greek goddess of love, beauty, pleasure, procreation. Her Roman equivalent is the Venus. She is identified with the planet Venus. As with many Greek deities, there is more than one story about her origins. According to Hesiod's Theogony, she arose from the sea foam. According to Homer's Iliad, she is the daughter of Zeus and Dione. According to Plato, these two origins were of entirely separate entities: Aphrodite Pandemos. Aphrodite had many lovers—both gods, such as Ares, men, such as Anchises. She later was both Adonis's lover and his surrogate mother. Many lesser beings were said to be children of Aphrodite. Aphrodite is also known after the two cult sites, Cythera and Cyprus, which claimed to be her place of birth. Myrtle, doves, sparrows, swans were said to be sacred to her. The ancient Greeks identified her with the Egyptian goddess Hathor. Aphrodite had other names, such as Acidalia, Cytherea, Cerigo, each used by a different local cult of the goddess in Greece. Hesiod derives Aphrodite from aphrós "sea-foam," interpreting the name as "risen from the foam".
Aphrodite
–
Aphrodite Pudica (Roman copy of 2nd century AD), National Archaeological Museum, Athens
Aphrodite
–
Petra tou Romiou ("The rock of the Greek "), Aphrodite's legendary birthplace in Paphos, Cyprus.
Aphrodite
–
The Birth of Venus by Sandro Botticelli, circa 1485.
Aphrodite
–
Venus and Adonis by Titian, circa 1554.
82.
Hanging Gardens of Babylon
–
The Hanging Gardens of Babylon, one of the Seven Wonders of the Ancient World, is the only one whose location has not been definitively established. The Hanging Gardens were described as a remarkable feat of engineering: an ascending series of tiered gardens containing all manner of trees, shrubs, vines. The gardens were said to have looked like a large green mountain constructed of mud bricks. Traditionally they were said to have been built in the ancient city of Babylon, near present-day Hillah, Babil province, in Iraq. There are no extant Babylonian texts which mention the gardens, no definitive archaeological evidence has been found in Babylon. He also built a grand palace that came to be known as "The Marvel of the Mankind". If it did indeed exist, it was destroyed sometime after the first century AD. There are five principal writers whose descriptions of Babylon are extant in some form today. These writers concern themselves with the size of the Hanging Gardens, their overall design and means of irrigation, why they were built. Josephus quotes a description of the gardens by Berossus, a Babylonian priest of Marduk writing circa 290 BC. Berossus described the reign of Nebuchadnezzar II, is the only source to credit that king with the construction of the Hanging Gardens. This he did to gratify his queen, because she had been brought up in Media, was fond of a mountainous situation. For his description of the gardens, Diodorus Siculus seems to have consulted the 4th century BC texts of both Cleitarchus and Ctesias of Cnidus. Diodorus ascribes the construction to a Syrian king. Furthermore, the walls, constructed at great expense, were twenty-two feet thick, while the passageway between each two walls was ten feet wide.
Hanging Gardens of Babylon
–
This hand-coloured engraving, probably made in the 19th century after the first excavations in the Assyrian capitals, depicts the fabled Hanging Gardens, with the Tower of Babel in the background
Hanging Gardens of Babylon
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Hanging Gardens of Babylon, 20th-century interpretation
Hanging Gardens of Babylon
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Illustration of the mythical Hanging Gardens of Babylon by Maerten van Heemskerck (1498–1574), published in 1572.
83.
Steamboat
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A steamboat is a boat, propelled primarily by steam power, typically driving propellers or paddlewheels. Steamboats sometimes use SS, S.S. or S/S or PS, however these designations are most often used for Steamships. The steamboat is used to refer to smaller, insular, steam-powered boats working on lakes and rivers, particularly riverboats. As using steam became more reliable, power became applied to larger, ocean-going vessels. Early attempts at powering a boat by steam were made by the English inventor Thomas Newcomen. Papin tried to market his idea in Britain. The steam could not produce enough pressure. Newcomen's design remained shackled to the inherent limitations of the engines of the time. A steamboat was patented by English physician John Allen in 1729. William Henry of Lancaster, Pennsylvania, having learned to England, made his own engine. In 1763 he put it in a boat. While Henry made an improved model, he did not appear to have much success, though he may have inspired others. At its first demonstration on 15 July 1783, Pyroscaphe travelled upstream on the Saône for some fifteen minutes before the engine failed. Presumably this was easily repaired as the boat is said to have made such journeys. Similar boats were made by John Fitch in Philadelphia and William Symington in Dumfries, Scotland.
Steamboat
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Look out (Transport Steamer) on Tennessee River, ca. 1860 - ca. 1865
Steamboat
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Denis Papin 's cylinder and piston apparatus, 1690
Steamboat
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Model of steamship, built in 1784, by Claude de Jouffroy.
Steamboat
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Charlotte Dundas, the first practical steamboat, built by William Symington.
84.
Propeller
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A propeller is a type of fan that transmits power by converting rotational motion into thrust. A fluid is accelerated behind the blade. Propeller dynamics, like those of aircraft wings, can be modelled by Newton's third law. Their disadvantages are higher cost. The principle employed in using a propeller is used in sculling. For example, propelling a canoe with a single paddle using side slipping a canoe with a "scull" involves a similar technique. In China, sculling, called "lu", was also used by the 3rd AD. The innovation introduced with the propeller was the extension of that arc through more than 360 ° by attaching the blade to a rotating shaft. In practice there are nearly always more than one so as to balance the forces involved. It was probably an application of movement in space to a hollow segmented water-wheel used for irrigation by Egyptians for centuries. Leonardo da Vinci adopted the principle to drive sketches of which involved a large canvas screw overhead. In 1784, J. P. Paucton proposed a gyrocopter-like aircraft using similar screws for both propulsion. At about the same time, James Watt proposed using screws to propel boats, although he did not use them for his steam engines. By 1827, Czech-Austrian inventor Josef Ressel had invented a propeller which had multiple blades fastened around a conical base. He had tested his propeller on a small ship, manually driven.
Propeller
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Propeller on a modern mid-sized merchant vessel. The propeller rotates clockwise to propel the ship forward when viewed from astern (right of picture), the person in the picture has his hand on the propeller's trailing edge
Propeller
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Archimedes' screw.
Propeller
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Propellers of the RMS Olympic, a sister ship to the RMS Titanic.
Propeller
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Smith's original 1836 patent for a screw propeller of two full turns. He would later revise the patent, reducing the length to one turn.
85.
SS Archimedes
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SS Archimedes was a steamship built in Britain in 1839. She is notable for being the world's first steamship to be driven by a propeller. Archimedes had considerable influence on development, encouraging the adoption of screw propulsion by the Royal Navy, in addition to her influence on commercial vessels. In 1807, the world's first commercially successful Robert Fulton's North River Steamboat, made its debut. As this vessel was powered by paddlewheels rather than a propeller, the paddlewheel thereby became the facto early standard for steamship propulsion. In 1835, John Ericsson and Francis Pettit Smith, began working separately on the problem. Smith would subsequently file a revised patent in keeping with this accidental discovery. In the meantime, Ericsson was conducting his own experiments. In 1837, he built a 45-foot screw propelled steamboat, Francis B. Ogden, named after his patron, the American consul to Liverpool. In spite of the boat achieving a speed of comparable with that of existing paddle steamers, Symonds and his entourage were unimpressed. Apparently aware of the Navy's view that screw propellers would prove unsuitable for seagoing service, Smith determined to prove this assumption wrong. In September 1837, he took his small vessel to sea, steaming from Blackwall, London with stops at Ramsgate, Dover and Folkestone. On the way back to London on the 25th, Smith's craft was observed making headway in stormy seas by officers of the Royal Navy. Smith was encouraged to build a full size ship to more conclusively demonstrate the technology's effectiveness.
SS Archimedes
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SS Archimedes
SS Archimedes
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Smith's original 1836 patent for a screw propeller of two full turns. He would later revise the patent, reducing the length to one turn.
SS Archimedes
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Smith's revised 1836 patent. This is the propeller design originally fitted to Archimedes.
SS Archimedes
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Archimedes under steam at sea
86.
Claw of Archimedes
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The Claw of Archimedes was an ancient weapon devised by Archimedes to defend the seaward portion of Syracuse's city wall against amphibious assault. When the Roman fleet approached the city walls under cover of darkness, the machines were deployed, throwing the attack into confusion. Historians such as Livy attributed heavy Roman losses together with catapults also devised by Archimedes. The producers of Superweapons brought together a group of engineers tasked with implementing a design, realistic, given what is known about Archimedes. While this does not prove the existence of the Claw, it suggests that it would have been possible. C. K.
Claw of Archimedes
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A painting of the Claw of Archimedes by Giulio Parigi, taking the name "iron hand" literally
87.
Parabolic reflector
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A parabolic reflector is a reflective surface used to collect or project energy such as light, sound, or radio waves. Its shape is part of a circular paraboloid, the surface generated by a parabola revolving around its axis. The parabolic reflector transforms an incoming plane wave traveling along the axis into a spherical wave converging toward the focus. Strictly, the three-dimensional shape of the reflector is called a paraboloid. A parabola is the two-dimensional figure. However, in informal language, its associated parabolic are often used in place of paraboloidal. All units must be the same. If two of these three quantities are known, this equation can be used to calculate the third. A more complex calculation is needed to find the diameter of the dish measured along its surface. Providing D ≠ 0.. Similarly, energy radiating from the focus to the dish can be transmitted outward in a beam, parallel to the axis of the dish. However, if the incoming beam makes a non-zero angle with the axis, parabolic reflectors suffer from an aberration called coma. This is primarily of interest in telescopes because most other applications do not require sharp resolution off the axis of the parabola. The precision to which a parabolic dish must be made in order to focus energy well depends on the wavelength of the energy. To prevent this, the dish must be made correctly to within about 1/20 of a wavelength.
Parabolic reflector
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One of the world's largest solar parabolic dishes at the Ben-Gurion National Solar Energy Center in Israel
Parabolic reflector
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Circular paraboloid
Parabolic reflector
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Off-axis satellite dish
Parabolic reflector
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Lighting the Olympic Flame
88.
Giulio Parigi
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Giulio Parigi was an Italian architect and designer. He was the main member of a family of designers working for the Grand Ducal court of the Medici. Alfonso Parigi the Elder, was an architect and designer working in Florence for the Grand Duke of Tuscany. Through his father's collaborations under the architect Bernardo Buontalenti, Giulio Parigi was trained in the practice of architecture. His is also the grand stairs of Palazzo Gianni-Lucchesini-Vegni. Giulio's son, Alfonso's grandson, Alfonso Parigi the Younger was also an architect and engraver. Arthur Blumenthal,'Giulio Parigi's Stage Designs: Florence and the Early Baroque Spectacle', PhD, New York University, 1984. Arthur Blumenthal, Theatre Art of the Medici, Dartmouth:1980 Berto, Luciano. Giulio e Alfonso Parigi. Media related to Giulio Parigi at Wikimedia Commons
Giulio Parigi
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Painting by Giulio Parigi in Florence, Italy, showing Archimedes ' mirror used to burn Roman ships.
89.
Lucian
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Lucian of Samosata was a rhetorician and satirist who wrote in the Greek language during the Second Sophistic. Lucian is noted for his witty and nature. He wrote solely in Greek, mainly Attic Greek, Lucian also occasionally wrote in faux-Ionian dialect. Few details of Lucian's life can be verified with any degree of accuracy. However it is clear that by "Assyria" he means Syria and not Mesopotamia, as he refers as "Assyrian". Lucian's claim to be a native speaker of a "barbarian tongue" has been suggested to refer a dialect of Aramaic. It has been suggested that in referring as a "barbarian", "he was from the Semitic and not the imported Greek population" of Samosata. His name added lustre to any sarcastic essay: more than 150 surviving manuscripts attest to his continued popularity. The first printed edition of a selection of his works was issued in 1499. His best known works are Dialogues of the Gods and Dialogues of the Dead. He was trained as a rhetorician, a vocation whose practitioners pleaded in court, taught the art of pleading. In this way he won much wealth and fame. There are 80 surviving works attributed to Lucian. Lucian wrote in a variety of styles which included comic dialogues, prose fiction. He was also one of the earliest novelists in Western civilization.
Lucian
90.
Siege of Syracuse (212 BC)
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The Romans stormed the city after a protracted siege giving control of the entire island of Sicily. During the siege, the city was protected by weapons developed by Archimedes. Sicily, wrested during the First Punic War, was the first province of the Roman Republic not directly part of Italy. A Roman force led by the General Marcus Claudius Marcellus consequently laid siege by sea and land. The city of Syracuse, located on the eastern coast of Sicily was renowned for great walls that protected the city from attack. Among the Syracuse defenders was the scientist Archimedes. The city was fiercely defended against all the measures the Romans could bring to bear. Realizing how difficult the siege would be, the Romans brought their unique devices and inventions to aid their assault. These included a floating siege tower with grappling hooks, as well as ship-mounted scaling ladders that were lowered with pulleys onto the city walls. These measures, along with the fire from onagers mounted on the city walls, frustrated the Romans and forced them to attempt costly direct assaults. The successes of the Syracusians in repelling the Roman siege had made them overconfident. In 212 BC, the Romans received information that the city's inhabitants were to participate to their goddess Artemis. The Romans now were successful in cutting off supplies to this reduced area. During a diversionary attack, he opened the gate. After setting guards on the houses of the pro-Roman faction, Marcellus gave Syracuse to plunder.
Siege of Syracuse (212 BC)
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Hiero II of Syracuse calls Archimedes to fortify the city by Sebastiano Ricci (1720s).
Siege of Syracuse (212 BC)
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Siege of Syracuse
Siege of Syracuse (212 BC)
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Detail of a wall painting of the Claw of Archimedes sinking a ship (c. 1600).
Siege of Syracuse (212 BC)
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Archimedes Directing the Defenses of Syracuse by Thomas Ralph Spence (1895).
91.
Anthemius of Tralles
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Anthemius of Tralles was a Greek from Tralles who worked as a geometer and architect in Constantinople, the capital of the Byzantine Empire. With Isidore of Miletus, he designed the Hagia Sophia for Justinian I. Anthemius was one of the five sons of Stephanus of Tralles, a physician. His brothers were Metrodorus. In addition to his familiarity with steam, some dubious authorities credited Anthemius with a knowledge of other explosive compound. Anthemius was a capable mathematician. This work was later known to Arab mathematicians such as Alhazen. Eutocius's commentary on Apollonius's Conics was dedicated to Anthemius. As an architect, Anthemius is best known for his work designing the Hagia Sophia. He is also said to have repaired the flood defenses at Daras. Other Anthemiuses "Anthemius", Encyclopædia Britannica, 9th ed. Vol. II, New York: Charles Scribner's Sons, 1878, p. 103. "Anthemius", Encyclopædia Britannica, 11th ed. Vol. II, Cambridge: Cambridge University Press, 1911, p. 93. Boyer, Carl Benjamin, A History of Mathematics, John Wiley & Sons, ISBN 0-471-54397-7. Editions of Anthemius's "On Burning-Glasses": Dupuy, L. Περί παραδόξων μηχανημάτων. Histoire de l'Academie des Instrumentistes, XLII.
Anthemius of Tralles
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The Hagia Sophia in cross section.
92.
Burning-glass
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Burning mirrors achieve a similar effect by using reflecting surfaces to focus the light. They were used for burning materials in closed glass vessels where the products of combustion could be trapped for analysis. The glass was a useful contrivance in the days before electrical ignition was easily achieved. The technology of the glass has been known since antiquity. Vases filled with water used to start fires were known in the ancient world. Burning lenses were used to light sacred fires in temples. Plutarch refers to a burning mirror made of joined metal mirrors installed at the temple of the Vestal Virgins. Aristophanes mentions The Clouds. "Strepsiades. Have you ever seen a transparent stone at the druggists', with which you may kindle fire?" The sacred fire in the classic temples as the Olympic torch had to be pure and to come directly from the gods. For this they used the sun's rays focused with lenses and not impure triggers. The renowned mathematician, was said to have used a burning glass as a weapon in 212 BC, when Syracuse was besieged by Marcus Claudius Marcellus. The Roman fleet was supposedly incinerated, though Archimedes was slain. The legend of Archimedes gave rise until the late 17th century.
Burning-glass
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A replica (on a smaller scale) of the burning lens owned by Joseph Priestley, in his laboratory
Burning-glass
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Close-up view of a flat Fresnel lens. These thin, light weight, non fragile and low cost lens can be used as burning-glass in emergency situations.
93.
Heliostat
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The target may be a physical object, a direction in space. In almost every case, the target is stationary relative to the heliostat, so the light is reflected in a fixed direction. According to contemporary sources the heliostata, as it was called at first, was invented by Willem's Gravesande. Other contenders are Daniel Gabriel Fahrenheit. Nowadays, most heliostats are used for the production of concentrated solar power, usually to generate electricity. They are also sometimes used in solar cooking. To reflect motionless beams of sunlight into solar telescopes. Before the availability of other electric lights, heliostats were widely used to produce intense, stationary beams of light for scientific and other purposes. Most modern heliostats are controlled by computers. The computer is given the longitude of the heliostat's position on the earth and the time and date. From these, using astronomical theory, it calculates the direction of the sun as e.g. its compass bearing and angle of elevation. This sequence of operations is repeated frequently to keep the mirror properly oriented. Large installations such as solar-thermal power stations include fields of heliostats comprising many mirrors. Usually, all the mirrors in such a field are controlled by a single computer. These are now quite rare.
Heliostat
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Heliostat by the Viennese instrument maker Ekling (ca. 1850)
Heliostat
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A heliostat at the THÉMIS experimental station in France. The mirror rotates on an altazimuth mount.
Heliostat
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The Solar Two solar-thermal power project near Daggett, California. Every mirror in the field of heliostats reflects sunlight continuously onto the receiver on the tower.
Heliostat
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The 11MW PS10 near Seville in Spain. When this picture was taken, dust in the air made the converging light visible.
94.
Solar furnace
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A solar furnace is a structure that uses concentrated solar power to produce high temperatures, usually for industry. Parabolic heliostats concentrate light onto a focal point. This heat can be used to generate electricity, melt steel, make hydrogen fuel or nanomaterials. The largest solar furnace is at Odeillo in the Pyrénées-Orientales in France, opened in 1970. It employs an array of plane mirrors to gather sunlight, reflecting it onto a larger curved mirror. An experiment to test this theory was carried out in 2005. The first solar furnace is believed to have been built in France in 1949 by Professor Félix Trombe. It is still in place at Mont Louis, near Odeillo. The Pyrenees were chosen as the site because the area experiences up to 300 days a year. Another solar furnace was built as a part of a Soviet Union "Sun" Complex Research Facility impulsed by Academician S.A. Asimov. The solar principle is being used to make inexpensive solar cookers and solar-powered barbecues, for solar water pasteurization. A prototype reflector is being constructed in India for use in a solar crematorium. This 50 m reflector will generate temperatures of 700 ° C and displace 200 -- 300 kg of firewood used per cremation.
Solar furnace
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The solar furnace at Odeillo in the Pyrénées-Orientales in France can reach temperatures up to 3,500 °C (6,330 °F)
95.
Bronze
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These additions produce a range of alloys that may have other useful properties, such as stiffness, ductility or machinability. The archeological period where bronze was the hardest metal in widespread use is known as the Age. The discovery of bronze enabled people to create metal objects which were harder and than previously possible. Bronze tools, weapons, building materials such as decorative tiles were harder and more durable than their stone and copper predecessors. It was later that tin was used, becoming the major non-copper ingredient of bronze in the late 3rd millennium BC. Also, unlike arsenic, metallic tin and fumes from refining are not toxic. The earliest bronze dates to 4500 BCE in a Vinča culture site in Pločnik. Early examples date to the late 4th millennium BC in Africa, Susa and some ancient sites in China, Luristan and Mesopotamia. The far rarer tin are not often found together, so serious bronze work has always involved trade. Tin sources and trade in ancient times had a major influence on the development of cultures. In Europe, a major source of tin was the British deposits of ore in Cornwall, which were traded far as Phoenicia in the Eastern Mediterranean. In Europe, typically socketed axes, are found, which mostly show no signs of wear. With Chinese ritual bronzes, which are documented from other sources, the case is very clear. These were made in enormous quantities for elite burials, also used by the living for ritual offerings. Careful control of the tempering eventually allowed for wrought iron with properties comparable to modern steel.
Bronze
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Yoruba bronze head sculpture, Ife, Nigeria c. 12th century AD
Bronze
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Bronze deer figurine dating from between the 9th and 6th centuries BC, National Archaeological Museum of Sofia
Bronze
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A hoard of bronze socketed axes from the Bronze Age found in modern Germany. This was the top tool of the period, and also seems to have been used as a store of value.
Bronze
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Chinese Ding, Western Zhou (1046–771 BC)
96.
Copper
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Copper is a chemical element with symbol Cu and atomic number 29. It is a soft, ductile metal with very high thermal and electrical conductivity. A freshly exposed surface of pure copper has a reddish-orange color. This was the first source of the metal to be used by humans, c. 8000 BC. Architectural structures built with copper corrode to give green verdigris. Decorative art prominently features copper, both in compounds as pigments. Copper compounds are also used as bacteriostatic agents, wood preservatives. Copper is essential to all living organisms as a trace mineral because it is a key constituent of the respiratory enzyme complex cytochrome c oxidase. In crustaceans copper is a constituent of the blood pigment hemocyanin, replaced by the iron-complexed hemoglobin in fish and other vertebrates. In humans, copper is found mainly in the liver, bone. The adult body contains between 2.1 mg of copper per kilogram of body weight. Hence a healthy human weighing 60 kilogram contains approximately 0.1 g of copper. However, this small amount is essential to the human well-being. The filled d-shells in these elements contribute little to interatomic interactions, which are dominated through metallic bonds. Unlike metals with incomplete d-shells, metallic bonds in copper are relatively weak.
Copper
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Native copper (~4 cm in size)
Copper
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A copper disc (99.95% pure) made by continuous casting; etched to reveal crystallites.
Copper
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Copper just above its melting point keeps its pink luster color when enough light outshines the orange incandescence color.
Copper
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Unoxidized copper wire (left) and oxidized copper wire (right).
97.
Skaramagas
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Skaramagkas is a port town in the western part of the Athens agglomeration, Greece. It is part of the municipality of Chaidari. It is known for its large shipyard. Skaramagkas is situated on the east coast of the Bay of a bay of the Saronic Gulf. The Aigaleo mountain to the east separates it from Athens and Piraeus. Greek National Road 8 passes through Skaramagkas. Since 1937 Skaramagkas harbour has been home to a shipyard of the Hellenic Navy. After destruction in World War II, it was refounded as a commercial shipyard in the Hellenic Shipyards Co.. This event often doubted by modern historians. Between May 1979, the battleship Tombazis underwent structural modifications at the shipyard. Official website of Municipality of Chaidari Hellenic Shipyards Co.
Skaramagas
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Skaramagkas from Salamina
98.
Athens
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Athens is the capital and largest city of Greece. In modern times, Athens is a large cosmopolitan metropolis and central to economic, financial, industrial, maritime, cultural life in Greece. In 2015, Athens was ranked the world's 29th richest city by the 67th most expensive in a UBS study. The municipality of Athens had a land area of 38.96 km2. The urban area of Athens extends with a population of 3,090,508 over an area of 412 km2. Athens is also the southernmost capital on the European mainland. The city also retains Byzantine monuments, as well as a smaller number of Ottoman monuments. Athens is home to two UNESCO World Heritage Sites, the medieval Daphni Monastery. 108 years later it welcomed home the 2004 Summer Olympics. In Ancient Greek, the name of the city was Ἀθῆναι a plural. In earlier Greek, such as Homeric Greek, the name had been current in the form though, as Ἀθήνη. It was possibly rendered in the plural on, like those of Θῆβαι and Μυκῆναι. During the medieval period the name of the city was rendered again in the singular as Ἀθήνα. In an attempt to compel the people, Poseidon created spring by striking the ground with his trident, symbolizing naval power. Different etymologies, commonly rejected, were proposed during the 19th century.
Athens
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From upper left: the Acropolis, the Hellenic Parliament, the Zappeion, the Acropolis Museum, Monastiraki Square, Athens view towards the sea
Athens
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Athena, patron goddess of Athens; National Archaeological Museum
Athens
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Acropolis of Athens, with Odeon of Herodes Atticus seen on bottom left
99.
Bitumen
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Asphalt, also known as bitumen is a sticky, black and highly viscous liquid or semi-solid form of petroleum. It may be a refined product; it is a substance classed as a pitch. Until the 20th century, the asphaltum was also used. The word is derived from the Ancient ἄσφαλτος ásphaltos. The primary use of asphalt/bitumen is in construction, where it is used as the glue or binder mixed with aggregate particles to create asphalt concrete. Its main uses are for bituminous waterproofing products, including production of roofing felt and for sealing flat roofs. The terms bitumen are often used interchangeably to mean both natural and manufactured forms of the substance. In American English, asphalt is the carefully refined residue from the process of selected crude oils. Outside the United States, the product is often called bitumen. Geologists often prefer the bitumen. Common usage often refers to various forms of asphalt/bitumen such as at the La Brea Tar Pits. Another archaic term for asphalt/bitumen is "pitch". Naturally occurring asphalt/bitumen is sometimes specified by the term "crude bitumen". The Canadian province of Alberta has most of the world's reserves of natural bitumen, covering an area larger than England. Additionally, most natural bitumens contain organosulfur compounds, resulting in an overall content of up to 4 %.
Bitumen
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Natural asphalt/bitumen from the Dead Sea
Bitumen
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refined asphalt/bitumen
Bitumen
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The University of Queensland pitch drop experiment, demonstrating the viscosity of asphalt/bitumen
Bitumen
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Bituminous outcrop of the Puy de la Poix, Clermont-Ferrand, France
100.
Massachusetts Institute of Technology
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The Massachusetts Institute of Technology is a private research university in Cambridge, Massachusetts. Researchers worked on computers, radar, inertial guidance during World War II and the Cold War. Post-war defense research contributed to the rapid expansion of the faculty and campus under James Killian. The current 168-acre campus opened in 1916 and extends over 1 mile along the northern bank of the Charles River basin. It is often cited as among the world's top universities. The school has a strong entrepreneurial culture, the aggregated revenues of companies founded by MIT alumni would rank as the eleventh-largest economy in the world. A professor from the University of Virginia, wanted to establish an institution to address technological advances. The Rogers Plan reflected the German model, emphasizing an independent faculty engaged in research, well as instruction oriented around seminars and laboratories. Two days after the charter was issued, the first battle of the Civil War broke out. After a long delay through the war years, MIT's first classes were held in the Mercantile Building in Boston in 1865. In 1863 under the same act, the Commonwealth of Massachusetts founded the Massachusetts Agricultural College, which developed as the University of Massachusetts Amherst. In 1866, the proceeds from land sales went toward new buildings in the Back Bay. MIT was informally called "Boston Tech". The institute adopted the European polytechnic university model and emphasized laboratory instruction from an early date. Despite chronic financial problems, the institute saw growth in the last two decades of the 19th century under President Francis Amasa Walker.
Massachusetts Institute of Technology
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Stereographic card showing an MIT mechanical drafting studio, 19th century (photo by E.L. Allen, left/right inverted)
Massachusetts Institute of Technology
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Massachusetts Institute of Technology
Massachusetts Institute of Technology
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A 1905 map of MIT's Boston campus
Massachusetts Institute of Technology
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Plaque in Building 6 honoring George Eastman, founder of Eastman Kodak, who was revealed as the anonymous "Mr. Smith" who helped maintain MIT's independence
101.
MythBusters
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MythBusters is a science entertainment television program created by Peter Rees and produced by Australia's Beyond Television Productions. The series premiered on the Discovery Channel on January 23, 2003. The series was transmitted by numerous international broadcasters, including SBS Australia, other Discovery channels worldwide. The show was one of the oldest—and the most popular—on Discovery Channel, being preceded only by How It's Made and Daily Planet, both in Canada. From 2006 to 2016, the show was overseen by British show-runner Dan Tapster, working out of Sydney, San Francisco and Manchester. During the second season, members of Savage and Hyneman's behind-the-scenes team were organized into a second team of MythBusters. They generally tested myths separately from the main duo and operated from another workshop. On October 21, 2015, it was announced that MythBusters would air its 14th and final season in 2016. The show aired its final episode on March 6, 2016. Adam Savage has confirmed that he and his former cohosts have no intentions of reuniting for future team projects. MythBusters refers both to the name of the documentary and also the cast members who test the experiments. The series concept was created for the Discovery Channel as Tall Tales or True by Australian writer and producer Peter Rees of Beyond Productions in 2002. Discovery rejected the proposal initially because they had just commissioned a series on the same topic. Rees refined the pitch to focus on testing key elements of the stories rather than just retelling them. Discovery agreed to develop and co-produce a three-episode series pilot.
MythBusters
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MythBusters
MythBusters
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Adam (left) and Jamie as keynote speakers at Symantec Vision 08.
MythBusters
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Adam Savage and Jamie Hyneman at the Discovery Channel Young Scientist Challenge pose with Skulls Unlimited International 's Jay Villemarette and Joey Williams 2004.
MythBusters
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MythBusters at the White House.
102.
San Francisco
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San Francisco is about 47.9 square miles in area. It is located on the north end of the San Francisco Peninsula. It is the smallest county in the state. The California Gold Rush of 1849 brought rapid growth, making it the largest city on the West Coast at the time. San Francisco became a consolidated city-county in 1856. After three-quarters of the city was destroyed by the 1906 earthquake and fire, San Francisco was quickly rebuilt, hosting the Panama-Pacific International Exposition nine years later. In World War II, San Francisco was the port of embarkation for service members shipping out to the Pacific Theater. Politically, the city votes strongly along liberal Democratic Party lines. As of 2016, San Francisco is ranked high on world liveability rankings. The earliest archaeological evidence of human habitation of the territory of the city of San Francisco dates to 3000 BC. Upon independence from Spain in 1821, the area became part of Mexico. Under Mexican rule, the mission system gradually ended, its lands became privatized. In 1835, Englishman William Richardson erected the independent homestead, near a anchorage around what is Portsmouth Square. Commodore John D. Sloat claimed California for the United States on July 7, 1846, during the Mexican–American War, Captain John B. Montgomery arrived to claim Yerba Buena two days later.
San Francisco
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San Francisco and the Golden Gate Bridge from Marin Headlands
San Francisco
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Mission San Francisco de Asís (Mission Dolores)
San Francisco
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1853 United States Coast Survey Map
San Francisco
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Francis Samuel Marryat, Hilltop of San Francisco, California, Looking toward the Bay, 1849. M.& N. Hanhart Chromolithograph
103.
Glare (vision)
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Glare is difficulty seeing in the presence of bright light such as direct or reflected sunlight or artificial light such as car headlamps at night. Because of this, some cars include mirrors with anti-glare functions. Glare is caused by a significant ratio of luminance between the glare source. Factors such as the angle between the glare source and eye adaptation have significant impacts on the experience of glare. Glare can be generally divided into two types, disability glare. Discomfort glare results in an instinctive desire to look away from a bright light source or difficulty in seeing a task. Disability glare impairs the vision of objects without necessarily causing discomfort. This could arise for instance when driving westward at sunset. When glare is so intense that vision is completely impaired, it is sometimes called dazzle. Reduction in contrast between print and paper by reflection of the light source in the printed matter. Some types of eyeglasses can reduce glare that occurs because of the imperfections on the surface of the eye. Light field measurements can be taken to reduce glare with digital post-processing. Glare is typically measured with luminance meters or luminance cameras, both of which are able to determine the luminance of objects within solid angles. The glare of a scene visual field of view, is then calculated from the luminance data of that scene. The CIE recommends the Unified rating as a quantitative measure of glare.
Glare (vision)
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Glare from a camera flash during a Sumo fight
Glare (vision)
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Example of a situation where glare can be problematic, if, for instance, the ability to determine the distance and speed of passing cars is reduced.
104.
Peripatetic school
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The Peripatetic school was a school of philosophy in Ancient Greece. Its teachings derived from its founder, Aristotle, peripatetic is an adjective ascribed to his followers. The school dates from around 335 BCE when Aristotle began teaching in the Lyceum. It was an informal institution whose members conducted philosophical and scientific inquiries. Aristotle's successors Theophrastus and Strato continued the tradition of exploring philosophical and scientific theories. Although the school died out, the study of Aristotle's works continued by scholars who were called Peripatetics through Late Antiquity, the Middle Ages, the Renaissance. The term "Peripatetic" is a transliteration of the ancient Greek word περιπατητικός peripatêtikos, which means "of walking" or "given to walking about". The Peripatetic school was actually known simply as the Peripatos. Aristotle's school came to be so named because of the peripatoi of the Lyceum where the members met. The legend that the name came from Aristotle's alleged habit of walking while lecturing may have started with Hermippus of Smyrna. Because of the school's association with the gymnasium, the school also came to be referred to simply as the Lyceum. Aristotle did teach and lecture there, but there was also philosophical and scientific research done in partnership with other members of the school. It seems likely that many of the writings that have come down to us in Aristotle's name were based on lectures he gave at the school. Among the members of the school in Aristotle's time were Theophrastus, Phanias of Eresus, Eudemus of Rhodes, Clytus of Miletus, Aristoxenus, Dicaearchus. Sometime shortly after Alexander's death in June 323 BCE, Aristotle left Athens to avoid persecution by anti-Macedonian factions in Athens due to his ties to Macedonia.
Peripatetic school
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Aristotle's School, a painting from the 1880s by Gustav Adolph Spangenberg
Peripatetic school
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Aristotelianism
Peripatetic school
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Aristotle and his disciples – Alexander, Demetrius, Theophrastus, and Strato; part of a fresco in the portico of the National University of Athens.
105.
Aristotle
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Aristotle was a Greek philosopher and scientist born in the city of Stagira, Chalkidice, on the northern periphery of Classical Greece. His father, Nicomachus, died when Aristotle was a child, whereafter Proxenus of Atarneus became his guardian. At eighteen years of age, he remained there until the age of thirty-seven. Shortly after Plato died, Aristotle left Athens and, at the request of Philip of Macedon, tutored Alexander the Great beginning in 343 BC. Teaching Alexander the Great gave an abundance of supplies. He established a library in the Lyceum which aided in the production of many of his hundreds of books. He believed all peoples' concepts and all of their knowledge was ultimately based on perception. Aristotle's views on natural sciences represent the groundwork underlying many of his works. Aristotle's views on physical science profoundly shaped medieval scholarship. Some such as on the hectocotyl arm of the octopus, were not refuted until the 19th century. His works contain the earliest formal study of logic, incorporated into modern formal logic. Aristotle was well known among medieval Muslim intellectuals and revered as "The First Teacher". His ethics, though always influential, gained renewed interest with the modern advent of virtue ethics. All aspects of Aristotle's philosophy continue to be the object of active academic study today. Aristotle, whose name means "the best purpose", was born in 384 BC in Stagira, Chalcidice, about 55 km east of modern-day Thessaloniki.
Aristotle
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Roman copy in marble of a Greek bronze bust of Aristotle by Lysippus, c. 330 BC. The alabaster mantle is modern.
Aristotle
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Aristotelianism
Aristotle
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School of Aristotle in Mieza, Macedonia, Greece
Aristotle
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"Aristotle" by Francesco Hayez (1791–1882)
106.
Archytas
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Archytas was an Ancient Greek philosopher, mathematician, astronomer, statesman, strategist. Famous for being the reputed founder of mathematical mechanics, as well as a good friend of Plato. Archytas was the son of Mnesagoras or Histiaeus. For a while, he was a teacher of mathematics to Eudoxus of Cnidus. Eudoxus' student was Menaechmus. As a Pythagorean, Archytas believed that not geometry, could provide a basis for satisfactory proofs. Archytas is believed to be the founder of mathematical mechanics. This machine, which its inventor called The pigeon, may have been pivot for its flight. Archytas also wrote some lost works, as he was included in the list of the twelve authors of works of mechanics. Thomas Winter has suggested that the pseudo-Aristotelian Mechanical Problems misattributed. Archytas named the harmonic mean, important later in projective geometry and number theory, though he did not invent it. According to Eutocius, Archytas solved the problem of doubling the cube in his manner with a geometric construction. Hippocrates of Chios before, reduced this problem to finding mean proportionals. The Archytas curve, which he used in his solution of the cube problem, is named after him. Militarily, Archytas appears to have been the dominant figure in Tarentum in his generation, somewhat comparable to Pericles in Athens a half-century earlier.
Archytas
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Bust from the Villa of the Papyri in Herculaneum, once identified as Archytas, now thought to be Pythagoras
107.
Pappus of Alexandria
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Nothing is known of his life, except that he had a son named Hermodorus, was a teacher in Alexandria. Collection, his best-known work, is a compendium of mathematics in eight volumes, the bulk of which survives. It covers a wide range of topics, including recreational mathematics, doubling the polyhedra. Pappus flourished in the 4th century AD. In a period of general stagnation in mathematical studies, he stands out as a remarkable exception. "In this respect the fate of Pappus strikingly resembles that of Diophantus." The Suda states that Pappus was of the same age as Theon of Alexandria, who flourished in the reign of Emperor Theodosius I. This works out as October 18, 320 AD, so Pappus must have flourished c. 320 AD. The Suda enumerates other works of Pappus: Χωρογραφια οἰκουμενική, commentary on the 4 books of Ptolemy's Almagest, Ποταμοὺς τοὺς ἐν Λιβύῃ, Ὀνειροκριτικά. Pappus himself mentions another commentary of his own on the Ἀνάλημμα of Diodorus of Alexandria. Pappus also wrote commentaries on Euclid's Elements, on Ptolemy's Ἁρμονικά. These discoveries form, in fact, a text upon which Pappus enlarges discursively. The portions of Collection which has survived can be summarized as follows. We can only conjecture that the lost Book I, like Book II, was concerned with arithmetic, Book III being clearly introduced as beginning a new subject. The whole of Book II discusses a method of multiplication from an unnamed book by Apollonius of Perga.
Pappus of Alexandria
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Title page of Pappus's Mathematicae Collectiones, translated into Latin by Federico Commandino (1589).
Pappus of Alexandria
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Mathematicae collectiones, 1660
108.
Pulley
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Pulleys are used in a variety of ways to transmit power. In nautical contexts, the assembly of wheel, supporting shell is referred to as a "block." A pulley may have a groove or grooves between two flanges around its circumference. The element of a pulley system can be a rope, cable, belt, or chain that runs over the pulley inside the groove or grooves. Hero of Alexandria identified the pulley as one of six simple machines used to lift weights. Pulleys are assembled to tackle in order to provide mechanical advantage to apply large forces. Pulleys are also assembled as part of chain drives in order to transmit power from one rotating shaft to another. A set of pulleys assembled so that they rotate independently on the same axle from a block. Two blocks with a rope threaded through the two sets of pulleys form a block and tackle. A tackle is assembled so one block is attached to fixed mounting point and the other is attached to the moving load. The mechanical advantage of the block and tackle is equal to the number of parts of the rope that support the moving block. This system is included in the list of simple machines identified by Renaissance scientists. This can be shown as follows. Consider the set of pulleys that form the parts of the rope that support this block. This means the force on the rope is T = W/p.
Pulley
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Pulleys on a ship. In this context, pulleys are usually known as blocks.
Pulley
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Pulley in oil derrick
Pulley
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A hoist using the compound pulley system yielding an advantage of 4. The single fixed pulley is installed on the hoist (device). The two movable pulleys (joined together) are attached to the hook. One end of the rope is attached to the crane frame, another to the winch.
Pulley
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A double tackle has two pulleys in both the fixed and moving blocks with four rope parts supporting the load W.
109.
Catapult
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Although the catapult has been used since ancient times, it has proven to be one of the most effective mechanisms during warfare. In modern times the term can apply to devices ranging to a mechanism for launching aircraft from a ship. The word ` catapult' comes from the Latin ` catapulta', which in turn comes from the Greek Greek: καταπέλτης, itself from, "downwards" + πάλλω, "to toss, to hurl". Catapults were invented by the ancient Greeks. The crossbow in Greece are closely intertwined. Primitive catapults were essentially "the product of relatively straightforward attempts to increase the penetrating power of missiles by strengthening the bow which propelled them". The historian Diodorus Siculus, described the invention of a mechanical arrow-firing catapult by a Greek force in 399 BC. The weapon was soon after employed against a key Carthaginian stronghold in Sicily. Diodorus is assumed to have drawn his description from the highly rated history of a contemporary of the events then. The "belly-bow", along with a watercolor drawing, is found in Heron's technical treatise Belopoeica. Zopyrus has been plausibly equated with a Pythagorean of that name who seems to have flourished in the 5th century BC. He probably designed his bow-machines between 421 BC and 401 BC. The bows of these machines already featured a winched could apparently throw two missiles at once. Philo of Byzantium provides probably the most detailed account on the establishment of a theory of belopoietics circa 200 BC. This kind of innovation is indicative of the increasing rate at which physics were being assimilated into military enterprises.
Catapult
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Ancient mechanical artillery: Catapults (standing), the chain drive of Polybolos (bottom center), Gastraphetes (on wall)
Catapult
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Engraving illustrating a Roman catapult design, 1581
Catapult
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Roman 'catapult-nest' in the Trajan's Dacian Wars
Catapult
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Replica of a Petraria Arcatinus
110.
Odometer
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An odometer or odograph is an instrument that indicates distance travelled by a vehicle, such as a bicycle or automobile. The device may be electronic, a combination of the two. The noun derives from métron. Possibly the first evidence for the use of an odometer can be found in the works of the ancient Greek Strabo. Both authors list the distances of routes traveled by Alexander the Great as by his bematists Diognetus and Baeton. However, the high accuracy of the bematists's measurements rather indicates the use of a mechanical device. Hero of Alexandria describes a similar device in chapter 34 of his Dioptra. Some researchers have speculated that the device might have included technology similar to that of the Greek Antikythera mechanism. The odometer of Vitruvius was based on chariot wheels of 4 feet diameter turning 400 times in one Roman mile. For each revolution a pin on the axle engaged a 400 cogwheel thus turning it one complete revolution per mile. This engaged another gear with holes along the circumference, where pebbles were located, that were to drop one into a box. The distance traveled would thus be given simply by counting the number of pebbles. Whether this instrument was ever built at the time is disputed. Leonardo da Vinci later failed. With this modification, the Vitruvius odometer functioned perfectly.
Odometer
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An electronic odometer (below) with digital display
Odometer
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A Smiths speedometer from the 1920s showing odometer and trip meter.
Odometer
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A Hubodometer on a wheel of a semitrailer
Odometer
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A Han Dynasty stone rubbing of a horse-drawn odometer cart.
111.
First Punic War
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The First Punic War was the first of three wars fought between Ancient Carthage and the Roman Republic. The war signaled the beginning of a strategic transformation in the western Mediterranean. Carthage began the war as the great sea-power of the western Mediterranean, while Rome had but a small fleet of fighting ships. The series of wars between Rome and Carthage took the name "Punic" for the Carthaginians, Punici. It refers to the Carthaginian heritage as Phoenician colonists. A Carthaginian name for the conflicts does not survive in any records. Rome had recently emerged as the leading city-state in a wealthy, powerful, expansionist republic with a successful citizen army. Over the past hundred years, Rome had come into conflict, defeated rivals on the Italian peninsula, then incorporated them into the Roman political world. By the beginning of the First Punic War, the Romans had secured the whole of the Italian peninsula, except Gallia Cisalpina in the Po Valley. It originated as a Phoenician colony near modern Tunis. Just before the First Punic War, Carthage was hostile to foreign ships in the western Mediterranean. African peoples such as the Berbers in the area around Carthage were loosely associated with Carthage. In the midst of the First Punic War some tribes would rebel against Carthage, opening a second front while the Carthaginians battled the Romans in Sicily. The rich, well-fortified Greek colony of Syracuse was politically independent of Rome and Carthage. Hostilities of the First Punic War began with developments involving the Romans, Greek colonists in Sicily and southern Italy.
First Punic War
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Roman arrival and neutralization of Syracuse.
First Punic War
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Western Mediterranean Sea in 264 BC. Rome is shown in red, Carthage in purple, and Syracuse in green.
First Punic War
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Hamilcar's attack.
First Punic War
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Continued Roman advance 260–256 BC.
112.
Dialogue
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Dialogue is a written or spoken conversational exchange between two or more people, a literary and theatrical form that depicts such an exchange. In the 20th century, philosophical treatments of dialogue emerged from thinkers including Mikhail Bakhtin, David Bohm. Although diverging in many details, these thinkers have articulated a holistic concept of dialogue as a context-dependent process of creating meaning. Educators such as Ramón Flecha have also developed a body of technique for using egalitarian dialogue as a pedagogical tool. The dialogue stems from the Greek διάλογος; its roots are λόγος. The first extant author who uses the term is Plato, in whose works it is closely associated with the art of dialectic. Latin took over the word as dialogus. In the West, Plato has commonly been credited as an literary form. These works, admired and imitated by Plato, have not survived and we have only the vaguest idea of how they may have been performed. The Mimes of Herodas, which were found in a papyrus in 1891, give some idea of their character. Plato further reduced it to pure conversation, while leaving intact the amusing element of character-drawing. By about 400 BC he had perfected the Socratic dialogue. All his extant writings, except the Apology and Epistles, use this form. Following Plato, important works both in Latin and in Greek were written. Soon after Plato, Xenophon wrote his own Symposium; also, Aristotle is said to have written several philosophical dialogues in Plato's style.
Dialogue
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Oldest extant text of Plato's Republic
Dialogue
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Frontispiece and title page of Galileo 's Dialogue Concerning the Two Chief World Systems, 1632
Dialogue
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David Bohm, a leading 20th-century thinker on dialogue.
Dialogue
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A classroom dialogue at Shimer College.
113.
De re publica
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De re publica is a dialogue on Roman politics by Cicero, written in six books between 54 and 51 BC. Cicero's treatise was politically controversial: by choosing the format of a philosophical dialogue he avoided naming his political adversaries directly. The dialogue is portrayed as taking place during three consecutive days. Each day is described with an introduction by Cicero preceding the dialogue of each book. A large part of the last book is taken by Scipio telling a dream he had: this passage is known as "Scipio's dream". In alphabetical order: Fannius, Gaius: Consul in 122 BC. Follower of Stoicism, historian and orator. Son-in-law to Laelius. Laelius, Gaius: Close friend and associate of Scipio, Consul in 140 BC, promoter of the study of literature and Philosophy. Manilius, Manius: Consul in 149 BC. Historian and legal scholar. Mucius Scaevola, Quintus: Legal scholar and patron of the young Cicero. Son-in-law to Laelius. Mummius, Spurius: Satirist and extreme defender of optimate interests. Brother of Lucius Mummius.
De re publica
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Treatises
114.
Thales
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Aristotle reported Thales's hypothesis that the nature of matter was a single material substance: water. In mathematics, Thales used geometry to calculate the distance of ships from the shore. He is the known individual to use deductive reasoning applied to geometry, by deriving four corollaries to Thales' theorem. He is the known individual to whom a mathematical discovery has been attributed. Apollodorus of Athens, writing during the 2nd century BCE, thought Thales was born about the year 625 BCE. The dates of Thales' life are roughly established by a few datable events mentioned in the sources. According to Herodotus, Thales predicted the solar eclipse of 585 BC. Several years later, anxious for family, he adopted his nephew Cybisthus. Thales involved himself in many activities, taking the role of an innovator. Some say that he left no writings, others say that he wrote On the Equinox. Thales identifies the Milesians as Athenian colonists. Thales' principal occupation was engineering. He was the first to be connected to knowledge of this in history. According to Aristotle, Thales thought lodestones had souls, because of the fact of iron being attracted to them. Also involved in business.
Thales
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Thales of Miletus
Thales
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An olive mill and an olive press dating from Roman times in Capernaum, Israel.
Thales
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Total eclipse of the Sun
Thales
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The Ionic Stoa on the Sacred Way in Miletus
115.
Planetarium
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A planetarium is a theatre built primarily for presenting educational and entertaining shows about astronomy and the night sky, or for training in celestial navigation. Whatever technologies are used, the objective is normally to link them together to provide an relative motion of the sky. Planetaria range in size to three-meter inflatable portable domes where children sit on the floor. Portable planetaria serve education programs outside of the permanent installations of museums and science centers. The planetarium is sometimes used generically to describe other devices which illustrate the solar system, such as a computer simulation or an orrery. Planetarium software refers to a application that renders a three-dimensional image of the sky onto a two-dimensional computer screen. The planetarian is used to describe a member of the professional staff of a planetarium. The discovery of the Antikythera mechanism proved that such devices already existed during antiquity, though likely after Archimedes' lifetime. Campanus of Novara included instructions on how to build one. The Globe of Gottorf built around 1650 had constellations painted on the inside. These devices would usually be referred to as orreries. The efforts of his sons are noteworthy in their attempts to fuse theatrical illusions with educational aspirations. Walker's Eidouranion was the heart of theatrical presentations. Every Planet and Satellite seems suspended without any support; performing their annual and diurnal revolutions without any apparent cause". These devices most probably sacrificed astronomical accuracy for sensational and awe-provoking imagery.
Planetarium
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Inside a planetarium projection hall. (Belgrade Planetarium, Serbia)
Planetarium
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Inside the same hall during projection. (Belgrade Planetarium, Serbia)
Planetarium
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A planetarium under construction in Nishapur, near the Mausoleum of Omar Khayyam.
Planetarium
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The Eise Eisinga Planetarium
116.
Orrery
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It has been dated between 100 BC. It was geocentric and used as a mechanical calculator designed to calculate astronomical positions. According to the Roman philosopher, writing in the first century BC, Posidonius constructed a planetary model. Dondi left a complete description of the astronomic gear trains of his clock. The clocks are now at the Astronomisch-Physikalisches Kabinett and in Dresden at the Mathematisch-Physikalischer Salon. He observed that some Greek philosophers had proposed a heliocentric universe. This simplified the epicyclic motions of the planets, making it feasible to represent the planets' paths as simple circles. This could be modelled by the use of gears. Tycho Brahe's improved instruments made precise observations from these Johannes Kepler deduced that planets orbited the Sun in ellipses. In 1687 Isaac Newton explained the cause of elliptic motion in his theory of gravitation. Orreries take three forms: Solid Models typically the size of a table. Real World Orreries typically the length of a walk. Virtual World Orreries where the human imagination is unlimited. Clock makers George Graham and Thomas Tompion built the first modern orrery in England. Graham gave its design, to the celebrated instrument maker John Rowley of London to make a copy for Prince Eugene of Savoy.
Orrery
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A small orrery showing earth and the inner planets
Orrery
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Antikythera mechanism (main fragment), ca. 125 BC
Orrery
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A Philosopher Lecturing on the Orrery (ca. 1766) by Joseph Wright of Derby
Orrery
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A 1766 Benjamin Martin Orrery, used at Harvard
117.
Antikythera mechanism
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Its remains were found as one lump, later separated in three main fragments, which are now divided after conservation works. Four of these fragments contain gears, while inscriptions are found on many others. The largest gear is approximately 140 millimetres in diameter and originally had 223 teeth. The artefact was recovered probably in July 1901 off the Greek island of Antikythera. All known fragments of the Antikythera mechanism are kept in Athens. The Antikythera mechanism was discovered off Point Glyphadia on the Greek island of Antikythera. All were transferred in Athens for storage and analysis. Investigations into the object were soon dropped until Yale University professor, Derek J. de Solla Price became interested in it in 1951. In 1971, a Greek nuclear physicist named Charalampos Karakalos made X-ray and gamma-ray images of the 82 fragments. Price published an extensive 70-page paper in 1974. Its construction relied upon theories of mathematics developed by Greek astronomers, is estimated to have been created around the late second century BC. Associates visited the wreck in 1976 and recovered coins dated to between 76 and 67 BC. The consensus among scholars is that the mechanism was made in the Greek-speaking world. Syracuse was the home of Archimedes, which might imply a connection with the school of Archimedes. With its many scrolls of science, it was second in importance only to the Library of Alexandria during the Hellenistic period.
Antikythera mechanism
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The Antikythera mechanism (Fragment A – front)
Antikythera mechanism
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Computer-generated front panel of the Freeth model
Antikythera mechanism
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Front panel of a 2007 reproduction
Antikythera mechanism
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Computer-generated back panel
118.
Differential (mechanical device)
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In wheeled vehicles, the differential allows the outer wheel to rotate faster than the inner drive wheel during a turn. The average of the rotational speed of the two driving wheels equals the speed of the shaft. An increase in the speed of one wheel is balanced by a decrease in the speed of the other. When used in this way, a differential couples the input shaft to the pinion, which in turn runs on the ring gear of the differential. This also works as reduction gearing. On rear wheel drive vehicles the differential may connect to half-shafts inside an axle housing, or drive shafts that connect to the rear driving wheels. There are individual drive-shafts to each wheel. Non-automotive uses of differentials include performing analog arithmetic. The ball was painted black and white in hemispheres, graphically showed the phase of the moon at a particular point in time. See also the Chinese South-pointing chariot. An equation clock that used a differential for addition was made in 1720. In the 20th Century, large assemblies of many differentials were used as analog computers, calculating, for example, the direction in which a gun should be aimed. However, the development of electronic digital computers has made these uses of differentials obsolete. Military uses may still exist. See Electromagnetic pulse.
Differential (mechanical device)
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A spur gear differential constructed by engaging the planet gears of two co-axial epicyclic gear trains. The casing is the carrier for this planetary gear train.
Differential (mechanical device)
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Automotive differential: The drive gear 2 is mounted on the carrier 5 which supports the planetary bevel gears 4 which engage the driven bevel gears 3 attached to the axles 1.
Differential (mechanical device)
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ZF Differential. The drive shaft enters from the front and the driven axles run left and right.
Differential (mechanical device)
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Car differential of a Škoda 422
119.
Pythagoras' Theorem
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In mathematics, the Pythagorean theorem, also known as Pythagoras's theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. There is some evidence that Babylonian mathematicians understood the formula, although little of it indicates an application within a mathematical framework. Mesopotamian, Indian and Chinese mathematicians all discovered the theorem independently and, in some cases, provided proofs for special cases. The theorem has been given numerous proofs – possibly the most for any mathematical theorem. They are very diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years. The Pythagorean theorem was known long before Pythagoras, but he may well have been the first to prove it. In any event, the proof attributed to him is very simple, is called a proof by rearrangement. Therefore, the white space within each of the two large squares must have equal area. Equating the area of the white space yields the Pythagorean theorem, Q.E.D. That Pythagoras originated this very simple proof is sometimes inferred from the writings of the later Greek philosopher and mathematician Proclus. Several other proofs of this theorem are described below, but this is known as the Pythagorean one. If the length of both a and b are known, then c can be calculated as c = a 2 + b 2. If the angle between the other sides is a right angle, the law of cosines reduces to the Pythagorean equation. This theorem may have more known proofs than any other; the book The Pythagorean Proposition contains 370 proofs.
Pythagoras' Theorem
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The Plimpton 322 tablet records Pythagorean triples from Babylonian times.
Pythagoras' Theorem
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Pythagorean theorem The sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c).
Pythagoras' Theorem
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Geometric proof of the Pythagorean theorem from the Zhou Bi Suan Jing.
Pythagoras' Theorem
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Exhibit on the Pythagorean theorem at the Universum museum in Mexico City
120.
Hexagon
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In geometry, a hexagon is a six sided polygon or 6-gon. The total of the internal angles of any hexagon is 720°. A regular hexagon can also be constructed as a truncated equilateral triangle, t, which alternates two types of edges. A regular hexagon is defined as a hexagon, both equiangular. It meaning that it is both cyclic and tangential. The common length of the sides equals the radius of the circumscribed circle, which equals 3 3 times the apothem. All internal angles are 120 degrees. A regular hexagon has 6 reflection symmetries, making up the dihedral group D6. The longest diagonals of a regular hexagon, connecting opposite vertices, are twice the length of one side. Like equilateral triangles, regular hexagons fit together without any gaps to tile the plane, so are useful for constructing tessellations. The cells of a beehive honeycomb are hexagonal for this reason and because the shape makes efficient use of building materials. The Voronoi diagram of a regular lattice is the honeycomb tessellation of hexagons. It is not usually considered a triambus, although it is equilateral. The maximal diameter, D is twice R, which equals the side length, t. The minimal diameter or the diameter of the inscribed circle, d, is twice the minimal radius or inradius, r.
Hexagon
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Giants causeway closeup
Hexagon
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The ideal crystalline structure of graphene is a hexagonal grid.
Hexagon
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Assembled E-ELT mirror segments
Hexagon
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A beehive honeycomb
121.
Integral
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In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, other concepts that arise by combining infinitesimal data. Integration is one of the two main operations of calculus, with its inverse, differentiation, being the other. The area above the x-axis adds to the total and that below the x-axis subtracts from the total. Roughly speaking, the operation of integration is the reverse of differentiation. For this reason, the integral may also refer to the related notion of a function F whose derivative is the given function f. In this case, it is called an indefinite integral and is written: F = ∫ f d x. The integrals discussed in this article are those termed definite integrals. A rigorous mathematical definition of the integral was given by Bernhard Riemann. It is based on a limiting procedure which approximates the area of a region by breaking the region into vertical slabs. In a surface integral, the curve is replaced by a piece of a surface in the three-dimensional space. A similar method was independently developed in China around the 3rd century AD by Liu Hui, who used it to find the area of the circle. This method was later used by father-and-son mathematicians Zu Chongzhi and Zu Geng to find the volume of a sphere. The next significant advances in integral calculus did not begin to appear until the 17th century. Further steps were made in the 17th century by Barrow and Torricelli, who provided the first hints of a connection between differentiation. Barrow provided the first proof of the fundamental theorem of calculus.
Integral
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A definite integral of a function can be represented as the signed area of the region bounded by its graph.
122.
Measurement of a Circle
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Measurement of a Circle is a treatise that consists of three propositions by Archimedes. The treatise is only a fraction of what was a longer work. Any circle with a radius r is equal in area with a right triangle with the two legs being c and r. This proposition is proved by the method of exhaustion. Proposition two states: The area of a circle is as 11 to 14. This proposition could not have been placed by Archimedes, for it relies on the outcome of the third proposition. Proposition three states: The ratio of the circumference of any circle to its diameter is 10 71 but less than 3 1 7. This approximates what we now call the constant π. He found these bounds by inscribing and circumscribing a circle with two similar 96-sided regular polygons. He gives the upper and lower bounds as 1351 780 > 3 > 265 153. Discussion of this approach was treated more explicitly by Hieronymus Georg Zeuthen. Although only one route to the bounds is mentioned, in fact there are two others, making the bounds almost inescapable however the method is worked. But the bounds can also be produced by an geometrical construction suggested by Archimedes' Stomachion in the setting of the regular dodecagon. In this case, the task is to give rational approximations to the tangent of π/12.
Measurement of a Circle
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The circle and the triangle are equal in area.
123.
Regular hexagon
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In geometry, a hexagon is a six sided polygon or 6-gon. The total of the internal angles of any hexagon is 720°. A regular hexagon can also be constructed as a truncated equilateral triangle, t, which alternates two types of edges. A regular hexagon is defined as a hexagon, both equiangular. It meaning that it is both cyclic and tangential. The common length of the sides equals the radius of the circumscribed circle, which equals 3 3 times the apothem. All internal angles are 120 degrees. A regular hexagon has 6 reflection symmetries, making up the dihedral group D6. The longest diagonals of a regular hexagon, connecting opposite vertices, are twice the length of one side. Like equilateral triangles, regular hexagons fit together without any gaps to tile the plane, so are useful for constructing tessellations. The cells of a beehive honeycomb are hexagonal for this reason and because the shape makes efficient use of building materials. The Voronoi diagram of a regular lattice is the honeycomb tessellation of hexagons. It is not usually considered a triambus, although it is equilateral. The maximal diameter, D is twice R, which equals the side length, t. The diameter of the inscribed circle, d, is twice the minimal radius or inradius, r.
Regular hexagon
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Giants causeway closeup
Regular hexagon
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A regular hexagon
Regular hexagon
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The ideal crystalline structure of graphene is a hexagonal grid.
Regular hexagon
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Assembled E-ELT mirror segments
124.
Square
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In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles. It can also be defined as a rectangle in which two adjacent sides have equal length. A square with vertices ABCD would be denoted ◻ ABCD. Opposite sides of a square are both equal in length. All four angles of a square are equal. All four sides of a square are equal. The diagonals of a square are equal. The square is the n = 2 case of the families of n-orthoplexes. A square has Schläfli symbol. T, is an octagon. H, is a digon. The area A is A = ℓ 2. In classical times, the second power was described in terms of the area of a square, as in the above formula. This led to the use of the square to mean raising to the second power. The area can also be calculated using the diagonal d according to A = d 2.
Square
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A regular quadrilateral (tetragon)
125.
Radius
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Remote Authentication Dial-In User Service is a networking protocol that provides centralized Authentication, Authorization, Accounting management for users who connect and use a network service. These networks may incorporate modems, DSL, access points, VPNs, network ports, etc.. RADIUS is a protocol that runs in the application layer, can use either TCP or UDP as transport. The gateways that control access to a network, usually contain a RADIUS client component that communicates with the RADIUS server. RADIUS is often the back-end of choice for 802.1 X authentication well. The RADIUS server is usually a process running on a UNIX or Microsoft Windows server. RADIUS is a AAA protocol which manages access in the following two-step process, also known as a AAA transaction. AAA stands for authentication, accounting. Authorization characteristics in RADIUS are described in RFC 2865 while accounting is described by RFC 2866. The machine sends a request to a Network Access Server to gain access to a particular network resource using access credentials. In turn, the NAS sends a RADIUS Access Request message to the RADIUS server, requesting authorization to grant access via the RADIUS protocol. This request includes access credentials, typically in security certificate provided by the user. The RADIUS server checks that the information is correct using authentication schemes such as PAP, CHAP or EAP. Historically, RADIUS servers checked the user's information against a locally stored flat database. The RADIUS server then returns one of three responses to the NAS: 1) Access Reject, 2) Access Challenge, or 3) Access Accept.
Radius
126.
On the Sphere and Cylinder
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On the Sphere and Cylinder is a work, published by Archimedes in two volumes c. 225 BC. On the sphere, he showed that the area is four times the area of its great circle. In modern terms, this means that the area is equal to: A S = 4 π r 2. Later, Roman philosopher Marcus Tullius Cicero discovered the tomb, overgrown by surrounding vegetation. His original method likely involved a clever use of levers. Vol. 62, No. 7, pp. 473–476 Lucio Lombardo Radice, La matematica da Pitagora a Newton, Roma, Editori Riuniti, 1971. Attilio Frajese, Opere di Archimede, Torino, U.T.E.T. 1974.
On the Sphere and Cylinder
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A page from "On the Sphere and Cylinder" in latin
127.
Archimedean property
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Roughly speaking, it is the property of having no infinitely small elements. It was Otto Stolz who gave its name because it appears as Axiom V of Archimedes' On the Sphere and Cylinder. A structure which has a pair of non-zero elements, one of, infinitesimal with respect to the other, is said to be non-Archimedean. For example, a linearly ordered group, Archimedean is an Archimedean group. This can be made precise in various contexts with slightly different formulations. The concept was named after the ancient Greek geometer and physicist Archimedes of Syracuse. Because Archimedes credited it to Eudoxus of Cnidus it is also known as the Eudoxus axiom. Archimedes used infinitesimals in heuristic arguments, although he denied that those were finished mathematical proofs. Let y be positive elements of a linearly ordered group G. The group G is Archimedean if there is no pair x,y such that x is infinitesimal with respect to y. Additionally, if K is an algebraic structure with a unit — for example, a ring — a similar definition applies to K. If x is infinitesimal with respect to 1, then x is an infinitesimal element. Likewise, if y is infinite with respect to 1, then y is an infinite element. The algebraic K is Archimedean if it has no infinite elements and no infinitesimal elements. An ordered field has some additional properties.
Archimedean property
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Illustration of the Archimedean property.
128.
Square root
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For example, 4 and 4 are square roots of 16 because 42 = 2 = 16. For example, the square root of 9 is 3, denoted √ 9 = 3, because 32 = 3 × 3 = 9 and 3 is non-negative. The term whose root is being considered is known as the radicand. The radicand is the expression underneath the radical sign, in this example 9. A has two square roots: √ a, positive, − √ a, negative. Together, these two roots are denoted ± √a. For positive a, the principal square root can also be written in exponent notation, as a1/2. Square roots of negative numbers can be discussed within the framework of complex numbers. A method for finding very good approximations to the square roots of 3 are given in the Baudhayana Sulba Sutra. Aryabhata in the Aryabhatiya, has given a method for finding the square root of numbers having many digits. This is the theorem Euclid X, 9 almost certainly due to Theaetetus dating back to 380 BC. The particular case √ 2 is traditionally attributed to Hippasus. It is exactly the length of the diagonal of a square with length 1. A 9th-century Indian mathematician, was the first to state that square roots of negative numbers do not exist. A symbol for square roots, written as an elaborate R, was invented by Regiomontanus.
Square root
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First leaf of the complex square root
Square root
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The mathematical expression 'The (principal) square root of x"
129.
John Wallis
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John Wallis was an English mathematician, given partial credit for the development of infinitesimal calculus. Between 1689 he served as chief cryptographer for Parliament and, later, the royal court. He is credited with introducing the ∞ for infinity. He similarly used 1/∞ for an infinitesimal. Wallis was born in the third of five children of Reverend John Wallis and Joanna Chapman. He was initially moved to James Movat's school in Tenterden in 1625 following an outbreak of plague. As it was intended that he should be a doctor, he was sent to Emmanuel College, Cambridge. His interests, however, centred on mathematics. He received his Bachelor of a Master's in 1640, afterwards entering the priesthood. From 1643 to 1649, he served at the Westminster Assembly. He was elected at Queens' College, Cambridge in 1644, from which he had to resign following his marriage. Throughout this time, Wallis had been close to the Parliamentarian party, perhaps as a result of his exposure at Felsted School. He rendered great practical assistance in deciphering Royalist dispatches. Most ciphers were hoc methods relying on a secret algorithm, as opposed to systems based on a variable key. He was also concerned by foreign powers refusing, for example, Gottfried Leibniz's request of 1697 to teach Hanoverian students about cryptography.
John Wallis
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John Wallis
John Wallis
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Opera mathematica, 1699
130.
Iteration
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Each repetition of the process is also called an "iteration", the results of one iteration are used as the starting point for the next iteration. In the context of mathematics or science, iteration is a standard block of algorithms. Iteration of apparently simple functions can produce complex difficult problems - for examples, see the Collatz juggler sequences. Another use of iteration in mathematics is in iterative methods which are used to produce numerical solutions to mathematical problems. Newton's method is an example of an iterative method. Manual calculation of a number's square root is a common use and a well-known example. Iteration in computing is the technique marking out within a program for a defined number of repetitions. That block of statements is said to be iterated; a computer scientist might also refer to that block of statements as an "iteration". In the example above, the line of code is using the value of i as it increments. This idea is found in the old adage, "Practice makes perfect." Unlike math, educational iterations are not predetermined; instead, the task is repeated according to some external criteria is achieved. In algorithmic situations, recursion and iteration can be employed to the same effect. Instead, those programming languages exclusively use recursion. The algorithm then "reverses" and reassembles the pieces into a complete whole. The classic example of recursion is in list-sorting algorithms such as Merge Sort.
Iteration
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A pentagon iteration. Connecting alternate corners of a regular pentagon produces a pentagram which encloses a smaller inverted pentagon. Iterating the process produces a sequence of nested pentagons and pentagrams and also demonstrates recursion.
131.
The Quadrature of the Parabola
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The Quadrature of the Parabola is a treatise on geometry, written by Archimedes in the 3rd century BC. The statement of the problem used the method of exhaustion. Archimedes may have dissected the area into many triangles whose areas form a geometric progression. He proves that this is the area of the parabolic segment. A parabolic segment is the region bounded by a line. To find the area of a parabolic segment, Archimedes considers a inscribed triangle. By Proposition 1, a line from the third vertex drawn parallel to the axis divides the chord into equal segments. The main theorem claims that the area of the parabolic segment is 4/3 that of the inscribed triangle. Archimedes gives two proofs of the main theorem. The second, more famous proof uses pure geometry, specifically the method of exhaustion. Of the twenty-four propositions, the first three are quoted from Euclid's Elements of Conics. The main idea of the proof is the dissection of the parabolic segment into many triangles, as shown in the figure to the right. Each of these triangles is inscribed in its parabolic segment in the same way that the blue triangle is inscribed in the large segment. In propositions eighteen through twenty-one, Archimedes proves that the area of each green triangle is one eighth of the area of the blue triangle. This simplifies to give Area = T.
The Quadrature of the Parabola
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A parabolic segment.
132.
Triangle
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A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, C is denoted △ A B C. In Euclidean geometry any three points, when non-collinear, determine a unique plane. This article is about triangles in Euclidean geometry except where otherwise noted. Triangles can be classified according to the lengths of their sides: An equilateral triangle has the same length. An equilateral triangle is also a regular polygon with all angles measuring 60°. An isosceles triangle has two sides of equal length. Some mathematicians define an isosceles triangle to have exactly two equal sides, whereas others define an isosceles triangle as one with at least two equal sides. The latter definition would make all equilateral isosceles triangles. The 45 -- 45 -- 90 right triangle, which appears in the square tiling, is isosceles. A scalene triangle has all its sides of different lengths. Equivalently, it has all angles of different measure. Hatch marks, also called tick marks, are used in diagrams of triangles and geometric figures to identify sides of equal lengths. In a triangle, the pattern is usually no more than 3 ticks.
Triangle
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The Flatiron Building in New York is shaped like a triangular prism
Triangle
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A triangle
133.
Series (mathematics)
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In mathematics, a series is, informally speaking, the sum of the terms of an infinite sequence. The sum of a finite sequence has defined first and last terms, whereas a series continues indefinitely. Given an infinite sequence, a series is informally the result of adding all those terms together: a1 + a2 + a3 + ···. These can be written more compactly using the summation symbol ∑. A value may not always be given to such an infinite sum, and, in this case, the series is said to be divergent. The terms of the series are often produced according to a rule, such as by a formula, or by an algorithm. To emphasize that there are an infinite number of terms, a series is often called an infinite series. The study of infinite series is a major part of mathematical analysis. Series are used through generating functions. In addition to their ubiquity in mathematics, infinite series are also widely used in quantitative disciplines such as physics, computer statistics and finance. This definition is usually written as L = ∑ n = 0 ∞ a n ⇔ L = lim k → ∞ S k. When the set is the natural numbers I = the function a: N ↦ G is a sequence denoted by a = a n. This definition is usually written as L = ∑ n = 0 ∞ a n ⇔ L = lim k → ∞ S k. A series ∑ an is said to ` be convergent' when the SN of partial sums has a finite limit. If the limit of SN is infinite or does not exist, the series is said to diverge.
Series (mathematics)
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Illustration of 3 geometric series with partial sums from 1 to 6 terms. The dashed line represents the limit.
134.
Geometric series
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In mathematics, a geometric series is a series with a constant ratio between successive terms. Geometric series are one of the simplest examples of infinite series with finite sums, although not all of them have this property. Historically, they continue to be central in the study of convergence of series. They have important applications in physics, engineering, biology, economics, computer science, queueing theory, finance. The terms of a geometric series form a geometric progression, meaning that the ratio of successive terms in the series is constant. This relationship allows for the representation of a geometric series using only two terms, a. A is the first term of the series. In the case above, where r is one half, the series has the one. If r is less than minus one the terms of the series become larger and larger in magnitude. The series has no sum. If r is equal to one, all of the terms of the series are the same. The series diverges. If r is minus one the terms take two values alternately. The sum of the terms oscillates between two values. This again the series has no sum.
Geometric series
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Each of the purple squares has 1/4 of the area of the next larger square (1/2× 1/2 = 1/4, 1/4×1/4 = 1/16, etc.). The sum of the areas of the purple squares is one third of the area of the large square.
135.
Secant line
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In geometry, a secant line of a curve is a line that intersects two points on the curve. A chord is an interval of a secant line, the portion of the line that lies within the curve. The word secant comes from the Latin word secare, meaning to cut. Secants can be used to approximate the tangent to a curve, at some point P. As a consequence, one could say that the limit, as Q approaches P, of the secant's slope, or direction, is that of the tangent. In calculus, this idea is the basis of the geometric definition of the derivative. MathWorld.
Secant line
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Common lines and line segments on a circle, including the secant line
136.
Doric Greek
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Doric or Dorian was an Ancient Greek dialect. Together with Northwest Greek, it forms the "Western group" of classical Greek dialects. It is widely accepted that Doric originated in the mountains of Epirus and Macedonia, northwestern Greece, the original seat of the Dorians. It was expanded to all other regions during the Dorian invasion and the colonisations that followed. Where the Doric dialect group fits in the overall classification of ancient Greek dialects depends to some extent on the classification. Several views are stated under Greek dialects. The prevalent theme of most views listed there is that Doric is a subgroup of West Greek. Some use the terms Northern Greek or Northwest Greek instead. The geographic distinction is only verbal and ostensibly is misnamed: all of Doric was spoken south of "Southern Greek" or "Southeastern Greek." When the distinction began is not known. Thus West Greek is the most accurate name for the classical dialects. Tsakonian, a descendant of Laconian Doric, is still spoken on the southern Argolid coast of the Peloponnese, in the modern prefectures of Arcadia and Laconia. Today it is a source of considerable interest to linguists, an endangered dialect. Sparta was the seat of ancient Laconia. Laconian is attested in inscriptions on pottery and stone from the seventh century BC.
Doric Greek
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Doric proper
137.
Euclid
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Euclid, sometimes called Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the "father of geometry". He was active in Alexandria during the reign of Ptolemy I. In the Elements, Euclid deduced the principles of what is now called Euclidean geometry from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, rigor. Euclid is the anglicized version of the Greek Εὐκλείδης, which means "renowned, glorious". Very original references to Euclid survive, so little is known about his life. The place and circumstances of both his birth and death are unknown and may only be estimated roughly relative to other people mentioned with him. He is usually referred to as" ὁ στοιχειώτης". The historical references to Euclid were written centuries after he lived by Proclus c. 450 AD and Pappus of Alexandria c. 320 AD. Proclus introduces Euclid only briefly in his Commentary on the Elements. This anecdote is questionable since it is similar to a story told about Alexander the Great. 247–222 BC. A detailed biography of Euclid is given by Arabian authors, mentioning, for example, a town of Tyre. This biography is generally believed to be completely fictitious. However, there is little evidence in its favor.
Euclid
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Euclid by Justus van Gent, 15th century
Euclid
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One of the oldest surviving fragments of Euclid's Elements, found at Oxyrhynchus and dated to circa AD 100 (P. Oxy. 29). The diagram accompanies Book II, Proposition 5.
Euclid
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Statue in honor of Euclid in the Oxford University Museum of Natural History
138.
Polyhedron
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In elementary geometry, a polyhedron is a solid in three dimensions with flat polygonal faces, straight edges and sharp corners or vertices. The polyhedron comes from the Classical Greek πολύεδρον, as poly - + - hedron. Pyramids are examples of polyhedra. A polyhedron is a 3-dimensional example of the more general polytope in any number of dimensions. Many definitions of "polyhedron" have been given within some more rigorous than others. For example, definitions based on the idea of a bounding surface rather than a solid are common. However such definitions are not always compatible in mathematical contexts. One modern approach treats a geometric polyhedron as an injection into a realisation, of some abstract polyhedron. It might not be realised as a solid body. 2 dimensions: A face is a polygon bounded by a circuit of edges, usually also realises the flat region inside the boundary. These polygonal faces together make up the polyhedral surface. 1 dimension: An edge joins one vertex to another and one face to another, is usually a line segment. The edges together make up the polyhedral skeleton. 0 dimensions: A vertex is a corner point. Different approaches - and definitions - may require different realisations.
Polyhedron
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Convex polyhedron blocks on display at the Universum museum in Mexico City
Polyhedron
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Regular tetrahedron
139.
Refraction
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Refraction is the change in direction of propagation of a wave due to a change in its transmission medium. The phenomenon is explained by the conservation of energy and the conservation of momentum. Due to the change of medium, the phase velocity of the wave is changed but its frequency remains constant. This is most commonly observed when a wave passes from one medium to another at any angle other than 0° from the normal. In general, the incident wave is partially refracted and partially reflected; the details of this behavior are described by the Fresnel equations. At the boundary between the media, the wave's phase velocity is altered, usually causing a change in direction. Its wavelength increases or decreases, but its frequency remains constant. For example, a light ray will refract as it enters and leaves glass, assuming there is a change in refractive index. A ray traveling along the normal will change speed, but not direction. Refraction still occurs in this case. Understanding of this concept led to the invention of lenses and the refracting telescope. Refraction can be seen when looking into a bowl of water. Air has a refractive index of about 1.0003, water has a refractive index of about 1.3330. This is due to the bending of light rays as they move from the water to the air. Once the rays reach the eye, the eye traces them back as straight lines.
Refraction
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Light on air–plexi surface in this experiment undergoes refraction (lower ray) and reflection (upper ray).
Refraction
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Refraction in a glass of water. The image is flipped.
Refraction
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An image of the Golden Gate Bridge is refracted and bent by many differing three-dimensional drops of water.
Refraction
140.
Byzantine Empire
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During most of its existence, the empire was the most powerful economic, military force in Europe. Several signal events from the 4th to 6th centuries mark the period of transition during which the Roman Empire's Greek East and Latin West divided. Constantine I reorganised the empire, legalised Christianity. Under Theodosius I, Christianity became other religious practices were proscribed. Finally, under the reign of Heraclius, the Empire's administration were restructured and adopted Greek for official use instead of Latin. The borders of the Empire evolved significantly over its existence, as it went through several cycles of recovery. During the reign of Maurice, the north stabilised. In a matter of years the Empire lost Egypt and Syria, to the Arabs. This battle opened the way for the Turks to settle as a homeland. The Empire recovered again during such that by the 12th century Constantinople was the largest and wealthiest European city. Its remaining territories were progressively annexed by the Ottomans over the 15th century. The Fall of Constantinople to the Ottoman Empire in 1453 finally ended the Byzantine Empire. The term comes from "Byzantium", the name of the city of Constantinople before it became Constantine's capital. This older name of the city would rarely be used from this point onward except in poetic contexts. However, it was not until the mid-19th century that the term came in the Western world.
Byzantine Empire
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Tremissis with the image of Justinian the Great (r. 527–565) (see Byzantine insignia)
Byzantine Empire
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Byzantine lamellar armour klivanium (Κλιβάνιον) - a predecessor of Ottoman krug mirror armour
Byzantine Empire
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The Baptism of Constantine painted by Raphael 's pupils (1520–1524, fresco, Vatican City, Apostolic Palace); Eusebius of Caesarea records that (as was common among converts of early Christianity) Constantine delayed receiving baptism until shortly before his death
Byzantine Empire
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Restored section of the Theodosian Walls.
141.
Gerard of Cremona
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Gerard of Cremona was an Italian translator of scientific books from Arabic into Latin. He obtained the Arabic books in the libraries at Toledo. Some of the books were unavailable in Greek or Latin in Europe at the time. One of Gerard's most famous translations is from Arabic texts found in Toledo. Gerard was born in northern Italy. Dissatisfied with the meager philosophies of his Italian teachers, Gerard went to Toledo. The first Latin translation was made, from the Greek around 1160 in Sicily. Although we do not have detailed information of the date when Gerard went to Castile, it was later than 1144. One of the great scholars associated with Toledo was Gerard's contemporary. The Jewish inhabitants of Toledo adopted the language and many customs of their conquerors, embodying Mozarabic culture. In Toledo Gerard devoted the remainder of his life to making Latin translations from the Arabic scientific literature. Gerard of Cremona's Latin translation of the Arabic version of Ptolemy’s Almagest made c. 1175 was the most widely known in Western Europe before the Renaissance. George of Trebizond and then Johannes Regiomontanus retranslated it in the fifteenth century. The Almagest formed the basis for Western astronomy until it was eclipsed by the theories of Copernicus. Gerard edited for Latin readers the Tables of the most accurate compilation of astronomical data ever seen in Europe at the time.
Gerard of Cremona
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European depiction of the Persian physician Rhazes, in Gerard of Cremona's "Recueil des traités de médecine" 1250-1260. Gerard de Cremona translated numerous works by Arab scholars.
Gerard of Cremona
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Al-Razi 's Recueil des traités de médecine translated by Gerard of Cremona, second half of the 13th century.
Gerard of Cremona
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Theorica Platenarum by Gerard of Cremona, 13th century.
142.
Basel
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Basel is a city in northwestern Switzerland on the river Rhine. The Basel region culturally extends into French Alsace. Basel joined the Swiss Confederacy in 1501. It emerged as a centre for the chemical and pharmaceutical industry in the 20th century. Basel is Switzerland's third-most-populous city with about inhabitants. Located where the Swiss, German borders meet, Basel also has suburbs in France and Germany. The Basel metropolitan area has around 830,000 inhabitants in 226 municipalities. The main spoken language is the local variant of the Alemannic Swiss German dialect. Basel German belongs to the Low Alemannic group, linking it more closely than with the other varieties of Swiss German. Basel has been the Age of Enlightenment. It has the oldest university of the Swiss Confederation. There are settlement traces on the Rhine knee from the early La Tène period. The city of Basel eventually grew around the castle. The name of Basel is derived from the Roman-era toponym Basilia, first recorded in the 3rd century. It is presumably derived from the personal name Basilius.
Basel
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Basel, as seen from the Elisabethenkirche
Basel
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Map of Basel in 1642, engraved by Matthäus Merian, oriented with SW at the top and NE at the bottom.
Basel
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A panoramic view of Basel, looking North from the Münster tower over Kleinbasel (Small Basel). The blue tower in the centre, the Messeturm, was Switzerland's tallest building 2003-10; the bridge on the extreme right is the Wettsteinbrücke, Basel's second oldest bridge, but recently replaced by a new structure. The first bridge on the left is the Mittlere Brücke (Middle or Central Bridge), the oldest bridge in Basel.
Basel
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The synagogue of Basel
143.
On the Equilibrium of Planes
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On the Equilibrium of Planes is a treatise by Archimedes in two volumes. The first book locates the centre of gravity of the triangle and the trapezoid. According to Pappus of Alexandria, I will move the Earth.". . The second book, which contains ten propositions, examines the centres of gravity of parabolic segments. Book one contains fifteen propositions with seven postulates. In proposition six Archimedes establishes the Law of the Lever, concluding that "Magnitudes are in equilibrium at distances reciprocally proportional to their weights." In propositions fourteen, respectively, Archimedes locates the centre of gravity of the parallelogram and the triangle. Additionally, in proposition 15, he establishes the centre of gravity of the trapezium. The second book, which contains ten propositions, studies parabolic segments exclusively. It examines these segments by substituting them with rectangles of equal area; an exchange made possible by results obtained in the Quadrature of the Parabola. Archimedes' proof of the Law of the Lever is executed within proposition six. It relies upon propositions four, five, on postulate one. In postulate one Archimedes states that "Equal weights at equal distances are in equilibrium". Now, double the length of ED by duplicating the shorter arm on the right.
On the Equilibrium of Planes
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Plutarch represented Archimedes as declaring that Any given weight can be moved by a given force.
144.
Torque
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Torque, moment, or moment of force is the tendency of a force to rotate an object around an axis, fulcrum, or pivot. Just as a force is a pull, a torque can be thought of as a twist to an object. Loosely speaking, torque is a measure of the force on an object such as a bolt or a flywheel. The symbol for torque is typically the lowercase Greek letter tau. When it is called moment of force, it is commonly denoted by M. The SI unit for torque is the metre. For more on the units of torque, see Units. This article follows US physics terminology in its use of the torque. In the UK and in US mechanical engineering, this is called moment of force, usually shortened to moment. Torque is defined mathematically as the rate of change of momentum of an object. The definition of torque states that the moment of inertia of an object are changing. For a rotational force applied to a shaft causing acceleration, such as a drill bit accelerating from rest, results in a moment called a torque. Similarly with any couple on an object that has no change to its angular momentum, such moment is also not called a torque. The concept of torque, also called couple, originated with the studies of Archimedes on levers. The torque was apparently introduced into English scientific literature by James Thomson, the brother of Lord Kelvin, in 1884.
Torque
145.
Center of mass
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The distribution of mass is balanced around the center of mass and the average of the weighted position coordinates of the distributed mass defines its coordinates. Calculations in mechanics are often simplified when formulated with respect to the center of mass. It is a hypothetical point where entire mass of an object may be assumed to be concentrated to visualise its motion. In other words, center of mass is particle equivalent of a given object for application of Newton's laws of motion. The center of mass may be located outside the physical body, as is sometimes the case for hollow or open-shaped objects, such as a horseshoe. In orbital mechanics, the equations of motion of planets are formulated as point masses located at the centers of mass. He developed mathematical techniques for finding the centers of mass of objects of uniform density of various well-defined shapes. Newton's second law is reformulated with respect to the center of mass in Euler's first law. In analogy to statistics, the center of mass is the mean location of a distribution of mass in space. The center of mass is not generally the point at which a plane separates the distribution of mass into two equal halves. In analogy with statistics, the median is not the same as the mean. The percentages of mass at each point can be viewed as projective coordinates of the point R on this line, are termed barycentric coordinates. Another way of interpreting the process here is the mechanical balancing of moments about an arbitrary point. The numerator gives the total moment, then balanced by an equivalent total force at the center of mass. This can be generalized to three points and four points to define projective coordinates in the plane, in space, respectively.
Center of mass
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This child's toy uses the principles of center of mass to keep balance on a finger.
Center of mass
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Estimated center of mass/gravity (blue sphere) of a gymnast at the end of performing a cartwheel. Notice center is outside the body in this position.
146.
Parallelogram
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In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. By comparison, a quadrilateral with just one pair of parallel sides is a trapezoid in American English or a trapezium in British English. The three-dimensional counterpart of a parallelogram is a parallelepiped. The etymology reflects the definition. Square – A parallelogram with four sides of equal length and angles of equal size. Two pairs of opposite angles are equal in measure. The diagonals bisect each other. One pair of opposite sides are parallel and equal in length. Adjacent angles are supplementary. Each diagonal divides the quadrilateral into two congruent triangles. The sum of the squares of the sides equals the sum of the squares of the diagonals. It has rotational symmetry of order 2. The sum of the distances from any interior point to the sides is independent of the location of the point. Opposite sides of a parallelogram are parallel and so will never intersect.
Parallelogram
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This parallelogram is a rhomboid as it has no right angles and unequal sides.
147.
On Spirals
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On Spirals is a treatise by Archimedes in 225 BC. Although Archimedes did not discover the Archimedean spiral, he employed it in this book to trisect an angle. Archimedes begins On Spirals with a message to Dositheus of Pelusium mentioning the death of Conon as a loss to mathematics. He then goes on to summarize the results of On the Sphere and Cylinder and On Conoids and Spheroids. He continues to state his results of On Spirals. The Archimedean spiral was later studied by Archimedes in On Spirals. Archimedes was able to find various tangents to the spiral. He defines the spiral as: The construction as to how Archimedes trisected the angle is as follows: Suppose the angle ABC is to be trisected. Find BD to be one third of BC. Radius BD. Suppose the circle with B intersects the spiral at point E. Angle ABE is one third angle ABC. To square the circle, Archimedes gave the following construction: Let P be the point on the spiral when it has completed one turn. Let the tangent at P cut the line perpendicular at T. OT is the length of the circumference of the circle with radius OP. So the area of the circle with radius OP is equal to the area of the triangle OPT.
On Spirals
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Example of how Archimedes trisected an angle in On Spirals.
148.
Archimedean spiral
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The Archimedean spiral is a spiral named after the 3rd century BC Greek mathematician Archimedes. Equivalently, in polar coordinates it can be described by the equation r = a + b θ with real numbers a and b. Changing the parameter a will turn the spiral, while b controls the distance between successive turnings. Archimedes described such a spiral On Spirals. The Archimedean spiral has one for θ > 0 and one for θ < 0. The two arms are smoothly connected at the origin. Only one arm is shown on the accompanying graph. Taking the image of this arm across the y-axis will yield the other arm. Some sources describe the Archimedean spiral as a spiral with a "constant distance" between successive turns. This is somewhat misleading. Sometimes the term spiral is used for the more general group of spirals r = a + b θ 1 / c. The normal Archimedean spiral occurs when c = 1. Other spirals falling into this group include the hyperbolic spiral, the lituus. Virtually all static spirals appearing in nature are logarithmic spirals, not Archimedean ones. Dynamic spirals are Archimedean.
Archimedean spiral
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Three 360° turnings of one arm of an Archimedean spiral
149.
Locus (mathematics)
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In geometry, a locus is a set of points, whose location satisfies or is determined by one or more specified conditions. In contrast to the set-theoretic view, the old formulation avoids considering infinite collections, as avoiding the actual infinite was an philosophical position of earlier mathematicians. Once theory became the universal basis over which the whole mathematics is built, the term of locus became rather old fashioned. Examples from geometry include: The set of points equidistant from two points is a perpendicular bisector to the line segment connecting the two points. The set of points equidistant from two lines that cross is the bisector. All conic sections are loci: Parabola: the set of points equidistant from a line. Circle: the set of points for which the distance from a single point is constant. Hyperbola: the set of points for each of which the absolute value of the difference between the distances to two given foci is a constant. Ellipse: the set of points for each of which the sum of the distances to two given foci is a constant. The circle is the special case in which the two foci coincide with each other. Other examples of loci appear in various areas of mathematics. Proof that all the points on the given shape satisfy the conditions. We find the locus of the points P that have a given ratio of distances k = d1/d2 to two given points. In this example we choose k= 3, A and B as the fixed points. It is the circle of Apollonius defined by these values of k, A, B.
Locus (mathematics)
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(distance PA) = 3.(distance PB)
150.
Angular velocity
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This speed can be measured in terms of degrees per second, degrees per hour, etc.. Angular velocity is usually represented by the omega. The direction of the angular vector is perpendicular to the plane of rotation, in a direction, usually specified by the right-hand rule. The velocity of a particle is measured around or relative to a point, called the origin. If there is no radial component, then the particle moves in a circle. On the other hand, if there is no cross-radial component, then the particle moves along a straight line from the origin. Therefore, the angular velocity is completely determined by this component. The velocity in two dimensions is a pseudoscalar, a quantity that changes its sign under a parity inversion. The positive direction of rotation is taken, by convention, to be from the x axis. If the parity is inverted, but the orientation of a rotation is not, then the sign of the velocity changes. There are three types of velocity involved in the movement on an ellipse corresponding to the three anomalies. In three dimensions, the velocity becomes a bit more complicated. The velocity in this case is generally thought of as a vector, or more precisely, a pseudovector. It now has not only a direction as well. The direction describes the axis of rotation that Euler's rotation theorem guarantees must exist.
Angular velocity
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The angular velocity of the particle at P with respect to the origin O is determined by the perpendicular component of the velocity vector v.
151.
Polar coordinate system
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The reference point is called the pole, the ray from the pole in the reference direction is the polar axis. The distance from the pole is called the radial coordinate or radius, the angle is called the angular coordinate, polar angle, or azimuth. The concepts of angle and radius were already used by ancient peoples of the first millennium BC. In On Spirals, Archimedes describes the Archimedean spiral, a function whose radius depends on the angle. The Greek work, however, did not extend to a full coordinate system. From the 8th century AD onward, astronomers developed methods for approximating and calculating the direction to Mecca —and its distance—from any location on the Earth. From the 9th century onward they were using spherical trigonometry and map projection methods to determine these quantities accurately. There are various accounts of the introduction of polar coordinates as part of a formal coordinate system. The full history of the subject is described in Harvard professor Julian Lowell Coolidge's Origin of Polar Coordinates. Grégoire de Saint-Vincent and Bonaventura Cavalieri independently introduced the concepts in the mid-seventeenth century. Saint-Vincent wrote about them privately in 1625 and published his work in 1647, while Cavalieri published his in 1635 with a corrected version appearing in 1653. Cavalieri first used polar coordinates to solve a problem relating to the area within an Archimedean spiral. Blaise Pascal subsequently used polar coordinates to calculate the length of parabolic arcs. In the journal Acta Eruditorum, Jacob Bernoulli used a system with a point on a line, called the pole and polar axis respectively. Coordinates were specified by the distance from the pole and the angle from the polar axis.
Polar coordinate system
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Hipparchus
Polar coordinate system
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Points in the polar coordinate system with pole O and polar axis L. In green, the point with radial coordinate 3 and angular coordinate 60 degrees or (3,60°). In blue, the point (4,210°).
Polar coordinate system
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A planimeter, which mechanically computes polar integrals
152.
Real number
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In mathematics, a real number is a value that represents a quantity along a line. The adjective real in this context was introduced by Descartes, who distinguished between real and imaginary roots of polynomials. The real numbers include all the rational numbers, such as the fraction 4/3, all the irrational numbers, such as √ 2. Included within the irrationals are the transcendental numbers, such as π. Complex numbers include real numbers. These descriptions of the real numbers are not sufficiently rigorous by the modern standards of pure mathematics. All these definitions are thus equivalent. Around 500 BC, the Greek mathematicians led by Pythagoras realized the need in particular the irrationality of the square root of 2. Arabic mathematicians merged the concepts of "number" and "magnitude" into a more general idea of real numbers. In the 17th century, Descartes introduced the term "real" to describe roots of a polynomial, distinguishing them from "imaginary" ones. In the 19th centuries, there was much work on irrational and transcendental numbers. Évariste Galois developed techniques for determining whether a given equation could be solved by radicals, which gave rise to the field of Galois theory. Charles Hermite first proved that e is transcendental, Ferdinand von Lindemann, showed that π is transcendental. Lindemann's proof has finally been made elementary by Adolf Hurwitz and Paul Gordan. The development of calculus in the 18th century used the entire set of real numbers without having defined them cleanly.
Real number
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A symbol of the set of real numbers (ℝ)
153.
Curve
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In mathematics, a curve is, generally speaking, an object similar to a line but that need not be straight. Thus, a curve is a generalization of a line, in that curvature is not necessarily zero. Various disciplines within mathematics have given different meanings depending on the area of study, so the precise meaning depends on context. However, many of these meanings are special instances of the definition which follows. A curve is a topological space, locally homeomorphic to a line. A simple example of a curve is the parabola, shown to the right. A large number of other curves have been studied in mathematical fields. Closely related meanings include the graph of a two-dimensional graph. Interest in curves began long before they were the subject of mathematical study. This can be seen on everyday objects dating back to prehistoric times. Curves, or at least their graphical representations, are simple to create, by a stick in the sand on a beach. Historically, the term "line" was used in place of the more modern term "curve". Hence "right line" were used to distinguish what are today called lines from "curved lines". Euclid's idea of a line is perhaps clarified by the statement "The extremities of a line are points,". Later commentators further classified lines according to various schemes.
Curve
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Megalithic art from Newgrange showing an early interest in curves
Curve
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A parabola, a simple example of a curve
154.
Point (geometry)
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In modern mathematics, a point refers usually to an element of some set called a space. More specifically, in Euclidean geometry, a point is a primitive notion upon which the geometry is built. Being a primitive notion means that a point cannot be defined in terms of previously defined objects. That is, a point is defined only by some properties, called axioms, that it must satisfy. In particular, the geometric points do not have any length, area, any other dimensional attribute. A common interpretation is that the concept of a point is meant to capture the notion of a unique location in Euclidean space. Points, considered within the framework of Euclidean geometry, are one of the most fundamental objects. Euclid originally defined the point as "that which has no part". Further generalizations are represented by an ordered tuplet of n terms, where n is the dimension of the space in which the point is located. Many constructs within Euclidean geometry consist of an infinite collection of points that conform to certain axioms. Similar constructions exist that define the plane, other related concepts. By the way, a degenerate segment consists of only one point. In spite of this, modern expansions of the system serve to remove these assumptions. There are several inequivalent definitions of dimension in mathematics. In all of the common definitions, a point is 0-dimensional.
Point (geometry)
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Projecting a sphere to a plane.
155.
Circumscribe
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In geometry, the circumscribed circle or circumcircle of a polygon is a circle which passes through all the vertices of the polygon. The center of this circle is called the circumcenter and its radius is called the circumradius. A polygon which has a circumscribed circle is called a cyclic polygon. All regular simple polygons, all rectangles are cyclic. A related notion is the one of a minimum bounding circle, the smallest circle that completely contains the polygon within it. All triangles are cyclic; i.e. every triangle has a circumscribed circle. Since this equation has three parameters only three points' coordinate pairs are required to determine the equation of a circle. Since a triangle is defined by its three vertices, exactly three points are required to determine a circle, every triangle can be circumscribed. The circumcenter of a triangle can be constructed by drawing any two of the three perpendicular bisectors. The center is the point where the perpendicular bisectors intersect, the radius is the length to any of the three vertices. In coastal navigation, a triangle's circumcircle is sometimes used as a way of obtaining a position line using a sextant when no compass is available. The horizontal angle between two landmarks defines the circumcircle upon which the observer lies. Suppose that A = B = C = are the coordinates of points A, B, C. Using the polarization identity, these equations reduce to the condition that the matrix has a nonzero kernel. Thus the circumcircle may alternatively be described as the locus of zeros of the determinant of this matrix: det = 0.
Circumscribe
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Circumscribed circle, C, and circumcenter, O, of a cyclic polygon, P
156.
Diameter
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It can also be defined as the longest chord of the circle. Both definitions are also valid for the diameter of a sphere. The word "diameter" is derived from Greek διάμετρος, "diameter of a circle", from δια -, "across, through" "measure". It is often abbreviated DIA, dia, ⌀. In more modern usage, the length of a diameter is also called the diameter. D = 2 r r = d 2. Both quantities can be calculated efficiently using rotating calipers. For an ellipse, the standard terminology is different. A diameter of an ellipse is any chord passing through the midpoint of the ellipse. The longest diameter is called the major axis. The definitions given above are only valid for circles, convex shapes. So, if A is the subset, the diameter is sup. If the distance function d is viewed here as having R, this implies that the diameter of the empty set equals − ∞. In geometry, the diameter is an important global Riemannian invariant. The variable for diameter, ⌀, is similar in size and design to ø, the Latin small letter o with stroke.
Diameter
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Circle with circumference (C) in black, diameter (D) in cyan, radius (R) in red, and centre or origin (O) in magenta.
157.
Cross section (geometry)
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In geometry and science, a cross section is the intersection of a body in three-dimensional space with a plane, or the analog in higher-dimensional space. Cutting an object into slices creates many parallel cross sections. A cross section of a polyhedron is a polygon. If instead the cross section is taken for a fixed value of the density, the result is an iso-density contour. For the normal distribution, these contours are ellipses. A cross section can be used to visualize the partial derivative of a function with respect to one of its arguments, as shown at left. Suppose z = f. In economics, a production function f specifies the output that can be produced by various quantities x and y of inputs, typically labor and physical capital. The production function of a firm or a society can be plotted in three-dimensional space. Cross sections are often used in anatomy to illustrate the inner structure of an organ, as shown at left. Cavalieri's principle states that solids with corresponding cross sections of equal areas have equal volumes. The cross-sectional area of an object when viewed from a particular angle is the total area of the orthographic projection of the object from that angle. A sphere of radius r has A ′ = π r 2 when viewed from any angle. For a convex body, each ray through the object from the viewer's perspective crosses just two surfaces. Descriptive geometry Exploded view drawing Graphical projection Plans
Cross section (geometry)
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Pinus taeda cross section showing annual rings, Cheraw, South Carolina.
158.
Cone (geometry)
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A cone is a three-dimensional geometric shape that tapers smoothly from a flat base to a point called the apex or vertex. If the enclosed points are included in the base, the cone is a solid object; otherwise it is a two-dimensional object in three-dimensional space. In the case of line segments, the cone does not extend beyond the base, while in the case of half-lines, it extends far. In the case of lines, the cone extends far in both directions from the apex, in which case it is sometimes called a double cone. Either half of a double cone on one side of the apex is called a nappe. The axis of a cone is the straight line, passing through the apex, about which the base has a circular symmetry. If the base is right circular the intersection of a plane with this surface is a conic section. In general, the apex may lie anywhere. Contrasted with right cones are oblique cones, in which the axis passes through the centre of the base non-perpendicularly. A cone with a polygonal base is called a pyramid. Depending on the context, "cone" may also mean specifically a projective cone. Cones can also be generalized to higher dimensions. The "radius" of a circular cone is the radius of its base; often this is simply called the radius of the cone. An "elliptical cone" is a cone with an elliptical base. A "generalized cone" is the surface created by the set of lines passing on a boundary.
Cone (geometry)
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In projective geometry, a cylinder is simply a cone whose apex is at infinity, which corresponds visually to a cylinder in perspective appearing to be a cone towards the sky.
Cone (geometry)
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A right circular cone and an oblique circular cone
159.
On Floating Bodies
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It is the known work on hydrostatics, of which Archimedes is recognized as the founder. It contains the first statement of what is now known as Archimedes' principle. Archimedes lived in the Greek city-state of Syracuse, Sicily. He is credited with calculating the underlying mathematics of the lever. A leading scientist of Archimedes also developed elaborate systems of pulleys to move large objects with a minimum of effort. His machines of war helped to hold back the armies of Rome in the First Punic War. The only known copy of "On Floating Bodies" in Greek comes from the Archimedes Palimpsest. Archimedes proves that water will adopt a spherical form around a center of gravity. This may have been an attempt at explaining the theory of Greek astronomers such as Eratosthenes that the Earth is round. Further, Proposition 5 of Archimedes' treatise On Floating Bodies states that: Any floating object displaces its own weight of fluid. This concept has come to be referred to by some as the principle of flotation. The second book rarely equaled since. It is restricted to the case when the base of the paraboloid lies either entirely above or entirely below the fluid surface. Archimedes' investigation of paraboloids was probably an idealization of the shapes of ships' hulls. Some of his sections float with the base above water similar to the way that icebergs float.
On Floating Bodies
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a page from Floating Bodies, Archimedes Palimpsest
160.
Ratio
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In mathematics, a ratio is a relationship between two numbers indicating how many times the first number contains the second. For example, if a bowl of fruit contains six lemons, then the ratio of oranges to lemons is eight to six. Thus, a ratio can be a fraction as opposed to a whole number. Also, the ratio of oranges to the total amount of fruit is 8:14. The numbers compared in a ratio can be any quantities such as objects, persons, lengths, or spoonfuls. A ratio is written "a to b" or a:b, or sometimes expressed arithmetically as a quotient of the two. When the two quantities have the same units, as is often the case, their ratio is a dimensionless number. A rate is a quotient of variables having different units. But in many applications, the ratio is often used instead for this more general notion as well. B being the consequent. The proportion expressing the equality of the ratios A:B and C:D is written A:B = C:D or A:B::C:D. B and C are called the means. The equality of three or more proportions is called a continued proportion. Ratios are sometimes used with three or more terms. The ratio of the dimensions of a "two by four", ten inches long is 2:4:10.
Ratio
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The ratio of width to height of standard-definition television.
161.
Ostomachion
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Ostomachion, also known as loculus Archimedius and also as syntomachion, is a mathematical treatise attributed to Archimedes. This work has survived fragmentarily in a copy of the original ancient Greek text made in Byzantine times. The Ostomachion has as its roots in the Greek Ὀστομάχιον, which means "bone-fight", from ὀστέον, "bone" and μάχη, "fight, battle, combat". Note that the manuscripts refer to an apparent corruption of the original Greek. Ausonius gives the correct name "Ostomachion". The Ostomachion which he describes was played perhaps by several persons with pieces made of bone. It is not known, older, the game. Victorinus, Bassus Ennodius and Lucretius have talked about the game too. The game is a 14-piece puzzle forming a square. Another suggestion is that it developed memory skills in the young. Archimedis opera omnia, vol. "In Archimedes' Puzzle, a New Eureka Moment." The New York Times. December 14, 2003 A tour of Archimedes' Stomachion, by Fan Chung and Ronald Graham. Ostomachion and others tangram Play with 38 Tangram games online: more that 7,300 shapes proposed by the program.
Ostomachion
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Ostomachion (after Suter): square reformed with some pieces turned over
Ostomachion
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Ostomachion (after Suter; this version requires a lateral stretch by a factor of two to match that in the Archimedes Palimpsest)
162.
Dissection puzzle
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The creation of new dissection puzzles is also considered to be a type of puzzle. Puzzles may include various restraints, such as pieces that can fold, or pieces that can twist. Dissection puzzles are an early form of geometric puzzle. Ancient dissection puzzles were used as graphic depictions of the Pythagorean theorem. In the 10th century, Arabic mathematicians used geometric dissections on Euclid's Elements. In the 18th century, Chinese scholar Tai Chen described an elegant dissection for approximating the value of π. The puzzles saw a major increase in general popularity in the 19th century when newspapers and magazines began running dissection puzzles. Puzzle creators Sam Loyd in the United Kingdom were among the most published. Some types of puzzle are intended to create a large number of different geometric shapes. The tangram is a popular puzzle of this type. Some geometric forms are easy to create, while others present an extreme challenge. This variability has ensured the puzzle's popularity. Other dissections are intended to move between a pair of geometric shapes, such as a triangle to a square, or a square to a five-pointed star. A puzzle of this description is the haberdasher's problem, proposed in 1907 by Henry Dudeney. The puzzle is a dissection of a triangle to a square, in only four pieces.
Dissection puzzle
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Ostomachion is a dissection puzzle attributed to Archimedes
163.
Tangram
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The tangram is a dissection puzzle consisting of seven flat shapes, called tans, which are put together to form shapes. The objective of the puzzle is to form a specific shape using all seven pieces, which may not overlap. It became very popular in Europe for a time then again during World War I. It is one of the most popular dissection puzzles in the world. A Chinese psychologist has albeit one made for entertainment rather than for analysis. The origin of the word'tangram' is unclear. The'-gram' element is apparently from Greek γράμμα'letter'. The'tan-' element is variously conjectured to be from Chinese t'an'to extend' or Cantonese t'ang'Chinese'. When it docked in Canton, the captain was given a pair of Sang-Hsia-koi's Tangram books from 1815. They were then brought to Philadelphia, where it docked in February 1816. The first Tangram book to be published in America was based on the pair brought by Donnaldson. The book included 700 shapes, some of which are possible to solve. The puzzle eventually reached England, where it became very fashionable indeed. The craze quickly spread to European countries. This was mostly Key.
Tangram
–
Like most modern sets, this wooden tangram is stored in the square configuration.
Tangram
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A caricature published in France in 1818, when the Tangram craze was at its peak. The caption reads: " 'Take care of yourself, you're not made of steel. The fire has almost gone out and it is winter.' 'It kept me busy all night. Excuse me, I will explain it to you. You play this game, which is said to hail from China. And I tell you that what Paris needs right now is to welcome that which comes from far away.' "
Tangram
–
Cover art from The 8th Book of Tan, by Sam Loyd, a spoof of the puzzle's history that began the Tangram Craze in the Western World
164.
Stanford University
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Stanford University, officially Leland Stanford Junior University, is a private research university in Stanford, California, adjacent to Palo Alto and between San Jose and San Francisco. Its 8,180-acre campus is one of the largest in the United States. Stanford also has land and facilities elsewhere. Stanford was a former Governor of California and U.S. Senator; he made his fortune as a railroad tycoon. The school admitted its first students 125 years ago on October 1, 1891, as a coeducational and non-denominational institution. Stanford University struggled financially after Leland Stanford's death in 1893 and again after much of the campus was damaged by the 1906 San Francisco earthquake. Following World War II, Provost Frederick Terman supported faculty and graduates' entrepreneurialism to build self-sufficient local industry in what would later be known as Silicon Valley. The rise of Silicon Valley helped Stanford become one of the world's most prestigious universities. There are three academic schools that have both undergraduate and graduate students and another four professional schools. Students compete in 36 varsity sports, the university is one of two private institutions in the Division I FBS Pac-12 Conference. It is the alma mater of 30 living billionaires, 17 astronauts, 20 Turing Award laureates. It is also one of the leading producers of members of the United States Congress. Seven Fields Medalists have been affiliated as alumni, staff. Stanford University was founded in 1885 by Leland and Jane Stanford, dedicated to Leland Stanford Jr, their only child.
Stanford University
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Leland Stanford, the university's founder, as painted by Jean-Louis-Ernest Meissonier in 1881 and now on display at the Cantor Center
Stanford University
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Seal of Stanford University
Stanford University
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Statue of the Stanford family, by Larkin G. Mead (1899)
Stanford University
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The ruins of the unfinished Stanford Library after the 1906 San Francisco earthquake
165.
Combinatorics
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Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Many combinatorial questions have historically been considered in isolation, giving an ad hoc solution to a problem arising in some mathematical context. In the later twentieth century, however, powerful and general theoretical methods were developed, making combinatorics into an independent branch of mathematics in its own right. One of the oldest and most accessible parts of combinatorics is graph theory, which also has numerous natural connections to other areas. Combinatorics is used frequently in computer science to obtain formulas and estimates in the analysis of algorithms. A mathematician who studies combinatorics is called a combinatorialist or a combinatorist. Basic combinatorial concepts and enumerative results appeared throughout the ancient world. Greek historian Plutarch discusses an argument between Chrysippus and Hipparchus of a rather delicate enumerative problem, later shown to be related to Schröder–Hipparchus numbers. In the Ostomachion, Archimedes considers a tiling puzzle. In the Middle Ages, combinatorics continued to be studied, largely outside of the European civilization. Later, in Medieval England, campanology provided examples of what is now known as Hamiltonian cycles in certain Cayley graphs on permutations. During the Renaissance, together with the rest of mathematics and the sciences, combinatorics enjoyed a rebirth. Works of Pascal, Newton, Jacob Bernoulli and Euler became foundational in the emerging field. In modern times, the works of J. J. Sylvester and Percy MacMahon helped lay the foundation for enumerative and algebraic combinatorics. Graph theory also enjoyed an explosion of interest at the same time, especially in connection with the four color problem.
Combinatorics
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An example of change ringing (with six bells), one of the earliest nontrivial results in Graph Theory.
166.
Ancient Greek
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Ancient Greek includes the forms of Greek used in ancient Greece and the ancient world from around the 9th century BC to the 6th century AD. It is often roughly divided into the Archaic period, Hellenistic period. It is antedated by Mycenaean Greek. The language of the Hellenistic phase is known as Koine. Prior to the Koine period, Greek of earlier periods included several regional dialects. Ancient Greek was the language of Homer and of classical Athenian historians, philosophers. It has been a standard subject of study in educational institutions of the West since the Renaissance. This article primarily contains information of the language. Ancient Greek was a pluricentric language, divided into many dialects. The main dialect groups are Doric, many of them with several subdivisions. Some dialects are found in literary forms used in literature, while others are attested only in inscriptions. There are also historical forms. Homeric Greek is a literary form of Archaic Greek used by other authors. Homeric Greek had significant differences in pronunciation from Classical Attic and other Classical-era dialects. The early form and development of the Hellenic language family are not well understood because of a lack of contemporaneous evidence.
Ancient Greek
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Inscription about the construction of the statue of Athena Parthenos in the Parthenon, 440/439 BC
Ancient Greek
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Ostracon bearing the name of Cimon, Stoa of Attalos
Ancient Greek
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The words ΜΟΛΩΝ ΛΑΒΕ as they are inscribed on the marble of the 1955 Leonidas Monument at Thermopylae
167.
Ausonius
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Decimius Magnus Ausonius was a Roman poet and teacher of rhetoric from Burdigala in Aquitaine, modern Bordeaux, France. For a time he was tutor to the future Gratian, who afterwards bestowed the consulship on him. His best-known poems are Mosella, Ephemeris, an account of a typical day in his life. His other verses show his concern for his family, friends, teachers, circle of well-to-do acquaintances and his delight in the technical handling of meter. Ausonius was given a strict upbringing by his grandmother, both named Aemilia. He received an excellent education at Toulouse, where his maternal uncle, Aemilius Magnus Arborius, was a professor. Ausonius professed that his progress in Greek was unsatisfactory. When his uncle was summoned to Constantinople to tutor one of the sons of emperor Constantine I, Ausonius accompanied him to the capital. He preferred teaching. In 334 he became a ` grammaticus' at a school of rhetoric in Bordeaux, afterwards professor. His teaching attracted many pupils, some of whom became eminent in public life. His most famous pupil was the poet Paulinus, who later became a Christian and Bishop of Nola. After thirty years of this work Ausonius was summoned by emperor Valentinian I to teach Gratian, the heir-apparent. When Valentinian took Gratian on the German campaigns of 368-9, Ausonius accompanied them. In recognition of his services emperor Valentinian bestowed on Ausonius the rank of quaestor.
Ausonius
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Monument to Ausonius in Milan.
Ausonius
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Ausonius, Bordeaux
Ausonius
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Modern reconstruction of Sutter's Mill, a water-powered 19th century Californian sawmill.
168.
Gotthold Ephraim Lessing
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Gotthold Ephraim Lessing was a German writer, philosopher, dramatist, publicist and art critic, one of the most outstanding representatives of the Enlightenment era. Theoretical writings substantially influenced the development of German literature. He is widely considered by theatre historians to be the first dramaturg in his role at Abel Seyler's Hamburg National Theatre. Lessing was born to Johann Gottfried Lessing and Justine Salome Feller. His father wrote on theology. Young Lessing studied from 1737 to 1741. With a father who wanted his son to follow in his footsteps, Lessing next attended the Fürstenschule St. Afra in Meissen. After completing his education at St. Afra's, he enrolled at the University of Leipzig where he pursued a degree in medicine, philosophy, philology. It was here that his relationship with a famous German actress, began. His interest in theatre grew. During this time, he wrote The Young Scholar. Neuber eventually produced the play in 1748. From 1748 to 1760, Lessing lived in Leipzig and Berlin. He began to work as a editor for the Vossische Zeitung and other periodicals. Lessing decided to follow him to Berlin.
Gotthold Ephraim Lessing
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Lessing, 1771
Gotthold Ephraim Lessing
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Portrait of Lessing by Anna Rosina Lisiewska during his time as dramaturg of Abel Seyler 's Hamburg National Theatre (1767/1768)
Gotthold Ephraim Lessing
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Eva Lessing
Gotthold Ephraim Lessing
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Home, Wolfenbüttel
169.
The Cattle of Helios
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In Greek mythology, the Cattle of Helios pastured on the island of Thrinacia, believed to be modern Sicily. Helios, also known as the god, is said to have had 7 herds of oxen and seven flocks of sheep, each numbering fifty head. In the Odyssey, Homer describes these immortal cattle as handsome, wide-browed, curved-horned. Circe both warn Odysseus to shun the isle of Helios. They are held by an unfavorable storm sent by Poseidon. When he returns to the ship, Odysseus rebukes his companions for disobeying his orders. But it is too late, the cattle are dead and gone. Lampetie tells Helios that Odysseus' men have slain his cattle. In turn, Helios begs the other gods to take vengeance on Odysseus' men. Zeus promises Helios to cleave it in pieces in the midst of the ocean. Soon the gods show wonders to the Odysseus' men. There is a sound like the voice of cattle. For six days, Odysseus's company feast on the kine of Helios. On the seventh day, the wind changes. After they set sail, Zeus keeps the ship is destroyed by lightning during a storm.
The Cattle of Helios
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Greek Mythology
170.
Diophantine equation
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In mathematics, a Diophantine equation is a polynomial equation, usually in two or more unknowns, such that only the integer solutions are sought or studied. A linear Diophantine equation is an equation between two sums of monomials of degree zero or one. An exponential Diophantine equation is one in which exponents on terms can be unknowns. Diophantine problems have fewer equations than unknown variables and involve finding integers that work correctly for all equations. In more technical language, they define an algebraic curve, algebraic surface, or more general object, ask about the lattice points on it. The mathematical study of Diophantine problems that Diophantus initiated is now called Diophantine analysis. Proof: If d is this greatest common divisor, Bézout's identity asserts the existence of integers e and f such that ae + bf = d. If c is a multiple of d, then c = dh for some integer h, is a solution. For every pair of integers x and y, the greatest common d of a and b divides ax + by. Thus, if the equation has a solution, then c must be a multiple of d. Finally, given two solutions such that ax1 + by1 = ax2 + by2 = c, one deduces that u + v = 0. Therefore, x2 = x1 + kv and y2 = y1 − ku, which completes the proof. The system to be solved may thus be rewritten as B = UC. If this condition is fulfilled, the solutions of the given system are V, where hk+1... hn are arbitrary integers. Hermite normal form may also be used for solving systems of linear Diophantine equations.
Diophantine equation
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Finding all right triangles with integer side-lengths is equivalent to solving the Diophantine equation.
171.
Square number
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For example, 9 is a square number, since it can be written as × 3. The equivalent exponentiation n2, usually pronounced as "n squared". The name square number comes from the name of the shape; see below. Square numbers are non-negative. Another way of saying that a integer is a square number, is that its square root is again an integer. For √ 9 = 3, so 9 is a square number. A positive integer that has no square divisors except 1 is called square-free. For a non-negative n, the nth square number is n2, with 02 = 0 being the zeroth one. The concept of square can be extended to some other number systems. Starting with 1, there are ⌊√m⌋ square numbers up to and including m, where the expression ⌊x⌋ represents the floor of the number x. Hence, a square with side length n has area n2. The expression for the square number is n2. The formula follows: n 2 = ∑ k = 1 n. So for example, 52 25 = 1 + 3 + 5 + 7 + 9. There are several recursive methods for computing square numbers.
Square number
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m = 1 2 = 1
172.
Heliocentrism
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Heliocentrism, or heliocentricism, is the astronomical model in which the Earth and planets revolve around the Sun at the center of the Solar System. The word comes from the Greek. Historically, Heliocentrism was opposed to geocentrism, which placed the Earth at the center. In the following century, Galileo Galilei presented supporting observations made using a telescope. However, with more scrutiny one will observe more complicated movements. The Ptolemaic system was a astronomical system that managed to calculate the positions for the planets to a fair degree of accuracy. However, he rejected the idea of a spinning earth as absurd as he believed it would create huge winds. His planetary hypotheses were sufficiently real that the distances of sun, planets and stars could be determined by treating orbits' celestial spheres as contiguous realities. The stars were stationary. The Earth maintained the hidden face towards the central fire, rendering both it and the "counter-earth" invisible from Earth. Kepler gave an alternative explanation of the Pythagoreans' "central fire" as the Sun, "as most sects purposely hid their teachings". Heraclides of Pontus said that the rotation of the Earth explained the daily motion of the celestial sphere. It used to be thought that he believed Mercury and Venus to revolve around the Sun, which in turn revolves around the Earth. The first person known to have proposed a heliocentric system, however, was Aristarchus of Samos. Like Eratosthenes, Aristarchus measured the size and distance of the Moon and Sun, in a treatise which has survived.
Heliocentrism
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Andreas Cellarius 's illustration of the Copernican system, from the Harmonia Macrocosmica (1708).
Heliocentrism
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Aristarchus's 3rd century BC calculations on the relative sizes of the Earth, Sun and Moon, from a 10th-century CE Greek copy
Heliocentrism
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Nicholas of Cusa, 15th century, asked whether there was any reason to assert that any point was the center of the universe.
Heliocentrism
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An illustration from al-Biruni 's astronomical works, explains the different phases of the moon, with respect to the position of the sun. Al-Biruni suggested that if the Earth rotated on its axis this would be consistent with astronomical theory. He discussed heliocentrism but considered it a problem of natural philosophy.
173.
Solar System
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The Solar System is the gravitationally bound system comprising the Sun and the objects that orbit it, either directly or indirectly. Of the objects that orbit the Sun indirectly, the moons, two are larger than Mercury. The Solar System formed billion years ago from the gravitational collapse of a giant interstellar molecular cloud. The vast majority of the system's mass is with most of the remaining mass contained in Jupiter. Mercury, Venus, Earth and Mars, are terrestrial planets, being primarily composed of rock and metal. The four outer planets are giant planets, being substantially more massive than the terrestrials. All planets have almost circular orbits that lie within a nearly flat disc called the ecliptic. The Solar System also contains smaller objects. The asteroid belt, which lies between the orbits of Mars and Jupiter, mostly contains objects composed, of rock and metal. Within these populations are several dozen to possibly tens of thousands of objects large enough that they have been rounded by their own gravity. Such objects are categorized as dwarf planets. Identified dwarf planets include Pluto and Eris. In addition to these two regions, various small-body populations, including comets, centaurs and interplanetary dust clouds, freely travel between regions. Each of the outer planets is encircled by planetary rings of dust and small objects. A stream of charged particles flowing outwards from the Sun, creates a bubble-like region in the interstellar medium known as the heliosphere.
Solar System
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The Sun and planets of the Solar System (distances not to scale)
Solar System
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Solar System
Solar System
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Andreas Cellarius 's illustration of the Copernican system, from the Harmonia Macrocosmica (1660)
Solar System
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The eight planets of the Solar System (by decreasing size) are Jupiter, Saturn, Uranus, Neptune, Earth, Venus, Mars and Mercury.
174.
Aristarchus of Samos
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Like Anaxagoras before him, he suspected that the stars were just other bodies like the Sun, albeit further away from Earth. His astronomical ideas were often rejected in favor of the incorrect geocentric theories of Aristotle and Ptolemy. Copernicus had attributed the heliocentric theory to Aristarchus. This is the common account as you have heard from astronomers. Since stellar parallax is only detectable with telescopes, his accurate speculation was unprovable at the time. It is a common misconception that the heliocentric view was held as sacrilegious by the contemporaries of Aristarchus. This is due to Gilles Ménage's translation of a passage from Plutarch's On the Apparent Face in the Orb of the Moon. The resulting misconception of an isolated and persecuted Aristarchus is still transmitted today. Still, no stellar parallax was observed, Plato, Aristotle and Ptolemy preferred the geocentric model, held as true throughout the Middle Ages. The heliocentric theory was successfully revived by Copernicus, after which Johannes Kepler described planetary motions with greater accuracy with his three laws. Isaac Newton later gave a theoretical explanation based on laws of gravitational attraction and dynamics. The only surviving work usually attributed to Aristarchus, On the Sizes and Distances of the Sun and Moon, is based on a geocentric world view. The discrepancy may come from a misinterpretation of what unit of measure was meant by a certain Greek term in Aristarchus' text. Aristarchus claimed that at half moon, the angle between the Sun and Moon was 87°. Aristarchus is known to have also studied light and vision.
Aristarchus of Samos
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Statue of Aristarchos of Samos at the Aristotle University of Thessaloniki
Aristarchus of Samos
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Aristarchus's 3rd-century BC calculations on the relative sizes of (from left) the Sun, Earth and Moon, from a 10th-century AD Greek copy
175.
The Method of Mechanical Theorems
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The Method of Mechanical Theorems, also referred to as The Method, is one of the major surviving works of Archimedes of Syracuse. In 1906 was rediscovered in the celebrated Archimedes Palimpsest. In these treatises, he proves the same theorems by exhaustion, finding upper lower bounds which both converge to the answer required. Nevertheless, the mechanical method was what he used to discover the relations for which he later gave rigorous proofs. His idea is to use the law of the lever to determine the areas of figures from the known center of mass of other figures. The simplest example in modern language is the area of the parabola. The idea is to mechanically balance the parabola with a certain triangle, made of the same material. The parabola is the region in the x-y plane between the x-axis and = x2 as x varies from 0 to 1. The triangle is the region in the line y = x, also as x varies from 0 to 1. Slice the parabola and triangle into vertical slices, one for each value of x. Imagine that the x-axis is a lever, with a fulcrum at x = 0. Since each pair of slices balances, moving the whole parabola to x = 1 would balance the whole triangle. The center of mass of a triangle can be easily found by the following method, also due to Archimedes. So the center of mass of a triangle must be at the point of the medians. For the triangle in question, one median is the line y = x/2, while a second median is the line y = 1 − x.
The Method of Mechanical Theorems
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Contents
176.
Book of Lemmas
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The Book of Lemmas is a book attributed to Archimedes by Thābit ibn Qurra, though the authorship of the book is questionable. It consists of fifteen propositions on circles. The Book of Lemmas was first introduced by Thābit ibn Qurra; he attributed the work to Archimedes. In 1661, the Arabic manuscript was edited by Giovanni A. Borelli. The Latin version was published under the name Liber Assumptorum. T. L. Heath translated Heiburg's Latin work in his The Works of Archimedes. Another possibility is that the Book of Lemmas may be a collection of propositions by Archimedes later collected by a Greek writer. The Book of Lemmas introduces new geometrical figures. Archimedes' first introduced the arbelos in proposition four of his book: The figure is used through eight. Archimedes' first introduced the salinon in proposition fourteen of his book: Archimedes proved that the circle are equal in area. If two circles touch at A, if CD, EF be parallel diameters in them, ADF is a straight line. If now DE be drawn perpendicular if AT, DE meet in F, then DF = FE. Let P let PN be perpendicular to AB. Take D on AB so that AN = ND. If now PQ be an arc equal to the arc PA, BQ be joined, then BQ, BD shall be equal.
Book of Lemmas
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The first page of the Book of Lemmas as seen in The Works of Archimedes (1897).
177.
Arabic language
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Arabic is a Central Semitic language, first spoken in Iron Age northwestern Arabia and is now the lingua franca of the Arab world. Some of the spoken varieties are mutually unintelligible, both written and orally, the varieties as a whole constitute a sociolinguistic language. If considered separate languages, the most-spoken variety would most likely be Egyptian Arabic with million native speakers -- still greater than any Afroasiatic language. Arabic also is a liturgical language of 1.6 billion Muslims. It is one of six official languages of the United Nations. The modern written language is derived from the language of the Quran. It is used to varying degrees in workplaces, the media. The two formal varieties are grouped together as Literary Arabic, the official language of 26 states and the liturgical language of Islam. Modern Standard Arabic largely follows the grammatical standards of Quranic Arabic and uses much of the same vocabulary. Much of the new vocabulary is used to denote concepts that have arisen in the post-Quranic era, especially in modern times. Arabic has influenced many languages around the globe throughout its history. During the Middle Ages, Literary Arabic was a major vehicle of culture in Europe, especially in philosophy. As a result, many European languages have also borrowed many words from it. Many words of Arabic origin are also found in ancient languages like Latin and Greek. Balkan languages, including Greek, have also acquired a significant number of Arabic vocabulary through contact with Ottoman Turkish.
Arabic language
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The Galland Manuscript of One Thousand and One Nights, 14th century
Arabic language
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al-ʿArabiyyah in written Arabic (Naskh script)
Arabic language
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Bilingual traffic sign in Qatar.
Arabic language
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Examples of how the Arabic root and form system works.
178.
Heron's formula
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Let △ ABC be the triangle with sides a = 4, c = 15. In this example, the side lengths and area are all integers, making a Heronian triangle. However, Heron's formula works well in cases where one or all of these numbers is not an integer. The formula is credited to Heron of Alexandria, a proof can be found in his book, Metrica, written c. AD 60. It was published in Shushu Jiuzhang, published in 1247. Heron's original proof made use of cyclic quadrilaterals, while other arguments appeal to trigonometry as to the incenter and one excircle of the triangle. A modern proof, quite unlike the one provided by Heron, follows. Let a, b, c be the sides of the triangle and α, β, γ the angles opposite those sides. The difference of two squares factorization was used in two different steps. The following proof is very similar to one given by Raifaizen. By the Pythagorean theorem we have a2 = h2 + 2 according to the figure at the right. Subtracting these yields a2 − b2 = − 2cd. Heron's formula as given above is numerically unstable for triangles with a very small angle when using floating arithmetic. A stable alternative involves arranging the lengths of the sides so that computing A = 1 4.
Heron's formula
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A triangle with sides a, b, and c.
179.
Hero of Alexandria
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Heron of Alexandria was a Greek mathematician and engineer, active in his native city of Alexandria, Roman Egypt. His work is representative of the Hellenistic scientific tradition. Heron published a well recognized description of a steam-powered device called an aeolipile. Among his most famous inventions was a windwheel, constituting the earliest instance of wind harnessing on land. He is said to have been a follower of the atomists. Some of his ideas were derived from the works of Ctesibius. Some of his works were preserved in Arabic manuscripts. Heron described the construction of the aeolipile, the first-recorded steam engine. It was created almost two millennia before the industrial revolution. Some historians have conflated the two inventions to assert that the aeolipile was capable of useful work. This was included in his list of inventions in his book Optics. When the coin was deposited, it fell upon a pan attached to a lever. The lever opened up a valve which let some flow out. An organ, marking the first instance of wind powering a machine in history. The sound of thunder was produced onto a hidden drum.
Hero of Alexandria
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Hero's wind-powered organ (reconstruction)
Hero of Alexandria
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Hero
180.
Johan Ludvig Heiberg (historian)
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Johan Ludvig Heiberg was a Danish philologist and historian. He also published an edition of Ptolemy's Almagest. Heiberg was born in Aalborg, the son of Johanne Henriette Jacoba and Emil Theodor Heiberg. Heiberg was Professor of Classical Philology at the University of Copenhagen from 1896 until 1924. Among his more than 200 publications were editions of the works of Archimedes, Euclid, Apollonius of Perga, Serenus of Antinouplis, Ptolemy, Hero of Alexandria. Many of his editions are still in use today. The French Academy of Sciences awarded him the Prix Binoux for 1912. Heiberg inspected the vellum manuscript in Constantinople in 1906, realized that it contained mathematical works by Archimedes that were unknown to scholars at the time. Heiberg's examination of the manuscript was with the naked eye only, while modern analysis of the texts has employed x-ray and ultraviolet light. The Archimedes Palimpsest is currently stored at the Walters Art Museum in Baltimore, Maryland. His sister married biochemist Max Henius. How do we know about Greek mathematicians? Eureka! 1,000-year-old text by Greek maths genius Archimedes goes on display Daily Mail, October 18, 2011. Works by Johan Ludvig Heiberg at Project Gutenberg Works by or about Johan Ludvig Heiberg at Internet Archive
Johan Ludvig Heiberg (historian)
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J. L. Heiberg
181.
Constantinople
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Constantinople was the capital city of the Roman/Byzantine Empire, also of the brief Latin, the later Ottoman empires. Constantinople was famed for its massive and complex defences. The first wall of the city was surrounded the city on both sea fronts. Constantinople never truly recovered from the devastation of the Fourth Crusade and the decades of misrule by the Latins. The founding myth of the city has it told that the settlement was named after the leader of the Megarian colonists, Byzas. During this time, the city was also called Roma Constantinopolitana. In the language of other peoples, Constantinople was referred to just as reverently. The medieval Vikings, who had contacts with the empire through their expansion in eastern Europe used the Old Norse name Miklagarðr, later Miklagard and Miklagarth. In Arabic, the city was sometimes called Rūmiyyat al-kubra and in Persian as Takht-e Rum. This was presumably a calque on a Greek phrase such as Βασιλέως Πόλις,'the city of the emperor'. The Turkish name for İstanbul, derives from the Greek phrase eis tin polin, meaning "into the city" or "to the city". In 1928, the Turkish alphabet was changed from Arabic script to Latin script. In time the city came to be known as Istanbul and its variations in most world languages. In Greece today, the city is still called Konstantinoúpolis/Konstantinoúpoli or simply just "the City". Apart from this, little is known about this initial settlement, except that it was abandoned by the time the Megarian colonists settled the site anew.
Constantinople
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Constantinople in the Byzantine era
Constantinople
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Map of Byzantine Constantinople
Constantinople
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Emperor Constantine I presents a representation of the city of Constantinople as tribute to an enthroned Mary and Christ Child in this church mosaic. Hagia Sophia, c. 1000
Constantinople
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Coin struck by Constantine I to commemorate the founding of Constantinople
182.
Palimpsest
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Other materials in the interest of economy were re-used wherever possible. The word "palimpsest" derives from the Greek παλίμψηστος, thus meaning "scraped clean and used again". The Ancient Romans wrote on wax-coated tablets, which were easily re-smoothed and reused; Cicero's use of the term "palimpsest" confirms such a practice. Where papyrus was in common use, reuse of writing media was less common because papyrus was cheaper and more expendable than costly parchment. Some papyrus palimpsests do survive, Romans referred to this custom of washing papyrus. The writing was washed from vellum using milk and bran. With the passing of time, the faint remains of the former writing would reappear so that scholars can decipher it. Medieval codices are sewn together at the fold. Faint legible remains were read by eye before 20th-century techniques helped make lost texts readable. To read palimpsests, scholars of the 19th century used chemical means that were sometimes very destructive, using tincture of gall or, later, ammonium bisulfate. Modern methods of reading palimpsests using ultraviolet light and photography are less damaging. Innovative digitized images aid scholars in deciphering unreadable palimpsests. For example, multispectral imaging undertaken by researchers at the Rochester Institute of Technology and Johns Hopkins University recovered much of the undertext from the Archimedes Palimpsest. One of the most successful techniques for reading through the paint proved to be imaging, through which the iron in the ink is revealed. A number of ancient works have survived only as palimpsests.
Palimpsest
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The Codex Ephraemi Rescriptus, a Greek manuscript of the Bible from the 5th century, is a palimpsest.
Palimpsest
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A Georgian palimpsest from the 5th or 6th century.
Palimpsest
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The Wolfenbüttel Codex Guelferbytanus A
Palimpsest
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Folio 20 recto with Greek text of Luke 9:22-33 (lower text)
183.
Vellum
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Vellum often refers to a parchment made from calf skin, as opposed to that from other animals. It is prepared for printing on, to produce single pages, scrolls, codices or books. The term is sometimes used with a more general meaning referring to finer-quality parchments made from a variety of animal skins. Vellum is generally durable, although there are great variations depending on preparation and the quality of the skin. The manufacture involves the cleaning, bleaching, scraping of the skin with a crescent-shaped knife. To create tension, scraping is alternated with drying. Modern "paper vellum" is a quite different synthetic material, used for a variety of purposes, including plans, blueprints. Although the term derives from the French for "calf", vellum can include hide from virtually any other mammal. Vellum is a translucent material produced from the skin, often split, of a young animal. The skin is washed with lime, but not together. It is then soaked in lime for several days to remove the hair. Once clear, the two sides of the skin are distinct: the side facing inside the hair side. The "inside side" of the skin is usually the lighter and more refined of the two. The hair follicles may be visible together with any scarring, made while the animal was alive. The membrane can also show the pattern of the animal's network called the "veining" of the sheet.
Vellum
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The Magna Carta written in Latin on vellum, held at the British Library
Vellum
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A vellum deed dated 1638, with pendent seal attached.
Vellum
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A portolan chart (map) by Jacobo Russo (Giacomo Russo) of Messina (1533)
Vellum
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A Volume Of Treatises On Natural Science, Philosophy, And Mathematics (1300) Ink on vellum.
184.
Christie's
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Christie's, founded in 1766 by James Christie, is the world's leading art business, with sales in 2015 that totalled £4.8 billion / $7.4 billion. Christie's has its main headquarters in New York City on Rockefeller Plaza. It is owned by the holding company of François-Henri Pinault. However, newspaper advertisements of Christie's sales dating from 1759 have also been traced. From 1859, the company was called Christie, Manson & Woods. In 1958, it established its overseas office, by placing a representative in Rome. The overseas salesroom opened in Geneva, where Christie's holds jewellery auctions. Christie's was a public company, listed from 1973 to 1999. In 1974, Jo Floyd was appointed chairman of Christie's. The house's subsidiary Christie's International Inc. held its first sale in the United States in 1977, 13 years later than Sotheby's. Christie's growth was steady since 1989, when it had 42 percent of the auction market. In 1990, the company guaranteed a minimum price for a collection of artworks in its May auctions. In 1996, the house's sales eclipsed Sotheby's for the first time since 1954. The company merged it with Spink to become Spink-Leger. Spink-Leger was closed in 2002.
Christie's
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Christie's American branch in Rockefeller Center, New York
Christie's
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In A Peep at Christies (1796), James Gillray caricatured actress Elizabeth Farren and huntsman Lord Derby examining paintings appropriate to their tastes and heights.
Christie's
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The Microcosm of London (1808), an engraving of Christie's auction room
Christie's
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Christie's Chinese preview exhibition
185.
New York City
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The City of New York, often called New York City or simply New York, is the most populous city in the United States. The five boroughs -- Brooklyn, Queens, Manhattan, Staten Island -- were consolidated into a single city in 1898. New York served as the capital of the United States until 1790. It has been the country's largest city since 1790. In the 21st century, New York has emerged as a global node of creativity and entrepreneurship, environmental sustainability. Several sources have ranked the most photographed city in the world. The names of many of the city's bridges, parks are known around the world. Manhattan's real market is among the most expensive in the world. Manhattan's Chinatown incorporates the highest concentration of Chinese people in the Western Hemisphere, with multiple signature Chinatowns developing across the city. Providing continuous 24/7 service, the New York City Subway is one of the most extensive metro systems worldwide, with 469 stations in operation. During the Wisconsinan glaciation, the New York City region was situated at the edge of a large sheet over 1,000 feet in depth. The sheet scraped away large amounts of soil, leaving the bedrock that serves as the geologic foundation for much of New York City today. On, movement of the ice sheet would contribute to the separation of what are now Long Island and Staten Island. He named it "Nouvelle Angoulême". He returned to Spain in August.
New York City
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Clockwise, from top: Midtown Manhattan, Times Square, the Unisphere in Queens, the Brooklyn Bridge, Lower Manhattan with One World Trade Center, Central Park, the headquarters of the United Nations, and the Statue of Liberty
New York City
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New Amsterdam, centered in the eventual Lower Manhattan, in 1664, the year England took control and renamed it "New York".
New York City
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The Battle of Long Island, the largest battle of the American Revolution, took place in Brooklyn in 1776.
New York City
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Broadway follows the Native American Wickquasgeck Trail through Manhattan.
186.
Suda
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The Suda or Souda is a massive 10th-century Byzantine encyclopedia of the ancient Mediterranean world, formerly attributed to an author called Suidas. The Suda is somewhere between an encyclopedia in the modern sense. It explains the source, meaning of words according to the philology of its period, using such earlier authorities as Harpocration and Helladios. The articles on literary history are especially valuable. These entries supply quotations from authors whose works are otherwise lost. They use older scholia for later writers, Polybius, Josephus, the Chronicon Paschale, George Syncellus, George Hamartolus, so on. The chief source for this is the encyclopedia of Constantine VII Porphyrogenitus, for Roman history the excerpts of John of Antioch. Krumbacher counts two main sources of the work: Hamartolus for the Byzantine age. Some editors -- for example, Immanuel Bekker -- rearranged the Suda alphabetically. It would thus appear that the Suda was compiled sometime after 975. Passages referring to Michael Psellus are considered later interpolations. It includes numerous quotations from ancient writers; the scholiasts on Aristophanes, Homer, Sophocles and Thucydides are also much used. Principal sources include a lexicon by "Eudemus," perhaps derived from the work On Rhetorical Language by Eudemus of Argos. The work deals with biblical well as pagan subjects, from which it is inferred that the writer was a Christian. A prefatory note gives a list of dictionaries from which the lexical portion was compiled, together with the names of their authors.
Suda
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First page of an early printed edition of the Suda
187.
Walters Art Museum
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The Walters Art Museum, located in Mount Vernon-Belvedere, Baltimore, Maryland, is a public art museum founded and opened in 1934. It holds collections established during the mid-19th Century. The following year, "The Walters" reopened its main building after replacement of internal utilities and infrastructure. The Archimedes Palimpsest was from a private collector for conservation and spectral imaging studies. This was one of the most such releases made by any museum. The Walters' collection of ancient art includes examples from Egypt, Nubia, Greece, Rome, Etruria and the Near East. The museum owns the oldest surviving Chinese wood-and-lacquer image of the Buddha. It is exhibited in a gallery dedicated solely to this work. The Museum holds one of the largest and finest collections of Thai bronze, scrolls, banner paintings in the world. Islamic art in all media is represented at the Walters. The Walters Museum owns an array of Islamic manuscripts. Henry Walters assembled a collection of art produced in all the artistic media of the period. This forms the basis of the Walters' medieval collection, for which the Museum is best known internationally. An ivory casket covered with scenes of jousting knights is one of about a dozen such objects to survive in the world. Many of these works are on display in the Museum's galleries.
Walters Art Museum
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North Charles Street original main entrance to the Walters Art Museum
Walters Art Museum
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Sculpture Garden (central "Great Hall") of the Walters Art Gallery (now Walters Art Museum) in the original Main Building of 1905-1909
Walters Art Museum
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Sumerian male worshiper, c.2300 BC
Walters Art Museum
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" Padiiset's Statue ", illustrates Canaan - Ancient Egypt trade, c.1700 B.C. (inscription c.900 B.C.)
188.
Baltimore
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Baltimore is the largest city in the U.S. state of Maryland, the 29th-most populous city in the country. It is not part of any county; thus, it is the largest independent city in the United States. Founded in 1729, Baltimore is the second largest seaport in the Mid-Atlantic. Baltimore's Inner Harbor was once the second leading port for immigrants to the United States and a major manufacturing center. Baltimore had a population of 621,849 in 2015; in 2010, that of Baltimore Metropolitan Area was the 21st largest in the country. With hundreds of identified districts, Baltimore has been dubbed "a city of neighborhoods". In the War of 1812, Francis Scott Key wrote The Star-Spangled Banner, later the national anthem, in the city. The city has 289 properties listed on the National Register of Historic Places. The historical records of the government of Baltimore are located at the Baltimore City Archives. The city is named after founding proprietor of the Province of Maryland. Baltimore Manor was the name of the estate in County Longford on which the Calvert family lived in Ireland. Baltimore is an anglicization of an Tí Mhóir, meaning "town of the big house." A century after John Smith's voyage, English colonists began to settle in Maryland. The area constituting the modern City of its metropolitan area was first settled by David Jones in 1661. He claimed known today as Harbor East on the east bank of the Jones Falls stream, which flows south into Baltimore's Inner Harbor.
Baltimore
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Sixth Regiment fighting railroad strikers, July 20, 1877
Baltimore
Baltimore
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The Battle Monument commemorates the Battle of Baltimore.
Baltimore
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The Great Baltimore Fire of 1904, looking west from Pratt and Gay streets
189.
Maryland
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Its capital is Annapolis. Among its occasional nicknames are Old Line State, the Free State, the Chesapeake Bay State. The state is named after Henrietta Maria of the wife of Charles I of England. George Calvert was the first English proprietor of the then-Maryland colonial grant. Maryland is one of the smallest states in terms of area, well as one of the most densely populated, with around six million residents. Maryland is comparable in overall area with Belgium. It is closest in size to the state of Hawaii, the next smallest state. Its neighbor West Virginia, is almost twice the size of Maryland. Maryland possesses a variety of topography within its borders, contributing to its nickname America in Miniature. This land was ceded to the United States Federal Government in 1790 to form the District of Columbia. . The counties east of the bay are known collectively as the Eastern Shore. Close to the small town of Hancock, in about two-thirds of the way across the state, there are 1.83 miles between its borders. This geographical curiosity makes Maryland the narrowest state, bordered by the Mason -- the northwards-arching Potomac River to the south. Portions of Maryland are included in unofficial geographic regions.
Maryland
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Western Maryland: known for its heavily forested mountains. A panoramic view of Deep Creek Lake and the surrounding Appalachian Mountains in Garrett County.
Maryland
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Flag
Maryland
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Dramatic example of Maryland's fall line, a change in rock type and elevation that creates waterfalls in many areas along the Southwest to Northeast geological boundary that crosses the state. Great Falls, cliffs and rapids.
Maryland
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Typical freshwater river above the tidal zone. The Patapsco River includes the famous Thomas Viaduct and is part of the Patapsco Valley State Park. Later, the river forms the Inner Harbor as it empties into the Chesapeake Bay.
190.
Ultraviolet
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Ultraviolet is an electromagnetic radiation with a wavelength from 10 nm to 400 nm, shorter than that of visible light but longer than X-rays. UV radiation is present in sunlight. It is also produced by specialized lights such as mercury-vapor lamps, tanning lamps, black lights. Consequently, many practical applications of UV radiation derive from its interactions with organic molecules. Suntan, sunburn are familiar effects of over-exposure, along with higher risk of skin cancer. More-energetic, shorter-wavelength "extreme" UV below nm ionizes air so strongly that it is absorbed before it reaches the ground. Ultraviolet is also responsible for the formation including humans. The UV spectrum thus has effects both harmful to human health. Near-UV radiation is visible to some insects, birds. Small birds have a fourth receptor for ultraviolet rays; this gives birds "true" UV vision. Reindeer use near-UV radiation to see polar bears, who are poorly visible in regular light because they blend in with the snow. UV also allows mammals to see urine trails, helpful for prey animals to find food in the wild. "Ultraviolet" means "beyond violet", violet being the color of the highest frequencies of visible light. Ultraviolet has a higher frequency than light. Heat rays were eventually dropped in favour of ultraviolet and infrared radiation, respectively.
Ultraviolet
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(left) Portable ultraviolet lamp. (right) UV light is also produced by electric arcs. Arc welders must wear eye protection to prevent welder's flash.
Ultraviolet
Ultraviolet
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Two black light fluorescent tubes, showing use. The longer tube is a F15T8/BLB 18 inch, 15 watt tube, shown in the bottom image in a standard plug-in fluorescent fixture. The shorter is an F8T5/BLB 12 inch, 8 watt tube, used in a portable battery-powered black light sold as a pet urine detector.
Ultraviolet
191.
X-ray
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X-radiation is a form of electromagnetic radiation. X-ray wavelengths are typically longer than those of gamma rays. Spelling of X-ray in the English language includes the variants x-ray, X ray. X-rays with high photon energies are called hard X-rays, while those with lower energy are called soft X-rays. Due to their penetrating ability, hard X-rays are widely used to image the inside of e.g. in medical radiography and airport security. The X-ray is metonymically used to refer to a radiographic image produced using this method, in addition to the method itself. Since the wavelengths of hard X-rays are similar to the size of atoms they are also useful for determining crystal structures by crystallography. By contrast, soft X-rays are easily absorbed in air; the length of 600 eV X-rays in water is less than 1 micrometer. There is no consensus for a distinguishing between X-rays and gamma rays. This definition has several problems: other processes also can generate these high-energy photons, or sometimes the method of generation is not known. This criterion is only possible if wavelength is known. X-ray photons carry enough energy to disrupt molecular bonds. This therefore harmful to living tissue. A very high dose over a short period of time causes radiation sickness, while lower doses can give an increased risk of radiation-induced cancer. In medical imaging this increased risk is generally greatly outweighed by the benefits of the examination.
X-ray
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Spectrum of the X-rays emitted by an X-ray tube with a rhodium target, operated at 60 kV. The smooth, continuous curve is due to bremsstrahlung, and the spikes are characteristic K lines for rhodium atoms.
X-ray
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X-rays are part of the electromagnetic spectrum, with wavelengths shorter than visible light. Different applications use different parts of the X-ray spectrum.
X-ray
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A chest radiograph of a female, demonstrating a hiatus hernia
X-ray
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An arm radiograph, demonstrating broken ulna and radius with implanted internal fixation.
192.
Light
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Light is electromagnetic radiation within a certain portion of the electromagnetic spectrum. The word usually refers to visible light, responsible for the sense of sight. This wavelength means a range of roughly 430 -- 750 terahertz. The main source of light on Earth is the Sun. This process of photosynthesis provides virtually all the energy used by living things. Historically, another important source of light for humans has been fire, to modern kerosene lamps. With the development of electric lights and power systems, electric lighting has effectively replaced firelight. Some species of animals generate their own light, a process called bioluminescence. For example, vampire squids use it to hide themselves from prey. Visible light, as with all types of electromagnetic radiation, is experimentally found to always move at this speed in a vacuum. In physics, the light sometimes refers to electromagnetic radiation of any wavelength, whether visible or not. In this sense, gamma rays, X-rays, radio waves are also light. Like all types of light, visible light exhibits properties of both waves and particles. This property is referred to as the wave–particle duality. The study of light, known as optics, is an important area in modern physics.
Light
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An example of refraction of light. The straw appears bent, because of refraction of light as it enters liquid from air.
Light
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A triangular prism dispersing a beam of white light. The longer wavelengths (red) and the shorter wavelengths (blue) get separated.
Light
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A cloud illuminated by sunlight
Light
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A city illuminated by artificial lighting
193.
Fields Medal
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The Fields Medal is sometimes viewed as the highest honor a mathematician can receive. The Abel Prize have often been described as the mathematician's "Nobel Prize". The Fields Medal differs from the Abel in view of the restriction mentioned above. The prize comes with a monetary award, which since 2006 has been C$15,000. The colloquial name is in honour of Canadian mathematician John Charles Fields. Fields was instrumental in establishing the award, funding the monetary component. Its purpose is to give support to younger mathematical researchers who have made major contributions. However, in contrast to the Nobel Prize, the Fields Medal is awarded only every four years. This is similar to restrictions applicable to the Clark Medal in economics. The monetary award is much lower than the 8,000,000 Swedish kronor given with each Nobel prize as of 2014. Other major awards such as the Abel Prize and the Chern Medal, have larger monetary prizes, comparable to the Nobel. In 1954, Jean-Pierre Serre became the youngest winner of the Fields Medal, at 27. He still retains this distinction. In 1966, Alexander Grothendieck boycotted the ICM, held in Moscow, to protest military actions taking place in Eastern Europe. Founder and director of the Institut des Hautes Études Scientifiques attended and accepted Grothendieck's Fields Medal on his behalf.
Fields Medal
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The obverse of the Fields Medal
Fields Medal
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The reverse of the Fields Medal
194.
Gottfried Wilhelm Leibniz
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Leibniz's notation has been widely used ever since it was published. It was only in the 20th century that his Law of Continuity and Transcendental Law of Homogeneity found mathematical implementation. He became one of the most prolific inventors in the field of mechanical calculators. He also refined the binary number system, the foundation of virtually all digital computers. Leibniz, along with René Descartes and Baruch Spinoza, was one of the three great 17th-century advocates of rationalism. Leibniz wrote works on philology. Leibniz's contributions to this vast array of subjects were scattered in various learned journals, in tens of thousands of letters, in unpublished manuscripts. He wrote in several languages, but primarily in Latin, French, German. There is no complete gathering of the writings of Leibniz. Gottfried Leibniz was born on July 1, 1646, toward the end of the Thirty Years' War, in Leipzig, Saxony, to Friedrich Leibniz and Catharina Schmuck. Friedrich noted in his family journal: 21. Juny am Sontag 1646 Ist mein Sohn Gottfried Wilhelm, post sextam vespertinam 1/4 uff 7 uhr abents zur welt gebohren, im Wassermann. In English: On Sunday 21 June 1646, my son Gottfried Wilhelm is born into the world a quarter after six in the evening, in Aquarius. Leibniz was baptized on July 3 of that year at St. Nicholas Church, Leipzig; his godfather was the Lutheran theologian Martin Geier. His father died when he was six and a half years old, from that point on he was raised by his mother.
Gottfried Wilhelm Leibniz
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Portrait by Christoph Bernhard Francke
Gottfried Wilhelm Leibniz
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Engraving of Gottfried Wilhelm Leibniz
Gottfried Wilhelm Leibniz
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Stepped Reckoner
Gottfried Wilhelm Leibniz
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Leibniz's correspondence, papers and notes from 1669-1704, National Library of Poland.
195.
Apollonius of Perga
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Apollonius of Perga was a Greek geometer and astronomer noted for his writings on conic sections. His innovative terminology, especially in the field of conics, influenced many later scholars including Ptolemy, Francesco Maurolico, Johannes Kepler, Isaac Newton, René Descartes. Apollonius gave the ellipse, the hyperbola their modern names. Ptolemy describes Apollonius' theorem in the Almagest XII.1. Apollonius also researched the history, for which he is said to have been called Epsilon. The crater Apollonius on the Moon is named in his honor. He is one of the ancient geometers. The degree of originality of the Conics can best be judged from Apollonius's own prefaces. Books i–iv he describes as an "elementary introduction" containing essential principles, while the other books are specialized investigations in particular directions. Allusions such as Euclid's four Books on Conics, show a debt not only to Euclid but also to Conon and Nicoteles. The way the cone is cut does not matter. It is the form of the fundamental property that leads him to give their names: parabola, ellipse, hyperbola. Thus Books v–vii are clearly original. He further developed relations between the corresponding ordinates that are equivalent to rhetorical equations of curves. Curves were not determined by equations.
Apollonius of Perga
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Pages from the 9th century Arabic translation of the Conics
Apollonius of Perga
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Parabola connection with areas of a square and a rectangle, that inspired Apollonius of Perga to give the parabola its current name.
196.
Impact crater
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Impact craters are the geographic features on solid Solar System objects including the Moon, Mercury, Callisto, Ganymede and most small moons and asteroids. Where such processes have destroyed most of the original topography, astrobleme are more commonly used. This indicates that there should be far more relatively young craters on the planet than have been discovered so far. Note that the rate of impact cratering in the outer Solar System could be different from the inner Solar System. Although Earth's active surface processes quickly destroy the impact record, about 190 terrestrial impact craters have been identified. They are also selectively found in the stable interior regions of continents. Impact craters are not to be confused with landforms that may appear similar, including calderas, sinkholes, glacial cirques, others. In the 1920s, the American geologist Walter H. Bucher studied a number of sites now recognized as impact craters in the United States. He concluded they had been created by some great explosive event, but believed that this force was probably volcanic in origin. However, in 1936, the geologists John D. Boon and Claude C. Albritton Jr. revisited Bucher's studies and concluded that the craters that he studied were probably formed by impacts. The concept of impact cratering remained more or less speculative until the 1960s. By 1970, they had tentatively identified more than 50. Because the processes of erosion on the Moon are minimal, craters persist almost indefinitely.
Impact crater
Impact crater
Impact crater
Impact crater
197.
Moon
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The Moon is Earth's only permanent natural satellite. It is the largest among planetary satellites relative to the size of the planet that it orbits. It is the second-densest satellite among those whose densities are known. The average distance of the Moon from the Earth is 1.28 light-seconds. The Moon is thought to have formed not long after Earth. It is the second-brightest regularly visible celestial object in Earth's sky, as measured by illuminance on Earth's surface. Its surface is actually dark, although compared to the sky it appears very bright, with a reflectance just slightly higher than that of worn asphalt. The Moon's gravitational influence produces the ocean tides, the slight lengthening of the day. This matching of visual size will not continue in the far future. This rate is not constant. Since the Apollo 17 mission in 1972, the Moon has been visited only by uncrewed spacecraft. The usual proper name for Earth's natural satellite is "the Moon". Occasionally, the name "Luna" is used. The principal English adjective pertaining to the Moon is lunar, derived from the Latin Luna. A less common adjective is selenic, derived from, derived the prefix "seleno -".
Moon
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Full moon as seen from Earth's northern hemisphere
Moon
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The Moon, tinted reddish, during a lunar eclipse
Moon
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Near side of the Moon
Moon
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Far side of the Moon
198.
Archimedes (crater)
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Archimedes is a large lunar impact crater on the eastern edges of the Mare Imbrium. The diameter of Archimedes is the largest of any crater on the Mare Imbrium. A triangular promontory extends 30 kilometers from the southeast of the rim. The interior of the crater is flooded with lava. It is devoid of significant raised features, although there are a tiny meteor craters near the rim. Scattered wisps of bright material lie across the floor, most likely deposited by the impact that created Autolycus. To the south of Archimedes extends the Montes Archimedes, a mountainous region. On the southeastern rim is the Palus Putredinis, a lava-flooded plain containing a system of rilles named the Rimae Archimedes, which extends over 150 kilometers. North-northwest of Archimedes stand a string of peaks in the Mare Imbrium. East of Archimedes is the crater Autolycus. Northeast of Archimedes is the prominent crater Aristillus. The plain between Archimedes, Aristillus, Autolycus forms the Sinus Lunicus bay of Mare Imbrium. A ridge leads away from Archimedes toward the north-northwest, crossing this mare. Archimedes is named after the Greek Archimedes. Like many of the craters on the Moon's near side, it was given its name by Giovanni Riccioli, whose 1651 nomenclature system has become standardized.
Archimedes (crater)
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Lunar Orbiter 4 image
Archimedes (crater)
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Archimedes from Apollo 15. NASA photo.
Archimedes (crater)
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Lunar crater Archimedes in the infrared. Image courtesy of NOT and SO: M. Gålfalk, G. Olofsson, and H.-G. Florén, taken with the SIRCA camera.
199.
Montes Archimedes
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Montes Archimedes is a mountain range on the Moon. It is named after the Archimedes that lies to the north, which in turn is an eponym of the Greek mathematician Archimedes. They are bounded on the eastern side by Archimedes. Farther to the east lies the impressive Montes Apenninus, a long mountain range. The selenographic coordinates of this range is 4.6 ° W. The remainder of the peaks are scattered with no particular structure or pattern.
Montes Archimedes
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Lunar Orbiter 4 image
200.
East Germany
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East Germany, formally the German Democratic Republic or GDR, was an Eastern Bloc state during the Cold War period. The Soviet zone surrounded West Berlin, but did not include it; as a result, West Berlin remained outside the jurisdiction of the GDR. The German Democratic Republic was established in the Soviet Zone, while the Federal Republic was established in the three western zones. The East was often described as a satellite state of the Soviet Union. Soviet occupation authorities began transferring administrative responsibility to German communist leaders in 1948, the GDR began to function as a state on 7 October 1949. Soviet forces, however, remained in the country throughout the Cold War. Until 1989, the GDR was governed by the Socialist Unity Party, though other parties nominally participated in its alliance organisation, the National Front of Democratic Germany. The economy was centrally planned, increasingly state-owned. Prices of basic services were set rather than rising and falling through supply and demand. Although the GDR had to pay substantial war reparations to the USSR, it became the most successful economy in the Eastern Bloc. Nonetheless it did not match the economic growth of West Germany. Emigration to the West was a significant problem—as many of the emigrants were well-educated young people, it further weakened the state economically. The government fortified its western borders and, in 1961, built the Berlin Wall. Many people attempting to emigrate were killed by border guards or booby traps, such as landmines. International negotiations led on the status and borders of Germany.
East Germany
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GDR leaders: President Wilhelm Pieck and Prime Minister Otto Grotewohl, 1949
East Germany
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Flag (1959–1990)
East Germany
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SED First Secretary, Walter Ulbricht, 1950
East Germany
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Head of State: Erich Honecker (1971–89)
201.
Greece
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Greece, officially the Hellenic Republic, historically also known as Hellas, is a country in southeastern Europe. Greece's population is approximately million as of 2015. Athens is largest city, followed by Thessaloniki. Greece is strategically located at the crossroads of Europe, Asia, Africa. Greece consists of nine geographic regions: Macedonia, Central Greece, the Peloponnese, Thessaly, Epirus, the Aegean Islands, Thrace, Crete, the Ionian Islands. The Aegean Sea lies to the south. Eighty percent of Greece is mountainous, with Mount Olympus being the highest peak at 2,918 metres. From the eighth BC, the Greeks were organised into various independent city-states, known as polis, which spanned the entire Mediterranean region and the Black Sea. The establishment of the Greek Orthodox Church in the first century transmitted Greek traditions to the wider Orthodox World. Falling under Ottoman dominion in the mid-15th century, the modern state of Greece emerged in 1830 following a war of independence. Greece's historical legacy is reflected by its 18 UNESCO World Heritage Sites, among the most in Europe and the world. Greece is a democratic and developed country with an advanced high-income economy, a very high standard of living. A founding member of the United Nations, Greece has been part of the Eurozone since 2001. Large tourism industry, prominent shipping sector and geostrategic importance classify it as a middle power. It is one of the most visited the largest economy in the Balkans, where it is an important regional investor.
Greece
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Fresco displaying the Minoan ritual of "bull leaping", found in Knossos, Crete.
Greece
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Flag
Greece
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The Lion Gate, Mycenae
Greece
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The Parthenon on the Acropolis of Athens is one of the best known symbols of classical Greece.
202.
Italy
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Italy, officially the Italian Republic, is a unitary parliamentary republic in Europe. Located in the heart of the Mediterranean Sea, Italy shares open land borders with Vatican City. With million inhabitants, it is the fourth most populous EU member state. Rome ultimately emerged as the dominant power, becoming the leading cultural, political, religious centre of Western civilisation. The legacy of the Roman Empire can be observed in the global distribution of civilian law, republican governments, Christianity and the Latin script. Italian culture flourished at this time, producing famous scholars, polymaths such as Leonardo da Vinci, Galileo, Michelangelo, Machiavelli. However, the southern areas of the country remained largely excluded from industrialisation, fuelling a large and influential diaspora. Italy has eighth largest economy in the world. It enjoys the highest life expectancy in the EU. The corpus of the solutions proposed by historians and linguists is very wide. Greek historian Dionysius of Halicarnassus states this account together with the legend that Italy was named after Italus, mentioned also by Aristotle and Thucydides. But by his time the name also applied to most of Lucania as well. Excavations throughout Italy revealed a Neanderthal presence dating back to the Palaeolithic period, some 200,000 years ago, modern Humans arrived about 40,000 years ago. Other Italian peoples of undetermined language families but of possible non-Indo-European origins include the Rhaetian people and Cammuni, known for their rock carvings. Also the Phoenicians established colonies on the coasts of Sardinia and Sicily.
Italy
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The Colosseum in Rome, built c. 70 – 80 AD, is considered one of the greatest works of architecture and engineering of ancient history.
Italy
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Flag
Italy
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The Iron Crown of Lombardy, for centuries symbol of the Kings of Italy.
Italy
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Castel del Monte, built by German Emperor Frederick II, UNESCO World Heritage site
203.
Nicaragua
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Nicaragua, officially the Republic of Nicaragua, is the largest country in the Central American isthmus. Managua, is the country's largest city and the third-largest city in Central America. The multi-ethnic population of million includes indigenous peoples, Europeans, Africans, Asians. The main language is Spanish. Native tribes on the eastern coast speak their own languages. The Spanish Empire conquered the region in the 16th century. Nicaragua gained independence in 1821. Nicaragua is a democratic republic. The biological diversity, active volcanoes make Nicaragua an increasingly popular tourist destination. The name "Nicaragua" was coined by chief of the most populous indigenous tribe. When Spaniard Gil González Dávila came in 1521 he found in the areas between Rivas and San Jorge the first pre-Columbian natives of Nicaragua. The cacique leader's name was Macuilmiquiztli, not Nicarao. The Spanish name incorporates the indigenous words NIC-ATL-NAHUAC which means "here at the lake" or NIC-ANAHUAC, "here the Anahuac", or "the Anahuac from here". The Pipil migrated to Nicaragua after 500 BC. Meanwhile, the Caribbean coast of Nicaragua was inhabited by other peoples, mostly Chibcha language groups.
Nicaragua
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2,100-year-old human footprints called "huellas de acahualinca" preserved in volcanic mud near Lake Managua.
Nicaragua
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Flag
Nicaragua
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The Colonial City of Granada near Lake Nicaragua, is one of the most visited sites in Central America.
Nicaragua
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The Fortress of the Immaculate Conception was constructed in the late 17th century to protect locals in neighboring Granada from pirate attacks. Today, it is one of Nicaragua's main tourist attractions.
204.
San Marino
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Its size is just over 61 km2, with a population of 33,562. Its largest city is Dogana. San Marino has the smallest population of all the members of the Council of Europe. The country takes its name from a stonemason originating from the Roman colony on the island of Rab, in modern-day Croatia. In 257 CE Marinus participated in the reconstruction of Rimini's city walls by Liburnian pirates. The country is considered to have the earliest written governing documents still in effect. The country's economy mainly relies on finance, services and tourism. It is one of the wealthiest countries in the world in terms of GDP, with a figure comparable to the most developed European regions. San Marino is considered to have a highly stable economy, with one of the lowest unemployment rates in Europe, a budget surplus. It is the only country with more vehicles than people. Saint Marinus went to the city of Rimini as a stonemason. The official date of the founding of what is now known as the Republic is September 301. In 1631, its independence was recognized by the Papacy. The offer was declined by the Regents, fearing future retaliation from other states' revanchism. In recognition of this support, Giuseppe Garibaldi accepted the wish of San Marino not to be incorporated into the Italian state.
San Marino
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The San Marino constitution of 1600
San Marino
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Flag
San Marino
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The front passes Mount Titano in September 1944.
San Marino
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Mount Titano
205.
Spain
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Along with France and Morocco, it is one of only three countries to have both Atlantic and Mediterranean coastlines. By population, Spain is the fifth in the European Union, after Italy. Largest city is Madrid, other major urban areas include Barcelona, Valencia, Seville, Bilbao and Málaga. Modern humans first arrived around 35,000 years ago. In the Middle Ages, the area was later by the Moors. Spain is a democracy organised under a constitutional monarchy. It is a developed country with the world's fourteenth largest economy by nominal GDP and sixteenth largest by purchasing power parity. Jesús Luis Cunchillos argues that the root of the span is the Phoenician word spy, meaning "to forge metals". Therefore, i-spn-ya would mean "the land where metals are forged". Don Isaac Abravanel and Solomon ibn Verga, gave an explanation now considered folkloric. This man was a Grecian by birth, but, given a kingdom in Spain. He became related by marriage to the nephew of king Heracles, who also ruled over a kingdom in Spain. Based upon their testimonies, this eponym would have already been by c. 350 BCE. Iberia enters written records as a land populated largely by Basques and Celts. After an arduous conquest, the peninsula came under the rule of the Roman Empire.
Spain
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Lady of Elche
Spain
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Flag
Spain
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Altamira Cave paintings, in Cantabria.
Spain
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Celtic castro in A Guarda, Galicia.
206.
California
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California is the most populous state in the United States and the third most extensive by area. The capital is Sacramento. Los Angeles is California's most populous city, largest after New York City. The state also has the nation's most populous county, its largest county by area, San Bernardino County. A major agricultural area, dominates the state's center. The Spanish Empire then claimed it in their New Spain colony. The western portion of Alta California then was admitted as the 31st state on September 9, 1850. If it were a country, California would be the 35th most populous. Fifty-eight percent of the state's economy is centered on finance, government, real estate services, professional, scientific and technical business services. Although it accounts for only 1.5 percent of the state's economy, California's industry has the highest output of any U.S. state. The kingdom of Queen Calafia, according to Montalvo, was said to be a remote land rich in gold. They were robust of body with great virtue. The island itself is one of the wildest in the world on account of the craggy rocks. This conventional wisdom that maps were drawn to reflect this way, lasted as late as the 1700's. Shortened forms of the state's name include CA, Cal. Calif. and US-CA.
California
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A forest of redwood trees in Redwood National Park
California
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Flag
California
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Mount Shasta
California
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Aerial view of the California Central Valley
207.
Sutter's Mill
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Sutter's Mill was a sawmill, owned by 19th-century pioneer John Sutter, where gold was found, setting off the California Gold Rush. It was located in Coloma, California. At the time, Marshall was working to build a water-powered sawmill owned by John Sutter. On February 1848, the Treaty of Guadalupe Hidalgo was signed in Mexico City which transferred the American Southwest to the United States. When the news got out about the gold, people from all over the world headed for California, permanently transforming the territory. Henry Bigler and Azariah Smith, like other workers at the mill, wrote about their experience in journals. Bigler recorded January 24, 1848, in his diary. This gold find started the next year. The site of the mill is located on the South Fork American River. Marshall Gold Discovery State Historic Park is registered as # 530. The current Sutter's Mill is a replica of the original building. It was built based on an early day photo of the mill. The mill was the inspiration for a song by singer-songwriter Dan Fogelberg. The mill was also the namesake for a song for Herb Sutter's blog. The original flake of gold discovered at the mill is currently at the Smithsonian Institution.
Sutter's Mill
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Sutter's Mill in 1850
208.
California Gold Rush
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The California Gold Rush began on January 24, 1848, when gold was found by James W. Marshall at Sutter's Mill in Coloma, California. All in the news of gold brought some 300,000 people to California from the rest of the United States and abroad. Of the 300,000, approximately half arrived by half came overland on the California Trail and the Gila River trail. The gold-seekers, called "forty-niners", often faced substantial hardships on the trip. While most of the newly arrived were Americans, the Gold Rush attracted tens of thousands from Latin America, Europe, China. At first, the prospectors retrieved the gold from riverbeds using simple techniques, such as panning. More sophisticated methods of gold recovery were later adopted around the world. At its peak, technological advances reached a point where significant financing was required, increasing the proportion of gold companies to individual miners. Gold worth tens of billions of today's dollars was recovered, which led for a few. However, many returned home with little more than they had started with. The effects of the Gold Rush were substantial. San Francisco grew from a small settlement of about 200 residents in 1846 by 1852. Roads, churches, other towns were built throughout California. In 1849 a constitution was written. The future state's interim first governor and legislature were chosen.
California Gold Rush
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Sailing to California at the beginning of the Gold Rush
California Gold Rush
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Merchant ships fill San Francisco harbor, 1850–51
California Gold Rush
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Panning for gold on the Mokelumne River
California Gold Rush
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"Independent Gold Hunter on His Way to California", circa 1850. The gold hunter is loaded down with every conceivable appliance, much of which would be useless in California. The prospector says: "I am sorry I did not follow the advice of Granny and go around the Horn, through the Straights, or by Chagres [Panama]."
209.
Arbelos
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The earliest known reference to this figure is in the Book of Lemmas, where some of its mathematical properties are stated through 8. Two of the semicircles are necessarily concave, with b; the third semicircle is convex, with diameter a + b. The area of the arbelos is equal to the area of a circle with diameter H A. So this equation simplifies algebraically to the statement that 2 =. This proof approximates the Greek argument; one many find the idea implemented as a proof without words. Let D and E be the points where the segments B H and C H intersect A B and A C, respectively. The quadrilateral A D H E is actually a rectangle. Proof: The angles B D A, B H C, A E C are right angles because they are inscribed in semicircles. The quadrilateral A D H E therefore has three right angles, so it is a rectangle. Q.E.D. The line D E is tangent to semicircle B A at D and semicircle A C at E. Proof: Since angle BDA is a right angle, angle DBA equals π/2 minus angle DAB. However, angle DAH also equals π / angle DAB. Therefore triangles DBA and DAH are similar. Therefore angle DIA equals angle DOH, where I is the midpoint of BA and O is the midpoint of AH.
Arbelos
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The type of shoemaker's knife that gave its name to the figure
Arbelos
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An arbelos (grey region)
Arbelos
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Arbelos skulpture in Kaatsheuvel, Netherlands
210.
Axiom of Archimedes
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Roughly speaking, it is the property of having no infinitely small elements. It was Otto Stolz who gave its name because it appears as Axiom V of Archimedes' On the Sphere and Cylinder. A structure which has a pair of non-zero elements, one of, infinitesimal with respect to the other, is said to be non-Archimedean. For example, a linearly ordered group, Archimedean is an Archimedean group. This can be made precise in various contexts with slightly different formulations. The concept was named after the ancient Greek geometer and physicist Archimedes of Syracuse. Because Archimedes credited it to Eudoxus of Cnidus it is also known as the Eudoxus axiom. Archimedes used infinitesimals in heuristic arguments, although he denied that those were finished mathematical proofs. Let y be positive elements of a linearly ordered group G. The group G is Archimedean if there is no pair x,y such that x is infinitesimal with respect to y. Additionally, if K is an algebraic structure with a unit — for example, a ring — a similar definition applies to K. If x is infinitesimal with respect to 1, then x is an infinitesimal element. Likewise, if y is infinite with respect to 1, then y is an infinite element. The algebraic K is Archimedean if it has no infinite elements and no infinitesimal elements. An ordered field has some additional properties.
Axiom of Archimedes
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Illustration of the Archimedean property.
211.
Archimedean solid
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In geometry, an Archimedean solid is one of the 13 solids first enumerated by Archimedes. They are the semi-regular convex polyhedrons composed of regular polygons excluding the prisms and antiprisms. They differ from the Johnson solids, whose regular polygonal faces do not meet in identical vertices. "Identical vertices" means that for any two vertices, there is a global isometry of the entire solid that takes one vertex to the other. Excluding these two infinite families, there are 13 Archimedean solids. All the Archimedan solids can be made from the Platonic solids with tetrahedral, icosahedral symmetry. The Archimedean solids take their name from Archimedes, who discussed them in a now-lost work. Pappus refers to it, stating that Archimedes listed 13 polyhedra. Kepler may have also found the elongated square gyrobicupola: at least, he once stated that there were 14 Archimedean solids. However, the clear statement of the pseudorhombicuboctahedron's existence was made in 1905, by Duncan Sommerville. There are 13 Archimedean solids. Here the vertex configuration refers to the type of regular polygons that meet at any given vertex. For example, a vertex configuration of means that octagon meet at a vertex. Some definitions of polyhedron include one more figure, "pseudo-rhombicuboctahedron". The number of vertices is 720 ° divided by the defect.
Archimedean solid
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The truncated icosidodecahedron, is the largest Archimedean solid, by volume with unit edge length, as well as having the most vertices and edges.
212.
Archimedes' circles
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In geometry, specifically in the study of the arbelos, the twin circles are two special circles associated with it. These circles first appeared in the Book of Lemmas, which showed that the two circles are congruent. Thābit ibn Qurra, who translated this book into Arabic, attributed it to Greek mathematician Archimedes. Based on this claim several other circles in the Arbelos congruent to them, have also been called Archimedes' circles. However, this attribution has been questioned by later scholarship. Specifically, let A, B, C be the three corners of the arbelos, with B between A and C. Let H be the point where the larger semicircle intercepts the line perpendicular to the A C through the point B. The segment B H divides the arbelos in two parts. Each of the two circles is uniquely determined by its three tangencies. Constructing it is a special case of the Problem of Apollonius. Alternative approaches to constructing two circles congruent to the twin circles have also been found. Let a and b be the diameters of two inner semicircles, so that the outer semicircle has a + b. The diameter of each twin circle is then d = a b a + b. The smallest circle that encloses both twin circles has the same area as the arbelos. Other circles, congruent to the twin circles, have also been constructed from an arbelos.
Archimedes' circles
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The Archimedes' circles (red) of an arbelos (grey)
213.
Methods of computing square roots
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In numerical analysis, a branch of mathematics, there are several square root algorithms or methods of computing the principal square root of a non-negative real number. For the square roots of a negative or complex number, see below. Finding S is the same as solving the equation f = x 2 − S = 0 for a positive x. Therefore, any general numerical root-finding algorithm can be used. Square root algorithms require an initial value. If the initial value is away from the actual square root, the algorithm will be slowed down. It is therefore useful to have a rough estimate, which may be very inaccurate but easy to calculate. For S = 125348 = 12.5348 × 4, the estimate is S ≈ 6 ⋅ 2 = 600. These approximations are useful to find better seeds for iterative algorithms, which results in faster convergence. It can be derived from Newton's method. The process of updating is iterated until desired accuracy is obtained. This is a quadratically convergent algorithm, which means that the number of correct digits of the approximation roughly doubles with each iteration. It proceeds as follows: Begin with an arbitrary positive starting value x0. Let xn + 1 be the average of xn and S/xn. Repeat step 2 until the desired accuracy is achieved.
Methods of computing square roots
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Graph charting the use of the Babylonian method for approximating the square root of 100 (10) using starting values x 0 = 50, x 0 = 1, and x 0 = −5. Note that using a negative starting value yields the negative root.
214.
Salinon
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The salinon is a geometrical figure that consists of four semicircles. It was first introduced in the Book of Lemmas, a work attributed to Archimedes. Let O be the origin on a Cartesian plane. Let A, D, E, B be with O bisecting line AB. Let AD = EB. Another semicircle is drawn below with diameter DE. A salinon is the figure bounded by these four semicircles. Archimedes introduced the salinon by applying Book II, Proposition 10 of Euclid's Elements. Namely, the area of the salinon is: 2. Let the radius of the midpoint of AD and EB be denoted as G and H, respectively. Therefore, AG = GD = EH = HB = r1. Because DO, OF, OE are all radii to the same semicircle, DO = OF = OE = r2. By addition, AG + GD + DO = OE + EH + HB = 2r1 + r2. Since AB is the diameter of the salinon, CF is the line of symmetry. Because they all are radii of the same semicircle, AO = BO = CO = + r2.
Salinon
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The salinon (red) and the circle (blue) have the same area.
215.
Steam cannon
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A steam cannon is a cannon that launches a projectile using only heat and water, or using a ready supply of high-pressure steam from a boiler. The first cannon was designed by Archimedes during the Siege of Syracuse. Leonardo Da Vinci was also known to have designed one. The early device would consist due to its high thermal conductivity, which would be placed in a furnace. One end of the tube would the other loaded with a projectile. Once the tube reached a enough temperature, a small amount of water would be injected in behind the projectile. In theory, Leonardo da Vinci believed, the water would rapidly expand into vapour, blasting the projectile out the front of the barrel. The viability of the concept has been explored, by both the television series MythBusters and students at the Massachusetts Institute of Technology. Unsuccessful efforts were made during the age of steam to create working steam machine guns and cannons using methods and technology derived from steam locomotives. The fundamental function of the device was basically the same as a engine, only with a projectile taking place of a piston. The Holman Projector was produced by Holman Brothers of Cornwall, who specialised for mining. The first Projectors were powered by compressed air, stored in high pressure cylinders. As these vessels had no compressed air system, the Admiralty requested Holmans to develop a steam-powered version of the Projector.
Steam cannon
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Experimental prototype of 17.5 mm steam cannon. Russian Empire, 1826-29 years.
Steam cannon
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Holman Projector prototype in action, 1940.
216.
Zhang Heng
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Zhang Heng, formerly romanized as Chang Heng, was a Han Chinese polymath from Nanyang who lived during the Han dynasty. Zhang Heng began his career in Nanyang. Eventually, he became Chief Astronomer, Prefect of the Majors at the imperial court. His uncompromising stance on calendrical issues led to his becoming a controversial figure, preventing him from rising to the status of Grand Historian. Zhang returned home to Nanyang before being recalled to serve in the capital once more in 138. He died a year later in 139. Zhang applied his extensive knowledge of gears in several of his inventions. He improved Chinese calculations for pi. His fu and poetry were renowned in his time and studied and analyzed by later Chinese writers. Zhang received many posthumous honors for his ingenuity; some modern scholars have compared his work in astronomy to that of the Greco-Roman Ptolemy. Born in Nanyang Commandery, Zhang Heng came from a distinguished but not very affluent family. At age ten, Zhang's father died, leaving him in the care of his grandmother. An accomplished writer in Zhang left home in the year 95 to pursue his studies in the capitals of Chang ` an and Luoyang. While traveling to Luoyang, Zhang dedicated one of his earliest fu poems to it. He acted modestly and declined.
Zhang Heng
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A stamp of Zhang Heng issued by China Post in 1955
Zhang Heng
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A 2nd-century lacquer-painted scene on a basket box showing famous figures from Chinese history who were paragons of filial piety: Zhang Heng became well-versed at an early age in the Chinese classics and the philosophy of China's earlier sages.
Zhang Heng
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A Western Han terracotta cavalier figurine wearing robes and a hat. As Chief Astronomer, Zhang Heng earned a fixed salary and rank of 600 bushels of grain (which was mostly commuted to payments in coinage currency or bolts of silk), and so he would have worn a specified type of robe, ridden in a specified type of carriage, and held a unique emblem that marked his status in the official hierarchy.
Zhang Heng
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A pottery miniature of a palace made during the Han Dynasty; as a palace attendant, Zhang Heng had personal access to Emperor Shun and the right to escort him
217.
Chord (geometry)
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A chord of a circle is a straight line segment whose endpoints both lie on the circle. A secant line, or just secant, is the infinite extension of a chord. More generally, a chord is a segment joining two points on any curve, for instance an ellipse. A chord that passes through a circle's point is the circle's diameter. The chord is from the Latin chorda meaning bowstring. Among properties of chords of a circle are the following: Chords are equidistant from the center if and only if their lengths are equal. A chord that passes through the center of a circle is the longest chord. If the line extensions of chords AB and CD intersect at a P, then their lengths satisfy AP · PB = CP · PD. The area that a circular chord "cuts off" is called a circular segment. The midpoints of a set of parallel chords of an ellipse are collinear. Chords were used extensively in the early development of trigonometry. The first trigonometric table, compiled by Hipparchus, tabulated the value of the chord function for every 7.5 degrees. The chord lengths are accurate to two base-60 digits after the integer part. The function is defined geometrically as shown in the picture. The chord of an angle is the length of the chord between two points on a circle separated by that angle.
Chord (geometry)
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The red segment BX is a chord (as is the diameter segment AB).
218.
Skiff
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The term skiff is used for a number of essentially unrelated styles of small boat. Traditionally these are coastal or craft used for leisure or fishing and have a one-person or small crew. Sailing skiffs have developed into performance competitive classes. "Ship" comes from the English "scip", which has the same Germanic predecessor. An even older root may be found in the Greek "σκάφος". The term has been used for a number of styles of sea going craft. He subsequently settled at Marlow where he regularly rowed his skiff through the locks. Shelley later drowned sailing off the coast of Italy. It was also used by Sir Walter Scott. The Thames skiff became formalised as a specific design in the early part of the 19th century. It is other rivers in England. Although general usage has declined, skiffs are still used for racing. During the year, skiffing regattas are held in various riverside towns in England—the major event being the Skiff Championships Regatta at Henley. Akin to the skiff is the Yoal or Yole, a clinker built boat used for fishing in the Orkney and Shetland Islands. The boat itself is a version of the Norwegian Oselvar, similar to a skiff in appearance, while the word is cognate with Yawl.
Skiff
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Boulter's Lock, Sunday Afternoon by Edward John Gregory shows skiffs among other craft coming out of the lock
Skiff
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Classic flat-bottom skiff in Maine.
Skiff
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Captured Somalian pirates with their skiff
Skiff
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Modern 12ft Skiff at speed.
219.
Elsevier
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Elsevier is one of the world's major providers of scientific, technical, medical information, a technology company originally established in 1880. It is now a part of the RELX Group, known as Reed Elsevier. Elsevier publishes approximately 400,000 articles annually in 2,500 journals. Its archives contain over 30,000 e-books. Yearly downloads amount to 900 million. Its copyright practices have subjected it to criticism by researchers. Elsevier took the name from the Dutch publishing house Elzevir which has no connection with the present company. The Elzevir family operated in the Netherlands; the founder, Lodewijk Elzevir, lived in Leiden and established the business in 1580. The weekly earned lots of money. In 1947, Elsevier began publishing Biochimica et Biophysica Acta. In 2013, Elsevier acquired a UK company making software for managing and sharing research papers. Mendeley's previously open system now allows exchange of paywalled resources only within private groups. In December 2013, Elsevier announced a collaboration with London, the UCL Big Data Institute. Elsevier's investment thought to be more than # 10 million. In the primary market during 2015, researchers submitted over 1.3 m research papers to Elsevier-based publications.
Elsevier
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Elsevier
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International Standard Book Number
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The International Standard Book Number is a unique numeric commercial book identifier. An ISBN is assigned to each variation of a book. For example, an e-book, a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned after 1 January 2007, 10 digits long if assigned before 2007. The method of assigning an ISBN varies from country to country, often depending on how large the publishing industry is within a country. The initial ISBN configuration of recognition was generated based upon the 9-digit Standard Book Numbering created in 1966. The 10-digit ISBN format was published in 1970 as international standard ISO 2108. The International Standard Serial Number, identifies periodical publications such as magazines; and the International Standard Music Number covers for musical scores. The ISBN configuration of recognition was generated in 1967 in the United Kingdom by Emery Koltay. The 10-digit ISBN format was published as international standard ISO 2108. The United Kingdom continued to use the 9-digit SBN code until 1974. The ISO on-line facility only refers back to 1978. An SBN may be converted by prefixing the digit "0". This can be converted to ISBN 0-340-01381-8; the digit does not need to be re-calculated. Since 1 ISBNs have contained 13 digits, a format, compatible with "Bookland" European Article Number EAN-13s.
International Standard Book Number
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A 13-digit ISBN, 978-3-16-148410-0, as represented by an EAN-13 bar code
221.
University of St Andrews
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The University of St Andrews is a British public research university in St Andrews, Fife, Scotland. It is the oldest of the four ancient universities of Scotland and the third oldest university in the English-speaking world. St Andrews was founded between 1413, when the Avignon Antipope Benedict XIII issued a papal bull to a small group of Augustinian clergy. St Andrews is made up including 18 academic schools organised into four faculties. The university occupies historic and modern buildings located throughout the town. The academic year is divided into Candlemas. In time, over one-third of the town's population is either a staff student of the university. It is ranked behind Oxbridge. The Times Higher Education World Universities Ranking names St Andrews among the world's Top 50 universities for Social Sciences, Arts and Humanities. St Andrews has the highest student satisfaction amongst all multi-faculty universities in the United Kingdom. St Andrews has affiliated faculty, including eminent mathematicians, scientists, theologians, politicians. Six Nobel Laureates are amongst St Andrews' alumni and former staff: two in Chemistry and Physiology or Medicine, one each in Peace and Literature. A charter of privilege was bestowed by the Bishop of Henry Wardlaw, on 28 February 1411. King James I of Scotland confirmed the charter of the university in 1432. Subsequent kings supported the university with King James V "confirming privileges of the university" in 1532.
University of St Andrews
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College Hall, within the 16th century St Mary's College building
University of St Andrews
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University of St Andrews shield
University of St Andrews
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St Salvator's Chapel in 1843
University of St Andrews
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The "Gateway" building, built in 2000 and now used for the university's management department
222.
Project Gutenberg
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Project Gutenberg is a volunteer effort to digitize and archive cultural works, to "encourage the creation and distribution of eBooks". It was founded in 1971 by Michael S. Hart and is the oldest digital library. Most of the items in its collection are the full texts of public domain books. The project tries to make these as free as possible, in long-lasting, open formats that can be used on almost any computer. As of 3 October 2015, Project Gutenberg reached 50,000 items in its collection. The releases are available in plain text but, wherever other formats are included, such as Plucker. Non-English works are also available. There are affiliated projects that are providing additional content, including language-specific works. Project Gutenberg is also closely affiliated with Distributed Proofreaders, an Internet-based community for proofreading scanned texts. Project Gutenberg was started by Michael Hart in 1971 with the digitization of the United States Declaration of Independence. A student at the University of Illinois, obtained access in the university's Materials Research Lab. Hart has said he wanted to "give back" this gift by doing something that could be considered to be of great value. This particular computer was one of the 15 nodes on the network that would become the Internet. Hart decided to make works of literature available for free. He used a copy of the United States Declaration of Independence in his backpack, this became the first Project Gutenberg e-text.
Project Gutenberg
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Michael Hart (left) and Gregory Newby (right) of Project Gutenberg, 2006
Project Gutenberg
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Project Gutenberg
Project Gutenberg
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Formats
223.
Courant Institute of Mathematical Sciences
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The Courant Institute is considered one of mathematical sciences research centers in the world. It is ranked # 12 in citation worldwide. On the Faculty Scholarly Productivity Index, it is ranked #3 with an index of 1.84. The Mathematics Department of the Institute has 18 members of the United States National Academy of Sciences and five members of the National Academy of Engineering. Louis Nirenberg also received the Chern Medal in 2010, Subhash Khot won the Nevanlinna Prize in 2014. The Courant Institute specializes in scientific computation. There is emphasis on partial differential equations and their applications. The department is consistently ranked as # 1 in applied mathematics. Strong points are geometry. Within the field of science, CIMS concentrates in machine learning, theory, programming languages, parallel computing. The program is ranked 28th among computer science programs in the US. Program reviews are holistic. A undergraduate GPA and high GRE score are not required. Majority of accepted candidates met these standards. However, evidence of quantitative skills are very important admission factors.
Courant Institute of Mathematical Sciences
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View of Warren Weaver Hall, Courant Institute of Mathematical Sciences from the Ground Floor of Gould Plaza
Courant Institute of Mathematical Sciences
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Lecture Hall at Warren Weaver Hall
Courant Institute of Mathematical Sciences
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Classroom at Warren Weaver Hall
Courant Institute of Mathematical Sciences
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The Courant Institute along with Microsoft Research are the founders of the Games for Learning Institute
224.
University of Chicago
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The University of Chicago is a private research university in Chicago, Illinois. It is one of most influential institutions of higher learning, with top-ten positions in numerous rankings and measures. The university currently enrolls approximately 5,700 students around 15,000 students overall. Chicago's department helped develop the world's first man-made, self-sustaining nuclear reaction beneath the viewing stands of university's Stagg Field. The university is also home to the University of Chicago Press, the largest press in the United States. The University of Chicago has prominent alumni. 92 Nobel laureates have been affiliated with the fourth most of any institution in the world. Similarly, 16 alumni have been awarded the MacArthur "Genius Grant". While the Rockefeller donation provided money for long-term endowment, it was stipulated that such money could not be used for buildings. The original physical campus was financed by donations from wealthy Chicagoans like Silas B. Cobb who provided the funds for the campus' first building, Cobb Lecture Hall, matched Marshall Field's pledge of $100,000. The university opened for classes on October 1, 1892. The law school was founded in 1902. Harper was replaced by a succession of three presidents whose tenures lasted until 1929. During this period, the Oriental Institute was founded to interpret archeological work in what was then called the Near East.
University of Chicago
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An early convocation ceremony at the University of Chicago
University of Chicago
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The University of Chicago
University of Chicago
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View from the Midway Plaisance
University of Chicago
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The campus of the University of Chicago. From the top of Rockefeller Chapel, the Main Quadrangles can be seen on the left (West), the Oriental Institute and the Becker Friedman Institute for Research in Economics can be seen in the center (North), and the Booth School of Business and Laboratory Schools can be seen on the right (East). The panoramic is bounded on both sides by the Midway Plaisance (South).
225.
Harvard University
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Although never formally affiliated with any denomination, the early College primarily trained Congregationalist and Unitarian clergy. James Bryant Conant began to liberalize admissions after the war. The undergraduate college became coeducational after its 1977 merger with Radcliffe College. Harvard's $37.6 billion financial endowment is the largest of any academic institution. Harvard is a large, highly residential research university. The University's large endowment allows it to offer financial aid packages. Harvard's alumni include eight U.S. presidents, several foreign heads of state, 242 Marshall Scholars. To date, 13 Turing Award winners have been affiliated as students, faculty, or staff. Harvard was formed by vote of the Massachusetts Bay Colony. It was initially called "New College" or "the college at New Towne". In 1638, the college became home to British North America's known press. In 1639, the college was renamed Harvard College after deceased clergyman John Harvard, an alumnus of the University of Cambridge. He had left his library of some 400 books. The charter creating the Harvard Corporation was granted in 1650. In the early years the College trained many Puritan ministers.
Harvard University
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Engraving of Harvard College by Paul Revere, 1767
Harvard University
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Harvard University
Harvard University
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John Harvard statue, Harvard Yard
Harvard University
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Richard Rummell's 1906 watercolor landscape view, facing northeast.
226.
Georgia State University
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Georgia State University is a public research university in downtown Atlanta, Georgia, United States. Founded in 1913, it is one of the University System of Georgia's four research universities. Georgia State University offers more than 250 graduate degree programs spread across eight academic colleges with around 3,500 faculty members. It is accredited by the Southern Association of Colleges and Schools. Approximately 27 % of the population is considered part-time while 73 % of the population is considered full-time. The university is classified according to the Carnegie Foundation for the Advancement of Teaching. The university has a full-time count of 1,142, with 69 percent of those faculty members either tenured or on tenure track. GSU has University library and Law library, which hold over 4.3 million volumes combined and serve as a federal document depository. The university has an economic impact on the Atlanta economy of more than $ billion annually. Initially intended as a school, Georgia State University was established in 1913 as the Georgia School of Technology's Evening School of Commerce. During this time, the school was divided into two divisions: Atlanta Junior College. In September 1947, the school was named the Atlanta Division of the University of Georgia. The school became the Georgia State College of Business Administration. In 1961, other programs at the school had grown enough that the name was shortened to Georgia State College. It became Georgia State University in 1969.
Georgia State University
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View of (from L-R) the Sports Arena and Library South on Decatur Street
Georgia State University
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Georgia State University
Georgia State University
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A Georgia State police vehicle on campus in Atlanta, Georgia
Georgia State University
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Rialto Center
227.
Drexel University
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Drexel University is a private research university with three campuses in Philadelphia. It was founded in 1891 by Anthony J. Drexel, a noted financier and philanthropist. As of 2015, more than 26,000 students are enrolled in over 70 undergraduate programs and more than 100 master's, doctoral, professional programs at the university. Drexel University was founded in 1891 as the Drexel Institute of Art, Science and Industry, by Philadelphia financier and philanthropist Anthony J. Drexel. The original mission of the institution was to provide educational opportunities in the "practical arts and sciences" for women and men of all backgrounds. The institution became known as the Drexel Institute of Technology in 1936, in 1970 the Drexel Institute of Technology gained university status, becoming Drexel University. The central aspect of Drexel University's focus on career preparation, in the form of its cooperative education program, was introduced in 1919. The program became integral to the university's unique educational experience. Participating students alternate periods of classroom-based study with periods of full-time, practical work experience related to their academic major and career interests. Papadakis oversaw Drexel's largest expansion in its history, with a 471 percent increase in its endowment and a 102 percent increase in student enrollment. Dr. Constantine Papadakis died of pneumonia in April 2009 while still employed as the university's president. His successor, John Anderson Fry, was formerly the president of Franklin & Marshall College and served as the Executive Vice President of the University of Pennsylvania. Under Fry's leadership, Drexel has continued its expansion, including the July 2011 acquisition of The Academy of Natural Sciences. The College of Arts and Sciences was formed in 1990 when Drexel merged the two existing College of Sciences and College of Humanities together. The College of Media Arts and design "fosters the study, exploration and management of the arts: media, design, the performing and visual."
Drexel University
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The Main Building, dedicated in 1891.
Drexel University
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A machine testing laboratory at Drexel University, circa 1904.
Drexel University
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Edmund D. Bossone Research Center, located on Market Street ' Avenue of Technology '
Drexel University
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The southern portion of Drexel's main campus
228.
Weber State University
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Weber State University is a public university in Ogden, Utah, United States. It is a coeducational, publicly supported university offering professional, liberal arts and technical certificates, as well as associate's, bachelor's and master's degrees. Weber State University is accredited by the Northwest Commission on Colleges and Universities. Programs throughout the university are accredited as well. The school was founded in 1889 as Weber Stake Academy, later changing names to Weber Academy, Weber Normal College, Weber College. Weber College became a junior college in 1933, in 1962 became Weber State College. It gained university status in 1991, when it was renamed to its current name of Weber State University. Weber State University was founded by The Church of Jesus Christ of Latter-day Saints as the Weber Stake Academy in 1889. "Weber" comes from the name of the county where the university is located. Weber County was named after John Henry Weber, an early fur trader. The university opened for students on January 7, 1889 with 98 students enrolled for classes. The first principal of Weber Stake Academy was Louis F. Moench. He served from 1889–1892 and again from 1894–1902. In the latter year, Moench was succeeded as principal by David O. McKay who served in that position until 1908. From 1914–1917, James L. Barker was the principal of the Weber Stake Academy.
Weber State University
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View of Weber State University campus from Ogden's east bench.
Weber State University
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Weber State University
Weber State University
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The Stewart Bell Tower is the most identifiable landmark of the Weber State campus and was built in 1972.
Weber State University
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Shepherd Student Union
229.
John Peter Oleson
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John Peter Oleson is a Canadian classical archaeologist and historian of ancient technology. His main interests are ancient technology, especially hydraulic technology, water-lifting devices, Roman concrete construction. Born in Hackensack, New Jersey, United States, Oleson was schooled at the Loomis School in Windsor, Connecticut. He received his BA at Harvard University in 1967 where he studied with Herbert Bloch. Oleson received his MA and PhD at Harvard University working in particular with George M.A. Hanfmann and David Mitten. From 1973–1976 Oleson taught in the Classics Department of Florida State University, Tallahassee. He was elected a Fellow of the Royal Society of Canada in 1994. From 1997 to 2001 he was a member of Canada. From 1999–2002 he was a Trustee of the Board of the Royal British Columbia Museum. He was appointed a Killam Research Fellow for 2000–2002. Since 1997 he has been a member of the Board of the American Center for Oriental Research in Amman. In 1997, along with McCann Taggart, he was a archaeologist at the Skerki Bank Deep Water Shipwreck Survey, directed by Robert Ballard. Since 2001 he has co-directed the Roman Maritime Concrete Study with Robert L. Hohlfelder. As of 2010 Oleson has published more than 95 articles concerning ancient technology, marine archaeology, the Nabataeans, the Roman Near East. He invited lectures since 1976.
John Peter Oleson
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Pioneers of diving
230.
Galen
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Galen's understanding of medicine was principally influenced by the then-current theory of humorism, as advanced by ancient Greek physicians such as Hippocrates. His theories influenced Western medical science for more than 1,300 years. Medical students continued to study Galen's writings into the 19th century. Galen saw himself as a philosopher, as he wrote in his treatise entitled That the Best Physician is Also a Philosopher. Although there is some debate over the date of his death, he was no younger than seventy when he died. Some of Galen's ideas were incorrect: he did the medieval lecturers. Galen's Greek texts gained renewed prominence during the early modern period. In the Belgian anatomist and physician Andreas Vesalius took on a project to translate many of Galen's Greek texts into Latin. De humani corporis fabrica, was greatly influenced by Galenic writing and form. Galen's name Γαληνός, Galēnos comes from the adjective "γαληνός", "calm". Galen describes his early life On the affections of the mind. Galen describes his father as a "highly amiable, just, good and man". His studies also took including Aristotelian and Epicurean. His father took care to expose him to literary and philosophical influences. There he came like Aeschrion of Pergamon, Stratonicus and Satyrus.
Galen
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Eighteenth-century portrait of Galenus by Georg Paul Busch
Galen
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Statue of Galen in Bergama, Turkey
Galen
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De curandi ratione
Galen
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Mondino dei Liuzzi, Anathomia, 1541
231.
John Wesley
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John Wesley was an Anglican cleric and theologian who, with his brother Charles and fellow cleric George Whitefield, founded Methodism. Educated at Oxford University, he was elected a fellow of Lincoln College, Oxford in 1726 and ordained a priest two years later. After an unsuccessful ministry of two years at Savannah in the Georgia Colony, he joined a religious society led by Moravian Christians. On May 1738 Wesley experienced what has come to be called his evangelical conversion, when he felt his "heart strangely warmed". Wesley subsequently departed from the Moravians, beginning his own ministry. A key step in the development of Wesley's ministry was, like Whitefield, to preach outdoors. In contrast to Whitefield's Calvinism, he embraced the Arminian doctrines that dominated the Church of England at the time. Moving across Great Britain and Ireland, Wesley helped form and organise Christian groups that developed intensive and personal accountability, discipleship and religious instruction. Most importantly, Wesley appointed unordained evangelists to travel and preach as he did and to care for these groups of people. Under Wesley's direction, Methodists became leaders including prison reform and the abolition of slavery. Although he was not a systematic theologian, he argued against its doctrine of predestination. Wesley held that, in this life, Christians could achieve a state where the love of God "reigned supreme in their hearts", giving outward holiness. Throughout his life, he remained within the Anglican church, insisting that the Methodist movement lay well within its tradition. In 2002, Wesley was placed in the BBC's poll of the 100 Greatest Britons. John Wesley was born in 1703 as the fifteenth child of Samuel Wesley and his wife Susanna Wesley.
John Wesley
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Portrait of Wesley by Frank O. Salisbury
John Wesley
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Samuel Wesley
John Wesley
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Susanna Wesley
John Wesley
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The Cathedral of Christ Church, Oxford University.
232.
Time (magazine)
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Time is an American weekly news magazine published in New York City. It was founded for decades was dominated by Henry Luce, who built a highly profitable stable of magazines. A European edition also covers the Middle East, Africa and, since 2003, Latin America. An Asian edition is based in Hong Kong. The South Pacific edition, which covers Australia, the Pacific Islands, is based in Sydney, Australia. In December 2008, Time discontinued publishing a Canadian edition. As of 2015, its circulation was 3,036,602. Richard Stengel was the managing editor to October 2013, when he joined the U.S. State Department. Nancy Gibbs has been the managing editor since October 2013. Time magazine was created by Briton Hadden and Henry Luce making it the first weekly news magazine in the United States. The two had previously worked together as chairman and managing editor respectively of the Yale Daily News. They first called the proposed magazine Facts. They wanted to emphasize brevity, so that a busy man could read it in an hour. They used the slogan "Take Time -- It's Brief". It set out to tell the news for many decades the magazine's cover depicted a single person.
Time (magazine)
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The first issue of Time (March 3, 1923), featuring Speaker Joseph G. Cannon.
Time (magazine)
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Bibi Aisha on the Cover of Time.
Time (magazine)
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Time Magazine red X covers: from left to right, Adolf Hitler, Saddam Hussein, Abu Musab al-Zarqawi, and Osama bin Laden.
233.
HowStuffWorks
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HowStuffWorks is an American commercial educational website founded by Marshall Brain to provide its target audience an insight into the way many things work. The site uses various media to explain complex concepts, mechanisms -- including photographs, diagrams, videos, animations, articles. A documentary series with the same name also premiered in November 2008 on the Discovery Channel. In 1998, North Carolina State University professor Marshall Brain started the site as a hobby. In 1999, Brain formed HowStuffWorks, Inc.. The headquarters moved to Atlanta, Georgia. HowStuffWorks originally focused on science and machines, ranging from submarines to common household appliances. After adding a staff of writers, editors, content expanded to a larger array of topics. In November 2004, HowStuffWorks moved its section to Stuffo. However, in 2006, the site now redirects visitors to the site's entertainment channel. The HowStuffWorks.com attracted at least 58 million visitors annually by 2008, according to a Compete.com survey. HowStuffWorks puts out an educational magazine called "HowStuffWorks Express" for middle school students. The company has also released a series of HowStuffWorks trivia "LidRock" discs -- CD-ROMs sold at Regal Theaters. Howstuffworks recently acquired Consumer Guide. Howstuffworks.com spun off its international division when they went public via an acquisition of a China-based company.
HowStuffWorks
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HowStuffWorks, Inc.
234.
The New York Times
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The New York Times has won more than any other news organization. The New York Times is ranked 39th in the world by circulation. Following industry trends, its circulation has fallen to fewer than one million daily since 1990. Nicknamed "The Gray Lady", The New York Times has long been regarded within the industry as a national "newspaper of record". The New York Times is owned by The New York Times Company. Jr. the Publisher and the Chairman of the Board, is a member of the Ochs-Sulzberger family that has controlled the paper since 1896. The New York Times international version, formerly the International Herald Tribune, is now called the International New York Times. The paper's motto, "That's Fit to Print", appears in the upper left-hand corner of the front page. The newspaper shortened its name in 1857. It dropped the hyphen in the 1890s. One of the earliest public controversies it was involved with was the subject of twenty editorials it published alone. In the 1880s, The New York Times transitioned gradually from editorially supporting Republican Party candidates to becoming analytical. In 1884, the paper supported Democrat Grover Cleveland in his presidential campaign. The New York Times was acquired in 1896. Under Ochs' guidance, expanding upon the Henry Raymond tradition, The New York Times achieved international scope, circulation, reputation.
The New York Times
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Cover of The New York Times (November 15, 2012), with the headline story reporting on Operation Pillar of Defense.
The New York Times
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First published issue of New-York Daily Times, on September 18, 1851.
The New York Times
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The Times Square Building, The New York Times ' publishing headquarters, 1913–2007
The New York Times
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The New York Times newsroom, 1942
235.
Stony Brook University
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The Stony Brook University is a public sea-grant and space-grant research university located in Stony Brook, New York in the United States. It is part of the State University of New York system. In 2001, SUNY Stony Brook was elected to the Association of American Universities, joining four private universities and one public university elsewhere in its state. It is also a member of the larger Universities Research Association for which its president Samuel Stanley is a council president. Stony Brook is the largest single-site employer on Long Island. More than 24,500 students are enrolled at the university, which has over 14,500 employees and over 2,400 faculty. Stony Brook has a number of athletics teams. SUCOLI opened with an inaugural class of 148 students, on the grounds of the William Robertson Coe Planting Fields estate. These first students were admitted on a tuition-free basis. Lee left later that year due to bureaucratic matters regarding the central administration at Albany. More recently, it has adopted the name Stony Brook University. In 1963, only three years after the release of the Heald Report, the Governor commissioned the “Education of Health Professions” report. The report outlined the need for expansion of the university system to prepare medical professionals for the future needs of the state. In 1965 the State University appointed John S. Toll, a renowned physicist from the University of Maryland as the second president of Stony Brook. In 1966 the University set forth initial timetables for the development of the Health Science Center which would house the University’s health programs and Hospital.
Stony Brook University
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Coe Hall on the original Oyster Bay campus (used 1957-1964)
Stony Brook University
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State University of New York at Stony Brook
Stony Brook University
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Main alley across the Stony Brook Campus
Stony Brook University
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The Staller Center for the Arts at Stony Brook University West Campus
236.
Rice University
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The university is situated near the Houston Museum District and is adjacent to the Texas Medical Center. Rice is generally considered the top university and the most selective institute of higher education in the state of Texas. Opened in 1912 after the murder of its namesake William Marsh Rice, Rice is now a research university with an undergraduate focus. Its emphasis on education is demonstrated by a small student body and 6:1 student-faculty ratio. The university has a very high level of activity with $ million in sponsored funding in 2011. Rice is noted in the fields of artificial heart research, nanotechnology. It was ranked first in the world in materials science research by the Times Higher Education in 2010. Rice is a member of the Association of American Universities. Rice students are bound by the strict Honor Code, enforced by a student-run Honor Council. Rice competes in 14 NCAA Division I varsity sports and is a part of Conference USA, often competing with its cross-town rival the University of Houston. Intramural and club sports are offered in a wide variety of activities such as jiu jitsu, water polo, crew. Rice's will specified the institution was to be "a competitive institution of the highest grade" and that only white students would be permitted to attend. On the morning of September 23, 1900, Rice, age 84, was found dead by his valet, presumed to have died in his sleep. Jones was not prosecuted since he cooperated with the district attorney, testified against Patrick. Baker helped Rice's estate direct the fortune, worth $4.6 million in 1904, towards the founding of what was to be called the Rice Institute.
Rice University
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Rice University
Rice University
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Seal of Rice University
Rice University
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Administration Building, Rice Institute, Houston, Texas (postcard, circa 1912-1924)
Rice University
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John F. Kennedy speaking at Rice Stadium in 1962
237.
Internet Archive
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The Internet Archive is a San Francisco–based nonprofit digital library with the stated mission of "universal access to all knowledge". As of October 2016, its collection topped 15 petabytes. In addition to its archiving function, the Archive is an activist organization, advocating for a open Internet. The Wayback Machine, contains over 150 billion web captures. The Archive also oversees one of the world's largest digitization projects. Founded by Brewster Kahle in May 1996, the Archive is a 501 nonprofit operating in the United States. Its headquarters are in California, where about 30 of its 200 employees work. Most of its staff work in its book-scanning centers. The Archive has data centers in three Californian cities, San Francisco, Richmond. The Archive was officially designated as a library by the State of California in 2007. Brewster Kahle founded the Archive at around the same time that he began the for-profit web crawling company Alexa Internet. The archived content wasn't available to the general public until 2001, when it developed the Wayback Machine. In late 1999, the Archive expanded its collections beginning with the Prelinger Archives. Now the Internet Archive includes texts, audio, software. According to its site: Most societies place importance on preserving artifacts of their culture and heritage.
Internet Archive
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Since 2009, headquarters have been at 300 Funston Avenue in San Francisco, a former Christian Science Church
Internet Archive
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Internet Archive
Internet Archive
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Mirror of the Internet Archive in the Bibliotheca Alexandrina
Internet Archive
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From 1996 to 2009, headquarters were in the Presidio of San Francisco, a former U.S. military base
238.
Mathematical Association of America
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The Mathematical Association of America is a professional society that focuses on mathematics accessible at the undergraduate level. The MAA is headquartered at 1529 18th Street, Northwest in the Dupont Circle neighborhood of Washington, D.C.. The organization publishes mathematics books, including the American Mathematical Monthly, the most widely read mathematics journal in the world according to records on JSTOR. The MAA cosponsors with the American Mathematical Society the Joint Mathematics Meeting, held in early January of each year. On occasion the Society for Industrial and Applied Mathematics joins in these meetings. Regional sections also hold regular meetings. The association publishes multiple journals: The American Mathematical Monthly is expository, aimed to research mathematicians. Mathematics Magazine is expository, aimed at the junior-senior level. The College Mathematics Journal is expository, aimed at the freshman-sophomore level. Math Horizons is expository, aimed at undergraduate students. MAA FOCUS is the association newsletter. The Association publishes Mathematical Sciences Digital Library. The service launched with the online-only Journal of Online Mathematics and its Applications and a set of classroom tools, Digital Classroom Resources. Ultimately, six high school students are chosen to represent the U.S. at the International Mathematics Olympiad. Allendoerfer, Trevor Evans, Lester R. Ford, George Pólya, Merten M. Hasse, Henry L. Alder and Euler Book Prize awards.
Mathematical Association of America
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MAA headquarters in Washington, D.C.
239.
Andrews University
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Andrews University is a university in Berrien Springs, Michigan. Andrews is the largest evangelical Christian college or university in terms of undergraduate and graduate enrollment. The university consists of colleges, offering 130 undergraduate majors and 70 graduate majors. In addition, post-baccalaureate degrees are offered by all. It is accredited by the Adventist Accrediting Association. Andrews University was founded as a small Seventh-day Adventist school called Battle Creek College in 1874 named for the nearby city of Michigan. In 1901, the school moved to its current location in Berrien Springs. It is said that the school had was packed up in 16 boxcars and sent on its way. The school was EMC for short. As "the first school among us having a distinctive Biblical name". This Battle Creek College operated until 1938. Emmanuel Missionary College continued to grow slowly through the 20th century. In the 1940s, the current location of the College of Arts and Sciences, was built as the administration building. Its construction marked the culmination of an aggressive program. In the 1930s Seventh-day Adventist leaders established a Theological Seminary.
Andrews University
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Aerial view of Andrews University
240.
University of Waterloo
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The University of Waterloo is a public research university with a main campus located in Waterloo, Ontario. The main campus is located in "Uptown" Waterloo, adjacent to Waterloo Park. The university offers academic programs administered by ten faculty-based schools. The university also operates four affiliated university colleges. Waterloo is a member of a group of research-intensive universities in Canada. University of Waterloo is most famous for its cooperative education programs, which allow the students to integrate their education with applicable work experiences. University of Waterloo operates the largest post secondary program of its kind in the world, with over 19,000 co-op students and 5,200 employers. It was established to fill the need to train technicians for Canada's growing postwar economy. The university as of 2016 has 30,600 undergraduate and 5,300 postgraduate students. Former students of the university can be found across Canada and in over 140 countries. Waterloo's varsity teams, known as the Waterloo Warriors, compete in the Ontario University Athletics conference of the Canadian Interuniversity Sport. When Gerald Hagey assumed the presidency of Waterloo College in 1953, he made his priority to procure the funds necessary to expand the institution. Following that method, Waterloo College established the Waterloo College Associate Faculties on 4 April 1956, as a non-denominational board affiliated with the college. The academic structure of the Associated Faculties was originally focused on co-operative education in the applied sciences – largely built around the proposals of Ira Needles. On 25 the Associated Faculties announced the purchase of over 74 hectares of land west of Waterloo College.
University of Waterloo
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Constructed in 1958, the Douglas Wright Engineering Building is the oldest building that was erected for use by the university.
University of Waterloo
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University of Waterloo
University of Waterloo
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The Dana Porter Library holds the university's main collection for humanities and social science.
University of Waterloo
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The Mackenzie King Village residences, constructed in 2002, are the latest set of residences constructed by the university.
241.
Smithsonian (magazine)
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Smithsonian is the official journal published by the Smithsonian Institution in Washington, D.C. The first issue was published in 1970. Thompson would later recall that his philosophy for the new magazine was that it "would stir curiosity in already receptive minds. It would deal with history as it is relevant to the present. It would present art, since true art is never dated, in the richest possible reproduction. It would peer into the future via coverage of social progress and of science and technology. Technical matters would be digested and made intelligible by skilled writers who would stimulate readers to reach upward while not turning them off with jargon. We would find the best writers and the best photographers—not unlike the best of the old Life." In 1973, the magazine turned a profit for the first time. By 1974, circulation had nearly quadrupled, to 635,000, it reached the one million milestone in 1975—one of the most successful launches of its time. Smithsonian magazine provides in-depth analysis of varied topics within a diverse range of scientific areas, adds fascinating photography to supplement its comprehensive features. Notable past and current contributors to Smithsonian have included: Official website
Smithsonian (magazine)
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Smithsonian
242.
CNN
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The Cable News Network is an American basic cable and satellite television channel, owned by the Turner Broadcasting System division of Time Warner. Upon its launch, CNN was the first all-news television channel in the United States. Its headquarters at the CNN Center in Atlanta is only used for programming. CNN is sometimes referred to as CNN/U.S. to distinguish the American channel from its international sister network, CNN International. As of August 2010, CNN is available in over million U.S. households. Broadcast coverage of the U.S. channel extends throughout Canada. Globally, CNN programming airs through CNN International, which can be seen by viewers in territories. As of February 2015, CNN is available to approximately 96,289,000 cable, telco television households in the United States. The Cable News Network was launched on June 1, 1980. By Ted Turner the husband and wife team of David Walker and Lois Hart anchored the channel's first newscast. Since its debut, CNN has expanded its reach to a number of cable and satellite television providers, specialized closed-circuit channels. The company has several regional and foreign-language networks around the world. CNN2, was launched on January 1, 1982 and featured a continuous 24-hour cycle of 30-minute news broadcasts. On October 1987, Jessica McClure, an 18-month-old toddler, fell down a well in Midland, Texas. The event helped make its name.
CNN
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Replica of the newsroom at CNN Center.
CNN
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CNN
CNN
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Operation Desert Storm as captured live on a CNN night vision camera with reporters narrating.
CNN
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The stage for the second 2008 CNN-YouTube presidential debate.
243.
NASA
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President Dwight D. Eisenhower established NASA in 1958 with a distinctly civilian orientation encouraging peaceful applications in science. The National Aeronautics and Space Act was passed on July 1958, disestablishing NASA's predecessor, the National Advisory Committee for Aeronautics. The new agency became operational on October 1958. The agency is also responsible for the Launch Services Program which provides countdown management for unmanned NASA launches. NASA shares data such as from the Greenhouse Gases Observing Satellite. From 1946, the National Advisory Committee for Aeronautics had been experimenting with rocket planes such as the supersonic Bell X-1. In the early 1950s, there was challenge to launch an artificial satellite for the International Geophysical Year. An effort for this was the American Project Vanguard. This led to an agreement that a federal agency mainly based on NACA was needed to conduct all non-military activity in space. The Advanced Research Projects Agency was created in February 1958 to develop technology for military application. On July 1958, Eisenhower signed the National Aeronautics and Space Act, establishing NASA. A NASA seal was approved by President Eisenhower in 1959. Elements of the United States Naval Research Laboratory were incorporated into NASA. Many of ARPA's early space programs were also transferred to NASA. In December 1958, NASA gained control of the Jet Propulsion Laboratory, a facility operated by the California Institute of Technology.
NASA
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1963 photo showing Dr. William H. Pickering, (center) JPL Director, President John F. Kennedy, (right). NASA Administrator James Webb in background. They are discussing the Mariner program, with a model presented.
NASA
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Seal of NASA
NASA
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At launch control for the May 28, 1964, Saturn I SA-6 launch. Wernher von Braun is at center.
NASA
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Mercury-Atlas 6 launch on February 20, 1962
244.
Wikisource
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Wikisource is an online digital library of free content textual sources on a wiki, operated by the Wikimedia Foundation. The project's aims are to host all forms of free text, in many languages, translations. Originally conceived as an archive to store important historical texts, it has expanded to become a general-content library. The project officially began under the name Project Sourceberg. It received its own domain name seven months later. It is also cited by organisations such as the National Archives and Records Administration. Verification was initially made offline, or by trusting the reliability of digital libraries. Now works are supported by online scans via the ProofreadPage extension, which ensures the accuracy of the project's texts. Each representing a specific language, now only allow works backed up with scans. While the bulk of its collection are texts, Wikisource as a whole hosts other media, to audio books. Some Wikisources allow user-generated annotations, subject to the specific policies of the Wikisource in question. Wikisource's early history included the move to language subdomains in 2005. The original concept for Wikisource was as storage for important historical texts. These texts were intended to support Wikipedia articles, as an archive in its own right. The collection was initially focused on important cultural material, distinguishing it from other digital archives such as Project Gutenberg.
Wikisource
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The original Wikisource logo
Wikisource
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Screenshot of wikisource.org home page
Wikisource
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::: Original text
Wikisource
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::: Action of the modernizing tool
245.
Eduard Jan Dijksterhuis
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Eduard Jan Dijksterhuis was a Dutch historian of science. He titled his Ph.D. thesis "A Contribution to the Knowledge of the Flat Helicoid." From 1916 to 1953 he taught mathematics, physics and cosmography. He wrote about Archimedes in early 1940s. He advocated changes in the mathematics was taught to reinforce the formal characteristics of the discipline. In 1950, he was appointed as a member of the Royal Netherlands Academy of Arts and Sciences. In 1953, he was appointed to teach the history of mathematics and the nature of science at Leiden University. In 1962 he was awarded the Sarton Medal by the History of Science Society.
Eduard Jan Dijksterhuis
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Dijksterhuis (1910s)
246.
Clifford A. Pickover
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Other Fellows have included Isaac Asimov. His The Math Book was winner of the 2011 Neumann Prize. He received his Ph.D. from Yale University's Department of Molecular Biophysics and Biochemistry where he conducted research on X-ray scattering and protein structure. Pickover graduated first in his class after completing the four-year undergraduate program in three years. For much of his career, Pickover has published technical articles in the areas of scientific visualization, recreational mathematics. Pickover is still employed at the IBM Thomas J. Watson Research Center, where he is the editor of the IBM Journal of Research and Development. He is an editorial board member for Odyssey and Leonardo. He is also the Brain-Strain columnist for magazine, for many years, he was the Brain-Boggler columnist for Discover magazine. Pickover has received more than 100 IBM invention achievement awards, four external honor awards. Pickover's primary interest is in finding new ways to expand creativity by melding art, science, other seemingly disparate areas of human endeavor. Pickover is an inventor with over 300 patents, puzzle contributor to magazines geared to children and adults. His Neoreality and Heaven Virus science-fiction series explores the fabric of religion. He also has published articles in the areas of skepticism, technical speculation. Additional work includes topics that involve breathing motions of proteins, snow-flake like patterns for speech sounds, cartoon-face representations of data, biomorphs. Pickover has also written extensively on the reported experiences of people on the psychotropic DMT.
Clifford A. Pickover
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Clifford Alan Pickover
Clifford A. Pickover
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In the 1990s, Pickover created virtual caverns from extremely simple numerical simulations that reminded him of the Lechuguilla Cave, pictured here.
Clifford A. Pickover
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Visualization of chaotic attractor. Pickover’s earliest books often focused on patterns that characterize mathematics such as fractals, chaos, and number theory. Computer graphics, reminiscent of this chaotic attractor, were common in his early works.
Clifford A. Pickover
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Forest troll. (Theodor Kittelsen, 1906). Some of Pickover’s later books often discussed "science at the edges," including such topics as parallel universes, quantum immortality, alien life, and elf-like beings seen by some people who use dimethyltryptamine.
247.
Oxford University Press
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Oxford University Press is the largest university press in the world, the second oldest after Cambridge University Press. They are headed to the delegates, who serves as OUP's chief executive and as its major representative on other university bodies. Oxford University has used a similar system to oversee OUP since the 17th century. The university grew into a major printer of Bibles, prayer books, scholarly works. OUP took on the project that expanded to meet the ever-rising costs of the work. Moves into international markets led to OUP opening its own offices outside the United Kingdom, beginning with New York City in 1896. By contracting out binding operations, the modern OUP publishes some 6,000 new titles around the world each year. OUP was first exempted from United Kingdom corporation tax in 1978. The Oxford University Press Museum is located on Oxford. Visits are led by a member of the archive staff. Displays include a 19th-century printing press, the printing and history of the Oxford Almanack, Alice in Wonderland and the Oxford English Dictionary. The first printer associated with Oxford University was Theoderic Rood. An edition of Rufinus's Expositio in symbolum apostolorum, was printed by another, anonymous, printer. Famously, this was mis-dated in Roman numerals as "1468", thus apparently pre-dating Caxton. Rood's printing included John Ankywyll's Compendium totius grammaticae, which set new standards for teaching of Latin grammar.
Oxford University Press
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Oxford University Press on Walton Street.
Oxford University Press
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2008 conference booth
248.
BBC
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The British Broadcasting Corporation is a British public service broadcaster. The BBC operates under its Agreement with the Secretary of State for Culture, Media and Sport. Britain's first public broadcast from the Marconi factory in Chelmsford took place in June 1920. It was featured the famous Australian Soprano Dame Nellie Melba. The broadcast caught the people's imagination and marked a turning point in the British public's attitude to radio. However, this public enthusiasm was not shared in official circles where such broadcasts were held to interfere with important civil communications. A Scottish Calvinist, was appointed its General Manager in December 1922 a few weeks after the company made its first official broadcast. The company was to be financed by a royalty on the sale of BBC wireless receiving sets from approved manufacturers. To this day, the BBC aims to follow the Reithian directive to "inform, entertain". The financial arrangements soon proved inadequate. Set sales were disappointing as amateurs made listeners bought rival unlicensed sets. By mid-1923, the Postmaster-General commissioned a review of broadcasting by the Sykes Committee. This was to be followed by a simple 10 shillings licence fee with no royalty once the wireless manufactures protection expired. The BBC's broadcasting monopoly was made explicit for the duration of its current licence, as was the prohibition on advertising. The BBC was also required to source all news from external wire services.
BBC
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BBC Television Centre at White City, West London, which opened in 1960 and closed in 2013
BBC
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BBC Pacific Quay in Glasgow, which was opened in 2007
BBC
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BBC New Broadcasting House, London which came into use during 2012–13.
BBC
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The headquarters of the BBC at Broadcasting House in Portland Place, London, England. This section of the building is called 'Old Broadcasting House'.
249.
PhilPapers
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PhilPapers is an international, interactive academic database of journal articles for professionals and students in philosophy. It is maintained for Digital Philosophy at the University of Western Ontario. As of 2012, the general editors are David Chalmers. It has a good position in the ranking of repositories. PhilPapers receives financial support including a substantial grant in early 2009 from the Joint Information Systems Committee in the United Kingdom. The archive is praised for its regular updates. In addition to archiving papers, the editors engage in surveying academic philosophers. List of academic databases and search engines Official website
PhilPapers
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PhilPapers
250.
Anaxagoras
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Anaxagoras was a Pre-Socratic Greek philosopher. Born in Clazomenae in Asia Minor, Anaxagoras was the first to bring philosophy to Athens. He introduced the concept of Nous as an ordering force, which separated out the original mixture, homogeneous, or nearly so. He also gave scientific accounts of natural phenomena. Anaxagoras is believed to have enjoyed some wealth and political influence in Asia Minor. However, he supposedly surrendered this out of a fear that they would hinder his search for knowledge. A sentence, denoted by Maximus, as being "possessed of sought-after wisdom!" Although a Greek, he may have been a soldier of the Persian army when Clazomenae was suppressed during the Ionian Revolt. In early manhood he went to Athens, rapidly becoming the centre of Greek culture. There he is said to have remained for thirty years. The poet Euripides derived from him an enthusiasm for science and humanity. Anaxagoras brought philosophy and the spirit of scientific inquiry to Athens. He was the first to explain that the moon shines by reflecting the sun's light. Disturbances in this air sometimes causes earthquakes. These speculations made him vulnerable to a charge of impiety.
Anaxagoras
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Anaxagoras; part of a fresco in the portico of the National University of Athens.
Anaxagoras
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Anaxagoras, depicted as a medieval scholar in the Nuremberg Chronicle
251.
Autolycus of Pitane
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Autolycus of Pitane was a Greek astronomer, mathematician, geographer. The crater Autolycus was named in his honour. Autolycus was born within Ionia, Asia Minor. Autolycus is known to have taught Arcesilaus. Another On Risings and Settings of celestial bodies. Autolycus' works were translated in the sixteenth century. On the Moving Sphere is believed to be the oldest mathematical treatise from ancient Greece, completely preserved. All mathematical works prior to Autolycus' Sphere are taken from later summaries, commentaries, or descriptions of the works. In Europe, it was brought back during the crusades in the 12th century, translated back into Latin. In his Sphere, Autolycus studied the characteristics and movement of a sphere. The theorem statement is clearly enunciated, finally a concluding remark is made. Moreover, it gives indications of what theorems were well known in his day. The second book is actually an expansion of higher quality. He wrote that "any star which sets always rises and sets at the same point in the horizon." Autolycus was a strong supporter of Eudoxus' theory of homocentric spheres.
Autolycus of Pitane
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De sphaera quae movetur liber
252.
Bion of Abdera
Bion of Abdera
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v
253.
Chrysippus
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Chrysippus of Soli was a Greek Stoic philosopher. He was a native of Soli, Cilicia, but moved to Athens as a young man, where he became a pupil of Cleanthes in the Stoic school. When Cleanthes died, around 230 BC, Chrysippus became the third head of the school. Chrysippus excelled in logic, the theory of knowledge, ethics and physics. He created an original system of propositional logic in order to better understand the workings of the universe and role of humanity within it. He adhered to a deterministic view of fate, but nevertheless sought a role for personal freedom in thought and action. He initiated the success of Stoicism as one of the most influential philosophical movements for centuries in the Greek and Roman world. Chrysippus, the son of Apollonius of Tarsus, was born at Soli, Cilicia. He was slight in stature, is reputed to have trained as a long-distance runner. While still young, he lost his substantial inherited property when it was confiscated to the king's treasury. Chrysippus moved to Athens, where he became the disciple of Cleanthes, then the head of the Stoic school. He is believed to have attended the courses of Arcesilaus and his successor Lacydes, in the Platonic Academy. Chrysippus threw himself eagerly into the study of the Stoic system. His reputation for learning among his contemporaries was considerable. He succeeded Cleanthes as head of the Stoic school when Cleanthes died, in around 230 BC.
Chrysippus
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Roman copy of a Hellenistic bust of Chrysippus (British Museum)
Chrysippus
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A partial marble bust of Chrysippus that is a Roman copy of a Hellenistic original (Louvre Museum).
Chrysippus
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Cleromancy in ancient Greece. Chrysippus accepted divination as part of the causal chain of fate.
Chrysippus
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Greek amphora depicting Euripides ' Medea. Chrysippus regarded Medea as a prime example of how bad judgments could give rise to irrational passions.
254.
Ctesibius
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Ctesibius or Ktesibios or Tesibius was a Greek inventor and mathematician in Alexandria, Ptolemaic Egypt. He wrote the first treatises on the science of compressed air and its uses in pumps. This, On pneumatics earned the title of "father of pneumatics." None of his written work has survived, including his Memorabilia, a compilation of his research, cited by Athenaeus. Ctesibius was probably the first head of the Museum of Alexandria. Very little is known of his life but his inventions were well known. It is said that his first career was as a barber. During his time as a barber, he invented a counterweight-adjustable mirror. His other inventions include a organ, considered the precursor of the modern pipe organ, improved the water clock or clepsydra. The principle of the siphon has also been attributed to him. According to Diogenes Laertius, Ctesibius was miserably poor. Proclus and Hero of Alexandria also mention him. Landels, J.G.. Engineering in the ancient world. Berkeley: Univ. of California Press.
Ctesibius
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Ctesibius' water clock, as visualized by the 17th-century French architect Claude Perrault
255.
Democritus
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Democritus was an influential Ancient Greek pre-Socratic philosopher primarily remembered today for his formulation of an atomic theory of the universe. Democritus was born around 460 BCE although, some thought it was BCE. His exact contributions are difficult to disentangle from those of his mentor Leucippus, as they are often mentioned together in texts. Largely ignored in ancient Athens, Democritus is said to have been disliked so much by Plato that the latter wished all of his books burned. He was nevertheless well known to his northern-born Aristotle. Many consider Democritus to be the "father of modern science". None of his writings have survived; only fragments are known from his vast body of work. Democritus was said to be born in an Ionian colony of Teos, although some called him a Milesian. It was said that Democritus's father was from a noble family and so wealthy that he received Xerxes on his march through Abdera. Democritus spent the inheritance which his father left him on travels into distant countries, to satisfy his thirst for knowledge. He traveled to Asia, was even said to have reached India and Ethiopia. It is known that he wrote on Babylon and Meroe; he visited Egypt, Diodorus Siculus states that he lived there for five years. Himself declared that among his contemporaries none had made greater journeys, met more scholars than himself. He particularly mentions the Egyptian mathematicians, whose knowledge he praises. Theophrastus, too, spoke of him as a man who had seen many countries.
Democritus
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Democritus
Democritus
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Democritus by Hendrick ter Brugghen, 1628.
Democritus
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Rembrandt, The Young Rembrandt as Democritus the Laughing Philosopher (1628-1629).
Democritus
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Democritus meditating on the seat of the soul by Léon-Alexandre Delhomme (1868).
256.
Diophantus
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These texts deal with solving algebraic equations. This led to tremendous advances in number theory, the study of Diophantine equations and of Diophantine approximations remain important areas of mathematical research. Diophantus coined the term παρισότης to refer to an approximate equality. Diophantus was the Greek mathematician who recognized fractions as numbers; thus he allowed rational numbers for the solutions. In modern use, Diophantine equations are usually algebraic equations with integer coefficients, for which integer solutions are sought. Diophantus also made advances in mathematical notation. Little is known about the life of Diophantus. He lived to 298. Much of our knowledge of the life of Diophantus is derived from a 5th-century Greek anthology of number games and puzzles created by Metrodorus. One of the problems states:'Here lies Diophantus,' the wonder behold. The dear child of sage After attaining half the measure of his father's life fate took him. After consoling his fate by the science of numbers for four years, he ended his life.' However, the accuracy of the information cannot be independently confirmed. The Arithmetica is the major work of Diophantus and the most prominent work on algebra in Greek mathematics. It is a collection of problems giving numerical solutions of both determinate and indeterminate equations.
Diophantus
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Title page of the 1621 edition of Diophantus' Arithmetica, translated into Latin by Claude Gaspard Bachet de Méziriac.
Diophantus
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Problem II.8 in the Arithmetica (edition of 1670), annotated with Fermat's comment which became Fermat's Last Theorem.
257.
Hipparchus
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Hipparchus of Nicaea was a Greek astronomer, geographer, mathematician. He is considered the founder of trigonometry but is most famous for his incidental discovery of precession of the equinoxes. Hipparchus was born in Nicaea, Bithynia, probably died on the island of Rhodes. He is known to have been a working astronomer at least from 162 to 127 BC. Hipparchus is considered the greatest ancient astronomical observer and, by some, the greatest overall astronomer of antiquity. He was the first whose quantitative and accurate models for the motion of the Sun and Moon survive. For this he certainly made perhaps the mathematical techniques accumulated over centuries from Mesopotamia. He developed trigonometry and constructed trigonometric tables, he solved several problems of spherical trigonometry. With his solar and lunar theories and his trigonometry, he may have been the first to develop a reliable method to predict solar eclipses. Relatively little of Hipparchus's direct work survives into modern times. Although he wrote at least fourteen books, only his commentary on the popular astronomical poem by Aratus was preserved by later copyists. There is a strong tradition that Hipparchus was born in Nicaea, in the ancient district of Bithynia, in what today is the country Turkey. His date was calculated based on clues in his work. Hipparchus must have lived some time after 127 BC because he analyzed and published his observations from that year. Hipparchus obtained information from Alexandria as well as Babylon, but it is not known when or if he visited these places.
Hipparchus
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Hipparchus as he appears in " The School of Athens " by Raphael.
258.
Hippasus
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Hippasus of Metapontum, was a Pythagorean philosopher. Little is known about his life or his beliefs, but he is sometimes credited with the discovery of the existence of irrational numbers. The discovery of irrationality is not specifically ascribed to Hippasus by any ancient writer. Some modern scholars though have suggested that he discovered the irrationality of √2, believed to have been discovered around the time that he lived. Little is known about the life of Hippasus. He may have lived in the late 5th century BC, about a century after the time of Pythagoras. Hippasus is recorded under the city of Sybaris in Iamblichus list of each city's Pythagoreans. Memory was the most valued faculty. According to one statement, Hippasus left no writings, according to another he was the author of the Mystic Discourse, written to bring Pythagoras into disrepute. Hippasus is sometimes credited with the discovery of the existence of irrational numbers, following which he was drowned at sea. Pythagoreans preached that all numbers could be expressed as the ratio of integers, the discovery of irrational numbers is said to have shocked them. However, the evidence linking the discovery to Hippasus is confused. Pappus merely says that the knowledge of irrational numbers originated in the Pythagorean school, that the member who first divulged the secret perished by drowning. Iamblichus gives a series of inconsistent reports. Iamblichus clearly states that the drowning at sea was a punishment from the gods for impious behaviour.
Hippasus
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Hippasus of Metapontum
259.
Hippocrates of Chios
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Hippocrates of Chios was an ancient Greek mathematician, geometer, astronomer, who lived c. 470 – c. 410 BCE. He was born on the isle of Chios, where he originally was a merchant. After some misadventures he went to Athens, possibly for litigation. There he grew into a leading mathematician. On Chios, Hippocrates may have been a pupil of the astronomer Oenopides of Chios. The reductio ad argument has been traced to him. Only a famous, fragment of Hippocrates' Elements is existent, embedded in the work of Simplicius. In this fragment the area is calculated of some Hippocratic lunes -- see Lune of Hippocrates. The strategy apparently was to divide a circle into a number of crescent-shaped parts. If it were possible to calculate the area of each of those parts, then the area of the circle as a whole would be known too. Only much later was it proven that this approach had no chance of success, because the factor pi is transcendental. In the century after Hippocrates at least four other mathematicians wrote their own Elements, steadily improving logical structure. In this way Hippocrates' pioneering work laid the foundation for Euclid's Elements, to remain the standard textbook for many centuries. Two other contributions by Hippocrates in the field of mathematics are noteworthy. He found a way to tackle the problem of ` duplication of the cube', the problem of how to construct a root.
Hippocrates of Chios
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The Lune of Hippocrates. Partial solution of the " Squaring the circle " task, suggested by Hippocrates. The area of the shaded figure is equal to the area of the triangle ABC. This is not a complete solution of the task (the complete solution is proven to be impossible with compass and straightedge).
260.
Hypatia
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Hypatia, often called Hypatia of Alexandria, was a Greek mathematician, astronomer, philosopher in Egypt, then a part of the Byzantine Empire. She was the head of the Neoplatonic school at Alexandria, where she taught philosophy and astronomy. The mathematician and philosopher Hypatia of Alexandria was the only daughter of the mathematician Theon of Alexandria. She was educated in Athens. However, not all Christians were as hostile towards her: some Christians even used Hypatia as symbolic of Virtue. Neither did she feel abashed in going to an assembly of men. For all men on account of her extraordinary dignity and virtue admired her the more. Together with the references by the pagan philosopher Damascius, these are the extant records left by Hypatia's pupils at the Platonist school of Alexandria. Hypatia was murdered during an episode of city-wide anger stemming from the Bishop of Alexandria. Her death is symbolic for some historians. Of the many accounts of Hypatia's death, the most complete is the one written around 415 by Socrates of Constantinople and included in the Historia Ecclesiastica. The edict angered Christians as well as Jews. At one such gathering, a Christian follower of Cyril, applauded the new regulations. Many people felt that Hierax was attempting to incite the crowd into sedition. Orestes reacted swiftly and violently out of what Scholasticus suspected was "jealousy the growing power of the bishops… encroached on the jurisdiction of the authorities".
Hypatia
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"Death of the philosopher Hypatia, in Alexandria" from Vies des savants illustres, depuis l'antiquité jusqu'au dix-neuvième siècle, 1866, by Louis Figuier.
Hypatia
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"Hypatia", at the Haymarket Theatre, January 1893
Hypatia
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Cameron 's 1867 photograph Hypatia
261.
Menelaus of Alexandria
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Menelaus of Alexandria was a Greek mathematician and astronomer, the first to recognize geodesics on a curved surface as natural analogs of straight lines. Ptolemy also mentions, in his Almagest, two astronomical observations made in January of the year 98. These were occultations of the stars Spica and Beta Scorpii by the moon, a few nights apart. Ptolemy used these observations to confirm precession of a phenomenon, discovered in the 2nd century BCE. Sphaerica is the only book that has survived, in an Arabic translation. Composed of three books, it deals with its application in astronomical calculations. It was later translated by the sixteenth century astronomer and mathematician Francesco Maurolico. The lunar crater Menelaus is named after him. Ivor Bulmer-Thomas. "Menelaus of Alexandria." Dictionary of Scientific Biography 9:296-302. "d'Alexandrie", in R. Goulet, Dictionnaire des Philosophes Antiques, vol. IV, 2005, p. 456-464. O'Connor, John J.; Robertson, Edmund F. "Menelaus of Alexandria", MacTutor History of Mathematics archive, University of St Andrews. Halley's Latin Translation from the Arabic and Hebrew Versions at Google Books
Menelaus of Alexandria
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Contents
Menelaus of Alexandria
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Sphaericorum libri tres
262.
Nicomedes (mathematician)
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Nicomedes was an ancient Greek mathematician. Almost nothing is known apart from references in his works. Studies have stated that Nicomedes was died in about 210 BC. But, we do because he criticized Eratosthenes' method of doubling the cube. Consequently, it is believed that Nicomedes lived before Apollonius of Perga. In the course of his investigations, Nicomedes created the conchoid of Nicomedes; a discovery, contained in his famous work entitled On conchoid lines. Nicomedes discovered three distinct types of conchoids, now unknown. T. L. Heath, A History of Greek Mathematics. G. J. Toomer, Biography in Dictionary of Scientific Biography. O'Connor, John J.; Robertson, Edmund F. "Nicomedes", MacTutor History of Mathematics archive, University of St Andrews.
Nicomedes (mathematician)
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Conchoids of line with common center.
263.
Philolaus
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Philolaus was a Greek Pythagorean and Presocratic philosopher. He argued that at the foundation of everything is the part played by the limiting and limitless, which combine together in a harmony. He is also credited with originating the theory that the Earth was not the center of the universe. According to August Böckh, who cites Nicomachus, Philolaus was the successor of Pythagoras. Philolaus is variously reported as being born in either Croton, or Tarentum, or Metapontum — all part of Magna Graecia. It is most likely that he came from Croton. He may have fled the second burning of the Pythagorean meeting-place around 454 BCE, after which he migrated to Greece. According to Plato's Phaedo, he was the instructor of Simmias and Cebes at Thebes, around the time the Phaedo takes place, in 399 BCE. This would make him a contemporary of Socrates, agrees with the statement that Philolaus and Democritus were contemporaries. The various reports about his life are scattered among the writings of much later writers and are of dubious value in reconstructing his life. He apparently lived for some time at Heraclea, where he was the pupil of Aresas, or Arcesus. The pupils of Philolaus were said to have included Xenophilus, Phanto, Echecrates, Diocles and Polymnastus. Diogenes Laërtius speaks of Philolaus composing one book, but elsewhere he speaks of three books, as do Aulus Gellius and Iamblichus. It might have been one treatise divided into three books. Plato is said to have procured a copy of his book from which, it was later claimed, Plato composed much of his Timaeus.
Philolaus
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Philolaus book, (Charles Peter Mason, 1870)
Philolaus
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Medieval woodcut by Franchino Gaffurio, depicting Pythagoras and Philolaus conducting musical investigations.
264.
Porphyry (philosopher)
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Porphyry of Tyre was a Neoplatonic philosopher, born in Tyre, in the Roman Empire. He published the Enneads, the only collection of the work of his teacher Plotinus. His commentary on Euclid's Elements was used by Pappus of Alexandria. He also wrote many works himself on a wide variety of topics. In Latin translation it was the standard textbook on logic throughout the Middle Ages. Porphyry was born in Tyre. Under Longinus he studied rhetoric. At one point he became suicidal. On the advice of Plotinus he went to live in Sicily for five years to recover his mental health. On returning to Rome, he completed an edition of the writings of Plotinus together with a biography of his teacher. The two men differed publicly on the issue of theurgy. In his later years, he married Marcella, an enthusiastic student of philosophy. The date of his death is uncertain. Porphyry is best known for his contributions to philosophy. In medieval textbooks, the all-important Arbor porphyriana illustrates his logical classification of substance.
Porphyry (philosopher)
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Porphire Sophiste, in a French 16th-century engraving
Porphyry (philosopher)
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Imaginary debate between Averroes (1126–1198 AD) and Porphyry (234–c. 305 AD). Monfredo de Monte Imperiali Liber de herbis, 14th century.
265.
Posidonius
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Posidonius "of Apameia" or "of Rhodes", was a Greek Stoic philosopher, politician, astronomer, geographer, historian and teacher native to Apamea, Syria. He was acclaimed as the greatest polymath of his age. His vast body of work exists today only in fragments. Writers such as Strabo and Seneca provide most of the information, from history, about his life. Posidonius, nicknamed "the Athlete", was born to a Greek family in Apamea, a Hellenistic city on the river Orontes in northern Syria. Posidonius completed his higher education in Athens, where he was a student of the aged Panaetius, the head of the Stoic school. But soon Posidonius was involved in heated debates with many Stoic philosophers of the school. The incidents concerning Posidonius's conflict and final break up with the Stoics are mentioned by Galen in his book On the Doctrines of Plato and Hippocrates. Posidonius settled around 95 BCE in a maritime state which became a citizen. In Rhodes, Posidonius actively took part in political life, his high standing is apparent from the offices he held. He attained the highest public office as one of the Prytaneis of Rhodes. Posidonius served during the Marian and Sullan era. Along with other Greek intellectuals, Posidonius favored Rome as the stabilizing power in a turbulent world. His connections to the Roman class were also important to his scientific research. His entry into government provided Posidonius with powerful connections to facilitate his travels to far away places, even beyond Roman control.
Posidonius
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Bust of Posidonius from the Naples National Archaeological Museum
Posidonius
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Posidonius's method for calculating the circumference of the earth, relied on the altitude of the star Canopus
Posidonius
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World map according to ideas by Posidonius (150-130 BCE), drawn in 1628 by cartographers Petrus Bertius and Melchior Tavernier. Many of the details could not have been known to Posidonius; rather, Bertius and Tavernier show Posidonius's ideas about the positions of the continents.
Posidonius
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Posidonius, depicted as a medieval scholar in the Nuremberg Chronicle
266.
Ptolemy
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Claudius Ptolemy was a Greek writer, known as a mathematician, astronomer, geographer, astrologer, poet of a single epigram in the Greek Anthology. He lived in the city of Alexandria in the Roman province of Egypt, held Roman citizenship. Beyond that, reliable details of his life are known. His birthplace has been given as Ptolemais Hermiou in the Thebaid by the 14th-century astronomer Theodore Meliteniotes. Ptolemy wrote several scientific treatises, three of which were of importance to later Byzantine, Islamic and European science. The first is the astronomical treatise now known as the Almagest, although it was originally then known as the "Great Treatise". The second is the Geography, a thorough discussion of the geographic knowledge of the Greco-Roman world. The third is the astrological treatise in which he attempted to adapt horoscopic astrology to the natural philosophy of his day. This is sometimes more commonly known as the Tetrabiblos from the Greek meaning "Four Books" or by the Latin Quadripartitum. If, as was common, this was the emperor, citizenship would have been granted between AD 68. The astronomer would also have had a praenomen, which remains unknown. Ptolemaeus is a Greek name. It is of Homeric form. All the kings after him, until Egypt became a Roman province in 30 BC, were also Ptolemies. Abu Ma ` shar recorded a belief that a different member of this royal line "attributed it to Ptolemy".
Ptolemy
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Engraving of a crowned Ptolemy being guided by the muse Astronomy, from Margarita Philosophica by Gregor Reisch, 1508. Although Abu Ma'shar believed Ptolemy to be one of the Ptolemies who ruled Egypt after the conquest of Alexander the title ‘King Ptolemy’ is generally viewed as a mark of respect for Ptolemy's elevated standing in science.
Ptolemy
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Early Baroque artist's rendition
Ptolemy
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A 15th-century manuscript copy of the Ptolemy world map, reconstituted from Ptolemy's Geography (circa 150), indicating the countries of " Serica " and "Sinae" (China) at the extreme east, beyond the island of "Taprobane" (Sri Lanka, oversized) and the "Aurea Chersonesus" (Malay Peninsula).
Ptolemy
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Prima Europe tabula. A C15th copy of Ptolemy's map of Britain
267.
Pythagoras
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Pythagoras of Samos was an Ionian Greek philosopher, mathematician, the putative founder of the movement called Pythagoreanism. Most of the information about Pythagoras was written down centuries after he lived, so little reliable information is known about him. He travelled, visiting Egypt and Greece, maybe India. Around 530 BC, there established some kind of school or guild. In 520 BC, he returned to Samos. Pythagoras made influential contributions in the late 6th century BC. He is best known for the Pythagorean theorem which bears his name. Many of the accomplishments credited to Pythagoras may actually have been accomplishments of his successors. Some accounts mention that numbers were important. Burkert states that Aristoxenus and Dicaearchus are the most important accounts. Aristotle had written a separate work On the Pythagoreans, no longer extant. However, the Protrepticus possibly contains parts of On the Pythagoreans. Dicaearchus, Aristoxenus, Heraclides Ponticus had written on the same subject. According to Clement of Alexandria, Pythagoras was a disciple of Soches, Plato of Sechnuphis of Heliopolis. Herodotus, other early writers agree that Pythagoras was the son of Mnesarchus, born on a Greek island in the eastern Aegean called Samos.
Pythagoras
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Bust of Pythagoras of Samos in the Capitoline Museums, Rome.
Pythagoras
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Bust of Pythagoras, Vatican
Pythagoras
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A scene at the Chartres Cathedral shows a philosopher, on one of the archivolts over the right door of the west portal at Chartres, which has been attributed to depict Pythagoras.
Pythagoras
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Croton on the southern coast of Magna Graecia (Southern Italy), to which Pythagoras ventured after feeling overburdened in Samos.
268.
Simplicius of Cilicia
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Simplicius of Cilicia was a disciple of Ammonius Hermiae and Damascius, was one of the last of the Neoplatonists. He wrote extensively on the works of Aristotle. His works have preserved much information about earlier philosophers which would have otherwise been lost. Simplicius was consequently one of the last members of the Neoplatonist school. The school had its headquarters in Athens. It became the centre of the last efforts to maintain Hellenistic religion against the encroachments of Christianity. Imperial edicts enacted in the 5th century against paganism gave legal protection against personal maltreatment. In the 528 the emperor Justinian ordered that pagans should be removed from government posts. Some were robbed of their property, some put to death. The order specified that if they did not within three months convert to Christianity, they were to be banished from the Empire. In addition, it was forbidden any longer to teach jurisprudence in Athens. But they were disappointed in their hopes. Of the subsequent fortunes of the seven philosophers we learn nothing. We know about where Simplicius lived and taught. As to his personal history, especially his migration to Persia, no definite allusions are to be found in the writings of Simplicius.
Simplicius of Cilicia
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Commentary on Aristotle's De Caelo by Simplicius. This 14th-century manuscript is signed by a former owner, Basilios Bessarion.
269.
Sporus of Nicaea
Sporus of Nicaea
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v
270.
Thales of Miletus
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Aristotle reported Thales's hypothesis that the nature of matter was a single substance: water. In mathematics, Thales used geometry to calculate the heights of pyramids and the distance of ships from the shore. He is the known individual to use deductive reasoning applied by deriving four corollaries to Thales' theorem. He is the first known individual to whom a mathematical discovery has been attributed. Apollodorus of Athens, writing during the 2nd BCE, thought Thales was born about the year 625 BCE. The dates of Thales' life are roughly established by a datable events mentioned in the sources. According to Herodotus, Thales predicted the solar eclipse of May 28, 585 BC. Nevertheless, several years later, anxious for family, he adopted his nephew Cybisthus. Thales involved himself in many activities, taking the role of an innovator. Some say that he left no writings, others say that he wrote On the Solstice and On the Equinox. Thales identifies the Milesians as Athenian colonists. Thales' principal occupation was engineering. He was aware of the existence of the lodestone, was the first to be connected to knowledge of this in history. According to Aristotle, Thales thought lodestones had souls, because of the fact of iron being attracted to them. Several anecdotes suggest Thales was not solely a philosopher, but also involved in business.
Thales of Miletus
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Thales of Miletus
Thales of Miletus
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An olive mill and an olive press dating from Roman times in Capernaum, Israel.
Thales of Miletus
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Total eclipse of the Sun
Thales of Miletus
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The Ionic Stoa on the Sacred Way in Miletus
271.
Theodosius of Bithynia
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Theodosius of Bithynia was a Greek astronomer and mathematician who wrote the Sphaerics, a book on the geometry of the sphere. Born in Bithynia, Theodosius is cited by Vitruvius as having invented a sundial suitable for any place on Earth. His Sphaerics may have been based on a work by Eudoxus of Cnidus. Francesco Maurolico translated his works in the 16th century. Ivor Bulmer-Thomas, "Theodosius of Bithynia," Dictionary of Scientific Biography 13:319–320. Also on line "Theodosius of Bithynia." Complete Dictionary of Scientific Biography. 2008. Encyclopedia.com. 25 Mar. 2015. Chisholm, Hugh, ed.. "Theodosius of Tripolis". Encyclopædia Britannica. 26. Cambridge University Press.
Theodosius of Bithynia
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v
272.
Xenocrates
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Xenocrates of Chalcedon was a Greek philosopher, mathematician, leader of the Platonic Academy from 339/8 to 314/3 BC. His teachings followed those of Plato, which he attempted to define more closely, often with mathematical elements. Xenocrates distinguished a third compounded of the two, to which correspond respectively, sense, intellect and opinion. Unity and duality he considered to be gods which rule the universe, the soul is a self-moving number. There are daemonical powers, intermediate between the mortal, which consist in conditions of the soul. He held that mathematical objects and the Platonic Ideas are identical, unlike Plato who distinguished them. In Ethics, Xenocrates taught that external goods can enable it to effect its purpose. Xenocrates was a native of Chalcedon. By the most probable calculation he was born 396/5 BC, died 314/3 BC at the age of 82. Moving in early youth, Xenocrates became the pupil of Aeschines Socraticus, but subsequently joined himself to Plato, whom he accompanied in 361. Upon his master's death, he paid a visit with Aristotle to Hermias of Atarneus. In 339/8 BC, Xenocrates succeeded Speusippus in the presidency of the school, defeating his competitors Menedemus of Pyrrha and Heraclides Ponticus by a few votes. On three occasions he was member of an Athenian legation, once to Philip, twice to Antipater. Xenocrates resented the Macedonian influence then dominant at Athens. In 314/3, Xenocrates died after tripping over a pot in his house.
Xenocrates
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Xenocrates
Xenocrates
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Xenocrates, depicted as a medieval scholar in the Nuremberg Chronicle
273.
Zeno of Elea
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Zeno of Elea was a pre-Socratic Greek philosopher of Magna Graecia and a member of the Eleatic School founded by Parmenides. Aristotle called the inventor of the dialectic. He is best known for his paradoxes, which Bertrand Russell has described as "immeasurably profound". Little is known for certain about Zeno's life. According to Diogenes Laertius, Zeno conspired to overthrow Nearchus the tyrant. Eventually, Zeno was arrested and tortured. When Nearchus leaned in to listen to the secret, Zeno bit his ear. The tyrant lost that part of his body." Within Men of the Same Name, Demetrius said it was the nose, instead. Zeno may have also interacted with other tyrants. According to Laertius, Heraclides Lembus, within his Satyrus, said these events occurred against Diomedon instead of Nearchus. This would be impossible as Phalaris had died before Zeno was even born. According to Plutarch, Zeno attempted to kill the tyrant Demylus. After failing, he had, "with his own teeth bit off his tongue, he spit it in the tyrant’s face." Although ancient writers refer to the writings of Zeno, none of his works survive intact.
Zeno of Elea
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Zeno shows the Doors to Truth and Falsity (Veritas et Falsitas). Fresco in the Library of El Escorial, Madrid.
Zeno of Elea
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Achilles and the tortoise
274.
Almagest
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The Almagest is the critical source of information on ancient Greek astronomy. It has also been valuable to students of mathematics because it documents Hipparchus's work, lost. Ptolemy set up a public inscription in 147 or 148. The late N. T. Hamilton found that the version of Ptolemy's models set out in the Canopic Inscription was earlier than the version in the Almagest. Hence it can not have been completed before about 150, a century after Ptolemy began observing. The Syntaxis Mathematica or Almagest consists of thirteen sections, called books. An example illustrating how the Syntaxis was organized is given below. It is a Latin edition printed in 1515 at Venice by Petrus Lichtenstein. Then follows an explanation of chords with table of chords; observations of the obliquity of the ecliptic; and an introduction to spherical trigonometry. There is also a study of the angles made by the ecliptic with tables. Book III covers the motion of the Sun. Ptolemy begins explaining the theory of epicycles. Book VI covers solar and lunar eclipses. Books VII and VIII cover the motions of the fixed stars, including precession of the equinoxes. They also contain a catalogue of 1022 stars, described by their positions in the constellations.
Almagest
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Ptolemy's Almagest became an authoritative work for many centuries.
Almagest
Almagest
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Picture of George Trebizond's Latin translation of Almagest
275.
Arithmetica
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Arithmetica is an Ancient Greek text on mathematics written by the mathematician Diophantus in the 3rd century AD. It is a collection of 130 algebraic problems giving numerical solutions of indeterminate equations. Equations in the book are called Diophantine equations. The method for solving these equations is known as Diophantine analysis. Most of the Arithmetica problems lead to quadratic equations. In Book 3, Diophantus solves problems of finding values which make two linear expressions simultaneously into cubes. In book 4, he finds rational powers between given numbers. He also noticed that numbers of 3 can not be the sum of two squares. Diophantus also appears to know that every number can be written as the sum of four squares. The Greek manuscripts that survived to the present contain no more than six books. The four books are thought to have been translated by Qusta ibn Luqa. Norbert Schappacher has written: resurfaced around 1971 in a copy from 1198 AD. Arithmetica became known to mathematicians in the Islamic world in the tenth century when Abu'l-Wefa translated it into Arabic. Muhammad ibn Mūsā al-Khwārizmī Diophantus Alexandrinus, Pierre de Fermat, Claude Gaspard Bachet de Meziriac, et De numeris multangulis liber unus. Cum comm.
Arithmetica
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Cover of the 1621 edition, translated into Latin from Greek by Claude Gaspard Bachet de Méziriac.
276.
Euclid's Elements
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Euclid's Elements is a mathematical and geometric treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt circa 300 BC. It is a collection of definitions, postulates, mathematical proofs of the propositions. The books cover the ancient Greek version of elementary number theory. It is the oldest extant axiomatic deductive treatment of mathematics. It has proven instrumental in the development of logic and modern science. According to Proclus, the term "element" was used to describe a theorem that helps furnishing proofs of many other theorems. The element in the Greek language is the same as letter. This suggests that theorems in the Elements should be seen as standing as letters to language. Euclid's Elements has been referred to as the most influential textbook ever written. Scholars believe that the Elements is largely a collection of theorems proven by other mathematicians, supplemented by some original work. The Heiberg manuscript, is from a Byzantine workshop around 900 and is the basis of modern editions. Papyrus Oxyrhynchus 29 only contains the statement of one proposition. Although known to, for instance, Cicero, no record exists of the text having been translated prior to Boethius in the fifth or sixth century. The Arabs received the Elements around 760; this version was translated into Arabic under Harun al Rashid circa 800. The Byzantine scholar Arethas commissioned the copying of the extant Greek manuscripts of Euclid in the late ninth century.
Euclid's Elements
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The frontispiece of Sir Henry Billingsley's first English version of Euclid's Elements, 1570
Euclid's Elements
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A fragment of Euclid's "Elements" on part of the Oxyrhynchus papyri
Euclid's Elements
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An illumination from a manuscript based on Adelard of Bath 's translation of the Elements, c. 1309–1316; Adelard's is the oldest surviving translation of the Elements into Latin, done in the 12th-century work and translated from Arabic.
Euclid's Elements
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Euclidis – Elementorum libri XV Paris, Hieronymum de Marnef & Guillaume Cavelat, 1573 (second edition after the 1557 ed.); in-8, 350, (2)pp. THOMAS-STANFORD, Early Editions of Euclid's Elements, n°32. Mentioned in T.L. Heath's translation. Private collection Hector Zenil.
277.
On the Sizes and Distances (Aristarchus)
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This work calculates the sizes of the Sun and Moon, well as their distances from the Earth in terms of Earth's radius. The book was presumably preserved by students of Pappus of Alexandria's course in mathematics, although there is no evidence of this. The editio princeps was published by John Wallis in 1688, using medieval manuscripts compiled by Sir Henry Savile. The earliest Latin translation was made by Giorgio Valla in 1488. There is also a 1572 Latin commentary by Frederico Commandino. The work's method relied on several observations: The apparent size of the Sun and the Moon in the sky. The rest of the article details a reconstruction of Aristarchus' method and results. From the trigonometry, we can calculate that S L = 1 cos φ = sec φ. φ is extremely close to 90 °. Aristarchus determined φ to be a thirtieth of a quadrant less than a right angle: in 87 °. Using geometrical analysis in the style of Euclid, Aristarchus determined that 18 < S L < 20. In other words, the distance to the Sun was somewhere between 20 times greater than the distance to the Moon. This value was accepted by astronomers for the next thousand years, until the invention of the telescope permitted a more precise estimate of solar parallax. The appearance of these equations can be simplified using = d / ℓ and x = s / ℓ. These formulae are likely a good approximation to those of Aristarchus.
On the Sizes and Distances (Aristarchus)
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Aristarchus's 3rd century BC calculations on the relative sizes of, from left, the Sun, Earth and Moon, from a 10th-century CE Greek copy
278.
On Sizes and Distances
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On Sizes and Distances is a text by the ancient Greek astronomer Hipparchus. Some of its contents have been preserved in the works of Ptolemy and his commentator Pappus of Alexandria. Modern historians have attempted to reconstruct the methods of Hipparchus using the available texts. Most of what is known about Hipparchus' text comes from two ancient sources: Ptolemy and Pappus. Their accounts have proven less useful in reconstructing the procedures of Hipparchus. In Almagest 11, Ptolemy writes: Now Hipparchus made such an examination principally from the sun. First, he assumes the sun to show the least perceptible parallax to find its distance. But with respect to the sun, not only the amount of its parallax, but also whether it shows any parallax at all is altogether doubtful. This passage gives a general outline of what Hipparchus provides no details. Ptolemy clearly did not agree with the methods employed by Hipparchus, thus did not go into any detail. The works of Hipparchus were still extant when Pappus wrote his commentary in the 4th century. He fills in some of the details that Ptolemy omits: Now, Hipparchus made such an examination principally from the sun, not accurately. In the first book "On Sizes and Distances" it is assumed that the earth has the ratio of a center to the sun. And by means of the eclipse adduced by him... Hence the mean is 77...
On Sizes and Distances
279.
Problem of Apollonius
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In Euclidean plane geometry, Apollonius's problem is to construct circles that are tangent to three given circles in a plane. This solution does not use only straightedge and compass constructions. Viète's approach, which uses simpler limiting cases to solve more complicated ones, is considered a plausible reconstruction of Apollonius' method. This has applications in positioning systems such as LORAN. Later mathematicians introduced algebraic methods, which transform a geometric problem into algebraic equations. These developments provide a classification of solutions according to 33 essentially different configurations of the given circles. Apollonius' problem has stimulated further work. Generalizations beyond have been studied. The configuration of three mutually tangent circles has received particular attention. René Descartes gave a formula relating the radii of the given circles, now known as Descartes' theorem. Solutions to Apollonius' problem are sometimes called Apollonius circles, although the term is also used for other types of circles associated with Apollonius. The property of tangency is defined as follows. Two geometrical objects are said to intersect if they have a point in common. In practice, two distinct circles are tangent if they intersect at only one point; if they intersect at two points, they are not tangent. The same holds true for a circle.
Problem of Apollonius
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Figure 1: A solution (in pink) to Apollonius' problem. The given circles are shown in black.
280.
Squaring the circle
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Squaring the circle is a problem proposed by ancient geometers. It may be taken to ask whether specified axioms of Euclidean geometry concerning the existence of lines and circles entail the existence of such a square. Approximate squaring to any given non-perfect accuracy, in contrast, is possible in a finite number of steps, since there are rational numbers arbitrarily close to π. The expression "squaring the circle" is sometimes used as a metaphor for trying to do the impossible. Methods to approximate the area of a given circle with a square were known already to Babylonian mathematicians. Indian mathematicians also found an approximate method, though less accurate, documented in the Sulba Sutras. Archimedes showed that the value of pi lay between 1/7 and 10/71. See Numerical approximations of π for more on the history. The first known Greek to be associated with the problem was Anaxagoras, who worked on it while in prison. Hippocrates of Chios squared certain lunes, in the hope that it would lead to a solution — see Lune of Hippocrates. Even then there were skeptics—Eudemus argued that magnitudes cannot be divided up without limit, so the area of the circle will never be used up. The problem was even mentioned in Aristophanes's play The Birds. It is believed that Oenopides was the first Greek who required a plane solution. James Gregory attempted a proof of its impossibility in Vera Circuli et Hyperbolae Quadratura in 1667. Although his proof was faulty, it was the first paper to attempt to solve the problem using algebraic properties of pi.
Squaring the circle
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Squaring the circle: the areas of this square and this circle are both equal to π. In 1882, it was proven that this figure cannot be constructed in a finite number of steps with an idealized compass and straightedge.
281.
Doubling the cube
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Doubling the cube, also known as the Delian problem, is an ancient geometric problem. As with the related problems of squaring the circle and trisecting the angle, doubling the cube is now known to be impossible. However, the nonexistence of a solution was finally proven by Pierre Wantzel in 1837. The impossibility of doubling the cube is therefore equivalent to the statement that 3√2 is not a constructible number. This implies that the degree of the field extension generated by a constructible point must be a power of 2. The field extension generated by 3√2, however, is of degree 3. We begin with the segment defined in the plane. We are required to construct a line segment defined by two points separated by a distance of 3√2. Therefore, the degree of the field extension corresponding to each new coordinate is 2 or 1. By Gauss's Lemma, p is also irreducible over ℚ, is thus a minimal polynomial over ℚ for 3√2. The field extension ℚ:ℚ is therefore of degree 3. The oracle responded that they must double the size of the altar to Apollo, a regular cube. This may be why the problem is referred to in the 350s BC by the author of the pseudo-Platonic Sisyphus as still unsolved. However another version of the story says that all three found solutions but they were too abstract to be of practical value. Menaechmus' original solution involves the intersection of two conic curves.
Doubling the cube
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Contents
282.
Angle trisection
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Angle trisection is a classical problem of compass and straightedge constructions of ancient Greek mathematics. It concerns equal to one third of a given arbitrary angle, using only two tools: an unmarked straightedge, a compass. The problem as stated is generally impossible to solve, as shown by Pierre Wantzel in 1837. However, although there is no way to trisect an angle in general with a straightedge, some special angles can be trisected. For example, it is relatively straightforward to trisect a right angle. It is possible to trisect an arbitrary angle by using tools other than straightedge and compass. For example, neusis construction, also known to ancient Greeks, involves simultaneous rotation of a marked straightedge, which can not be achieved with the original tools. Other techniques were developed by mathematicians over the centuries. These "solutions" are simply incorrect. Three problems proved elusive, specifically, trisecting the angle, squaring the circle. Pierre Wantzel published a proof of the impossibility of classically trisecting an arbitrary angle in 1837. Wantzel's proof, restated in modern terminology, uses the abstract algebra of a topic now typically combined with Galois theory. From a solution of these two problems, one may pass to a solution of the other by a compass and straightedge construction. The triple-angle formula gives an expression relating the cosines of its trisection: cos θ = 4cos3 − 3cos. This equivalence reduces the geometric problem to a purely algebraic problem.
Angle trisection
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Rulers. The displayed ones are marked — an ideal straightedge is un-marked
Angle trisection
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Angles may be trisected via a Neusis construction, but this uses tools outside the Greek framework of an unmarked straightedge and a compass.
Angle trisection
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compasses
283.
Cyrene, Libya
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Cyrene was an ancient Greek and Roman city near present-day Shahhat, Libya. It was most important of the five Greek cities in the region. It gave the classical name Cyrenaica that it has retained to modern times. Cyrene lies in a lush valley in the Jebel Akhdar uplands. The city was named after Kyre, which the Greeks consecrated to Apollo. It was also a famous school of philosophy in the 3rd century BC, founded by Aristippus, a disciple of Socrates. It was then nicknamed the "Athens of Africa". The Oracle had offered the advice to find a new city in Libya. Not knowing how to get to Libya they sent a messenger to Crete to find someone to lead them on their journey. They found a dealer in purple dyes named Corobius. He had once traveled across from Libya called Platea. After two years of settling the colony they went back to the Oracle to get advice. The Oracle had repeated his advice to move directly to the country of Libya instead of across to Libya. So they moved to a place called Aziris. They were settled into what is now Cyrene.
Cyrene, Libya
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The ruins of Cyrene
Cyrene, Libya
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Apollo Kitharoidos from Cyrene. Roman statue from the 2nd century AD now in the British Museum.
Cyrene, Libya
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Detail of the Cyrene bronze head in the British Museum (300 BC).
284.
Library of Alexandria
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The Royal Library of Alexandria or Ancient Library of Alexandria in Alexandria, Egypt, was one of the largest and most significant libraries of the ancient world. It was dedicated to the nine goddesses of the arts. The library was part of a larger institution called the Musaeum of Alexandria, where many of the most famous thinkers of the ancient world studied. The library was created by Ptolemy I Soter, the successor of Alexander the Great. Most of the books were kept as papyrus scrolls. Estimates range from 40,000 to 400,000 at its height. Sources differ on when it occurred. The library may in truth have suffered several fires over many years. After the main library was destroyed, scholars used a "library" in a temple known as the Serapeum, located in another part of the city. The library may have finally been destroyed in AD 642. The library itself is known to have had a cataloguing department. A hall contained shelves for the collections of papyrus scrolls known as bibliothekai. According to popular description, an inscription above the shelves read: The place of the cure of the soul. The library was but one part of the Musaeum of Alexandria, which functioned as a sort of institute. In addition to the library, even a zoo containing exotic animals.
Library of Alexandria
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The Great Library of Alexandria, O. Von Corven, 19th century
Library of Alexandria
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This Latin inscription regarding Tiberius Claudius Balbilus of Rome (d. c. AD 79) mentions the "ALEXANDRINA BYBLIOTHECE" (line eight).
Library of Alexandria
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The Burning of the Library at Alexandria in 391 AD, an illustration from 'Hutchinsons History of the Nations', c. 1910
Library of Alexandria
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5th century scroll which illustrates the destruction of the Serapeum by Theophilus
285.
Platonic Academy
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The Academy was founded by Plato in ca. 387 BC in Athens. Aristotle studied there before founding his own school, the Lyceum. The Academy persisted throughout the Hellenistic period until coming to an end after the death of Philo of Larissa in 83 BC. The Platonic Academy has been cited by historians as the first higher institution in the Western world. Among the religious observances that took place at the Akademeia was a torchlit race from altars within the city to Prometheus' altar in the Akademeia. Funeral games also took place from Athens to the Hekademeia and then back to the polis. The road to Akademeia was lined with the gravestones of Athenians. The site of the Academy is located near Colonus, approximately, 1.5 km north of Athens' Dipylon gates. The site was rediscovered in modern Akadimia Platonos neighbourhood; considerable excavation has been accomplished and visiting the site is free. Today can visit the archaeological site of the Academy located on either side of the Cratylus street in the area of Colonos and Plato's Academy. According to Debra Nails, Speusippus "joined the group in about 390 BC". She claims, "It is not until Eudoxus of Cnidos arrives in the mid-380s BC that Eudemus recognizes a formal Academy." Originally, the location of the meetings was on Plato's property often as it was the nearby Academy gymnasium; this remained so throughout the fourth century. Though the Academic club was exclusive, not open to the public, it did not, during at least Plato's time, charge fees for membership. Therefore, there was not at that time a "school" in the sense of a clear distinction between teachers and students, or even a formal curriculum.
Platonic Academy
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Plato from The School of Athens by Raphael, 1509
Platonic Academy
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Ancient road to the Academy.
Platonic Academy
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Map of Ancient Athens. The Academy is north of Athens.
Platonic Academy
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The School of Athens by Raphael (1509–1510), fresco at the Apostolic Palace, Vatican City.
286.
Ancient Greece
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Ancient Greece was a civilization belonging to a period of Greek history from the Greek Dark Ages to c. 5th century BC to the end of antiquity. Immediately following this period was the beginning of the Byzantine era. Included in ancient Greece is the period of Classical Greece, which flourished during the 5th to 4th centuries BC. Classical Greece began with the era of the Persian Wars. Because of conquests by Alexander the Great of Macedonia, Hellenistic civilization flourished to the western end of the Mediterranean Sea. Classical Antiquity in the Mediterranean region is commonly considered to have ended in the 6th century AD. Classical Antiquity in Greece is preceded by the Dark Ages, archaeologically characterised by the protogeometric and geometric styles of designs on pottery. The end of the Dark Ages is also frequently dated to the year of the first Olympic Games. The earliest of these is the Archaic period, in which artists made larger free-standing sculptures with the dreamlike "archaic smile". The Archaic period is often taken to end in 508 BC. This period saw Greco-Persian Wars and the Rise of Macedon. Following the Classical period was the Hellenistic period, during which Greek culture and power expanded into the Near and Middle East. This period ends with the Roman conquest. Herodotus is widely known as the "father of history": his Histories are eponymous of the entire field. Herodotus was succeeded by authors such as Thucydides, Xenophon, Demosthenes, Plato and Aristotle.
Ancient Greece
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The Parthenon, a temple dedicated to Athena, located on the Acropolis in Athens, is one of the most representative symbols of the culture and sophistication of the ancient Greeks.
Ancient Greece
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Dipylon Vase of the late Geometric period, or the beginning of the Archaic period, c. 750 BC.
Ancient Greece
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Political geography of ancient Greece in the Archaic and Classical periods
287.
Regions of ancient Greece
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The regions of ancient Greece were areas identified by the ancient Greeks as geographical sub-divisions of the Hellenic world. These regions are described in the legends and myths of the ancient Greeks. Conceptually, there is no clear theme to the structure of these regions. Some, particularly in the Peloponnese, can be seen primarily as geo-physical units, defined by physical boundaries such as mountain ranges and rivers. These regions retained their identity, even when the identity of the people living there changed during the Dark Ages. Nevertheless, these regions also survived the upheaval of the Dark Ages, showing that they had acquired less political connotations. Outside the Peloponnese and central Greece, geographical identities did change over time suggesting a closer connection with tribal identity. Over time political bodies uniting the cities of a region became common in the Classical period. These traditional sub-divisions of Greece form the basis for the modern system of regional units of Greece. However, there are important differences, with many of the smaller ancient regions not represented in the current system. To fully understand the ancient history of Greece therefore requires more detailed description of the ancient regions. Continental Greece was a geographic region of Greece. The equivalent Greek term is more rarely used. It forms the western part of the regional unit of Aetolia-Acarnania. The capital and city in ancient times was Stratos.
Regions of ancient Greece
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Political structure in ancient Greece
Regions of ancient Greece
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Map showing the major regions of mainland ancient Greece, and adjacent "barbarian" lands
288.
Cycladic culture
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Cycladic civilization is an Early Bronze Age culture of the Cyclades, Greece, in the Aegean Sea, spanning the period from approximately 3200–2000 BC. These figures have been stolen from burials to satisfy the Cycladic antiquities market since the early 20th century. Only about 40% of the 1,400 figurines found are of known origin, since looters destroyed evidence of the rest. Excavated sites include Saliagos and Kephala, which showed signs of copper-working. The chronology of Cycladic civilization is divided into three major sequences: Early, Middle and Late Cycladic. The early period, beginning c. 3000 BC segued into the archaeologically murkier Middle Cycladic c. 2500 BC. By the end of the Late Cycladic sequence there was essential convergence between Cycladic and Minoan civilization. There is some tension between the dating systems used for Cycladic civilization, one "cultural" and one "chronological". Sites were looted and a brisk trade in forgeries arose. The context for many of these Cycladic Figurines has thus been mostly destroyed; their meaning may never be completely understood. Another intriguing and mysterious object is that of the Cycladic frying pans. Early Cycladic culture evolved in three phases, between c. 3300 and 2000 BC, when it was increasingly submerged in the rising influence of Minoan Crete. Cycladic art Goulandris Museum of Cycladic Art History of the Cyclades
Cycladic culture
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Cycladic culture
Cycladic culture
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Frying-pan with incised decoration of a ship. Early Cycladic II, Chalandriani, Syros 2800–2300 BC)
289.
Minoan civilization
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It belongs to a period of Greek history preceding both the Mycenaean civilization and Ancient Greece. It was rediscovered at the beginning of the 20th century through the work of British archaeologist Arthur Evans. The term "Minoan" refers to the mythic King Minos, was originally given as a description to the pottery of this period. Minos was associated in Greek myth with the labyrinth and the Minotaur, which Evans identified with the site at Knossos, the largest Minoan site. The poet Homer recorded a tradition that Crete once had 90 cities. The Minoan period saw significant contacts between Crete, the Aegean and the Mediterranean, particularly the Near East. Some of its best art is preserved in the city of Akrotiri, on the island of Santorini, destroyed during the Thera eruption. The term "Minoan" refers to the mythic "king" Minos of Knossos. Who first coined the term is debated. It is commonly attributed to the archeologist Arthur Evans. Minos was associated in Greek myth with the labyrinth, which Evans identified with the site at Knossos. Likely, Arthur Evans read the book, continuing the use of the term in his own writings and findings. Evans claims to have applied it, but not to have invented it. Hoeck had in mind the Crete of mythology. He had no idea that the archaeological Crete had existed.
Minoan civilization
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Minoan civilization
Minoan civilization
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Minoan copper ingot.
Minoan civilization
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Fresco showing three women who were possibly queens. [citation needed]
290.
Mycenaean Greece
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Mycenaean Greece was the last phase of the Bronze Age in Ancient Greece. It represents the advanced civilization in mainland Greece, with urban organization, works of system. The most prominent site was Mycenae, in Argolid, to which the culture of this era owes its name. Mycenaean-influenced settlements also appeared on the coast of Asia Minor, the Levant, Italy. Mycenaean Greece was consisted of a network of palace states that developed rigid economic systems. At the head of this society was the king, known as wanax. Various theories have been proposed for the end of this civilization, among them the Dorian invasion or activities connected to the “Sea Peoples”. Additional theories such as natural disasters and climatic changes have been also suggested. The Mycenaean period became the historical setting of much ancient Greek literature and mythology, including the Trojan Epic Cycle. The Age in mainland Greece is generally termed after the Greek name for Greece. The Middle Helladic period faced a slower pace of development, as well as the evolution of megaron-type cist graves. Finally, the Late Helladic period roughly coincides with Mycenaean Greece. The transition period from the Bronze Age to the Iron Age in Greece is known as Sub-Mycenaean. Homer used the ethnonyms Achaeans, Danaans and Argives, to refer to the besiegers. Egyptian records mention a T-n-j or Danaya land for the first time in circa 1437 BC, during the reign of Pharaoh Thutmoses III.
Mycenaean Greece
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Mycenaean Greece
Mycenaean Greece
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The Lion Gate, the main entrance of the citadel of Mycenae, 13th century BC.
Mycenaean Greece
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Two Mycenaean Greek warriors with boar's tusk helmets on a dual-chariot on a fresco from Pylos (about 1350 BC) (left) and Two Mycenaean female charioteers from Tiryns, 1200 BCE (right)
291.
Greek Dark Ages
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Around then, the Hittite civilization suffered serious disruption and cities from Troy to Gaza were destroyed. Following the collapse, smaller settlements suggest depopulation. In Greece, the Linear B writing of the Greek language used by Mycenaean bureaucrats ceased. The decoration on Greek pottery after about 1100 BC is restricted to generally geometric styles. The Mycenaean civilization started to collapse from 1200 BC. The foreign countries... made a conspiracy in their islands. All at once the lands were on the move, scattered in war. No country could stand before their arms…. Their league was Peleset, Tjeker, Shekelesh, Denyen and Weshesh. The world of organized state armies, kings, redistributive systems disappeared. Most of the information about the period comes from burial sites and the grave goods contained within them. The autonomous cultures of reduced complexity are noted for such diversity of their material cultures in pottery styles, burial practices and settlement structures. The pottery style, Proto- Geometric signaled the loss of previous designs that were more complex. These newer designs were simpler, including only lines and curves, signaling a simplified society. Generalizations about the "Dark Age Society" are generally considered false, because the various cultures throughout Greece cannot be grouped into a large "Dark Age Society" category.
Greek Dark Ages
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Greek Dark Ages
Greek Dark Ages
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The Protogeometric building and the cemetery at Toumba Lefkandi.
292.
Archaic Greece
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According to Anthony Snodgrass, the Archaic period in ancient Greece was bounded by two revolutions in the Greek world. The Archaic period saw developments in Greek politics, economics, international relations, culture. It laid the groundwork for the classical period, both politically and culturally. The word "archaic" derives from the Greek word archaios, which means "old". It refers before the classical. However, Archaic Greece has come to be studied for its own achievements. The term is still in use. Much of our evidence about the classical period of ancient Greece comes from written histories, such as Thucydides' History of the Peloponnesian War. By contrast, we have no such evidence from the Archaic period. However, none of this evidence is in the quantity for which we have it in the classical period. What is lacking in written evidence, however, is made up in the rich archaeological evidence from the Archaic Greek world. Indeed, where much of our knowledge of Greek art comes from later Roman copies, all of the surviving Archaic Greek art is original. Other sources for the period are the traditions recorded by later Greek writers such as Herodotus. Indeed, Herodotus does not even record any dates before 480 BC. Politically, the Archaic period saw the development of the polis as the predominant unit of political organisation.
Archaic Greece
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Archaic kouros from Thebes
Archaic Greece
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Orientalizing style
Archaic Greece
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Black-figure style
293.
Classical Greece
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Classical Greece was a period of around 200 years in Greek culture. This Classical period saw the annexation of much of modern-day Greece by its subsequent independence. Classical Greece had a powerful influence on the foundations of western civilization. Much of modern Western politics, artistic thought, scientific thought, theatre, philosophy derives from this period of Greek history. The Classical period in this sense is in turn succeeded by the Hellenistic period. From the perspective of Athenian culture in Classical Greece, the period generally referred to as the 5th BC extends slightly into the 4th century BC. The Persians were defeated in 490 BC. The Delian League then formed, as Athens' instrument. After both forces were spent, a brief peace came about; then the war resumed to Sparta's advantage. Internal Athenian agitations mark the end of the 5th century BC in Greece. Since its beginning, Sparta had been ruled by a diarchy. This meant that Sparta had two kings ruling concurrently throughout its entire history. The two kingships were both hereditary, vested in the Eurypontid dynasty. According to legend, the respective hereditary lines of these two dynasties sprang from twin descendants of Hercules. They were said to have conquered Sparta two generations after the Trojan War.
Classical Greece
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The Parthenon, in Athens, a temple to Athena
Classical Greece
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Statue of King Leonidas of Sparta
Classical Greece
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Cities at the beginning of the Peloponnesian War
294.
Hellenistic Greece
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During the Hellenistic period the importance of Greece proper within the Greek-speaking world declined sharply. The great centers of Hellenistic culture were Alexandria and Antioch, capitals of Seleucid Syria respectively. Increasing urbanization of the Eastern Mediterranean was characteristic of the time. The quests of Alexander had a number of consequences for the Greek city-states. It led to a steady emigration, particularly of the ambitious, to the new Greek empires in the east. Macedon fell to son of Alexander's leading general Antipater, who after several years of warfare made himself master of most of the rest of Greece. He was generally a constructive ruler. Cassander's power was challenged by ruler of Anatolia, who promised the Greek cities that he would restore their freedom if they supported him. This led against Cassander's local rulers. In 307 BC, Antigonus's son Demetrius restored its democratic system, suppressed by Alexander. But in 301 BC a coalition of the other Hellenistic kings defeated Antigonus at the Battle of Ipsus, ending his challenge. After Cassander's death in 298 BC, however, Demetrius gained control of most of Greece. Mastery of Greece passed to the king Lysimachus of Thrace. Lysimachus was in turn killed in 280 BC. His family retained the Macedonian throne until it was abolished by the Romans in 146 BC.
Hellenistic Greece
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Coin depicting Cassander, First post-Argead leader of Hellenistic Greece and Founder of Thessaloniki
Hellenistic Greece
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Hellenistic Greek tomb door bas relief, Leeds City Museum.
Hellenistic Greece
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Philip V, " the darling of Hellas ", wearing the royal diadem.
295.
Aegean Sea
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The Aegean Sea is an elongated embayment of the Mediterranean Sea located between the Greek and Anatolian peninsulas, i.e. between the mainlands of Greece and Turkey. In the north, it is connected by the Dardanelles and Bosphorus. The Aegean Islands are within some bound it on its southern periphery, including Crete and Rhodes. In ancient times, there were various explanations for the Aegean. A possible etymology is a derivation from the Greek αἶγες -- aiges = "waves", hence "wavy sea", cf. also αἰγιαλός, hence meaning "sea-shore". In some South Slavic languages the Aegean is often called White Sea. The Aegean Sea measures about 610 kilometres longitudinally and 300 kilometres latitudinally. The sea's maximum depth is 3,543 metres, east of Crete. The Aegean Islands are found with the following islands delimiting the sea on the south: Kythera, Antikythera, Crete, Kasos, Karpathos and Rhodes. Chains of islands, are actually extensions of the mountains on the mainland. The International Hydrographic Organization defines the limits of the Aegean Sea as follows: On the South. A line joining Kum Kale and Cape Helles. The Black Sea outflow moves westward along the northern Aegean Sea, then flows southwards along the east coast of Greece. Aegean Sea Intermediate Water – Aegean Sea Intermediate Water extends from 40–50 m to 200–300 metres with temperatures ranging from 11–18 °C. Aegean Sea Bottom Water – occurring at depths below 500–1000 m with a very uniform temperature and salinity.
Aegean Sea
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Map of the Aegean Sea
Aegean Sea
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Topographical and bathymetric map
Aegean Sea
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Panoramic view of the Santorini caldera, taken from Oia.
296.
Aeolis
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Aeolis incorporated the southern parts of Mysia which bounded it to the north, Lydia to the east. Aeolis was an ancient district on the western coast of Asia Minor. It extended along the Aegean Sea to the Hermus River. It was named for the Aeolians, some of whom migrated there before 1000 BC. Aeolis was, however, an ethnological and linguistic enclave rather than a geographical unit. The district often was considered part of the larger region of Mysia. According to Homer's description, Odysseus, after his stay with the Cyclopes, reached the island of Aeolia, who provided him with the west Zephyr. In 699 BC, Smyrna became part of an Ionian confederacy. The remaining cities were conquered by king of Lydia. Later they were held successively by Pergamenes. The last king of Pergamum, bequeathed Aeolis to Rome in 133 BC. Afterward, it was made part of the Roman province of Asia. Autolycus of Pitane Andriscus Elias Venezis Pierluigi Bonanno, Aiolis. Storia e archeologia di una regione dell’Asia Minore alla fine del II millennio a.C. USA, 2006
Aeolis
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Ancient Region of Anatolia Aeolis (Αἰολίς)
297.
Antioch
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Antioch on the Orontes was an ancient Greco-Roman city on the eastern side of the Orontes River. Its ruins lends the modern city its name. Antioch was founded near the end of the 4th century BC by Seleucus I Nicator, one of Alexander the Great's generals. The city's geographical, economic location benefited its occupants, particularly such features as the spice trade, the Silk Road, the Persian Royal Road. It eventually rivaled Alexandria as the chief city of the Near East. It was also the main center of Hellenistic Judaism at the end of the Second Temple period. The Christian New Testament asserts that the name "Christian" first emerged in Antioch. Its residents were known as Antiochenes. A single route proceeds south in the Orontes valley. The settlement of Meroe pre-dated Antioch. A shrine of the Semitic goddess Anat, called by the "Persian Artemis," was located here. This site was included in the eastern suburbs of Antioch. There was a village on the spur of Mount Silpius named Iopolis. Io may have been a early colony of trading Greeks. John Malalas also mentions Bottia, in the plain by the river.
Antioch
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Ancient Roman road located in Syria which connected Antioch and Chalcis.
Antioch
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Map of Antioch in Roman and early Byzantine times
Antioch
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This argenteus was struck in Antioch mint, under Constantius Chlorus.
Antioch
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The Antioch Chalice, first half of 6th century, Metropolitan Museum of Art.
298.
Cappadocia
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Cappadocia is a historical region in Central Anatolia, largely in the Nevşehir, Kayseri, Kırşehir, Aksaray, Niğde Provinces in Turkey. In these lists of countries, the Old Persian name is Haspaduya, which according to some researchers is derived from Iranian Huw-aspa-dahyu- "the land/country of beautiful horses". Others proposed that Kat-patuka came from the Luwian language, meaning "Low Country". Subsequent research suggests that the adverb katta meaning'down, below' is exclusively Hittite, while its Luwian equivalent is zanta. AotJ I:6. Cappadocia appears in the biblical account given in the book of Acts 2:9. Acts 2:5 seems to suggest that the Cappadocians in this account were "God-fearing Jews". See Acts of the Apostles. The region is also mentioned in the Jewish Mishnah, in Ketubot 13:11. This division had already come about before the time of Xenophon. The kingdom of Cappadocia still existed as a independent state. Cilicia was the name given to the district in which Caesarea, the capital of the whole country, was situated. The only two cities of Cappadocia considered by Strabo to deserve that appellation were Caesarea and Tyana, not far from the foot of the Taurus. Cappadocia lies in central Anatolia, in the heartland of what is now Turkey. The boundaries of historical Cappadocia are vague, particularly towards the west.
Cappadocia
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Ancient Region of Anatolia Cappadocia
Cappadocia
Cappadocia
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Fairy Chimneys rock formation near Göreme, in Cappadocia
Cappadocia
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16th-century map of Anatolia from Münster's Cosmographia showing "Capadocia"
299.
Crete
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A number of surrounding islands and islets constitute the region of Crete, one of the 13 top-level administrative units of Greece. The largest city is Heraklion. As of 2011, the region had a population of 623,065. Crete forms cultural heritage of Greece, while retaining its own local cultural traits. It was once the centre of the Minoan civilization, currently regarded as the earliest recorded civilization in Europe. It was also known in ancient Egyptian as Keftiu, strongly suggesting a similar Minoan name for the island. The current name of Crete is thought to be first attested in Greek texts written in Linear B, through the words, ke-re-te, ke-re-si-jo, "Cretan". In Ancient Greek, the Crete first appears in Homer's Odyssey. Its etymology is unknown. One proposal derives it from a hypothetical Luvian word kursatta. In Latin, it became Creta. In Ottoman Turkish, Crete was called Girit. Crete is the fifth largest island in the Mediterranean Sea. It is located in the southern part of the Aegean Sea separating the Aegean from the Libyan Sea. It lies approximately 160 km south of the Greek mainland.
Crete
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NASA photograph of Crete
Crete
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Lefka Ori
Crete
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Port of Heraklion
Crete
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Lefka Ori (White mountains).
300.
Cyprus
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Cyprus, officially the Republic of Cyprus, is an island country in the Eastern Mediterranean and the third largest and third most populous island in the Mediterranean. It is located south of Turkey, west of Syria and Lebanon, northwest of Israel and Palestine, southeast of Greece. The earliest human activity on the island dates to around the 10th millennium BC. Cyprus is home to some of the oldest water wells in the world. Cyprus was settled by Mycenaean Greeks in two waves in the 2nd millennium BC. Cyprus was formally annexed by Britain in 1914. Following nationalist violence in the 1950s, Cyprus was granted independence in 1960. The resulting political situation are matters of a continuing dispute. The Cyprus Republic has de jure sovereignty over the island of Cyprus, well as its territorial sea and exclusive economic area, according to international law. Another nearly 4 % of the island's area is covered by the UN zone. The international community considers the northern part of the island as territory of the Republic of Cyprus occupied by Turkish forces. The occupation is viewed amounting to illegal occupation of EU territory since Cyprus became a member of the European Union. Cyprus is a major destination in the Mediterranean. On 1 the Republic of Cyprus joined the eurozone. The earliest attested reference to Cyprus is the 15th century BC Mycenaean ku-pi-ri-jo, meaning "Cypriot", written in Linear B syllabic script.
Cyprus
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A copper mine on Cyprus. In antiquity, Cyprus was a major source of copper.
Cyprus
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Flag
Cyprus
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Archeologic site of Choirokoitia with early remains of human habitation during Aceramic Neolithic period (reconstruction)
Cyprus
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Sanctuary of Apollo Hylates, Kourion
301.
Doric hexapolis
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The hexapolis thus became the Doric Pentapolis. He makes Doris begin at Cnidus. In the bay of Doris he places Hamaxitus, etc.. An attempt has been made among scholars to ascertain which of two bays Pliny calls the more probable being the Ceramic Gulf. Places in it Halicarnassus, Ceramus, Cnidus. The Doris, applied to a part of Asia, does not appear to occur in other writers. This article incorporates text from a publication now in the public domain: Smith, ed.. "name needed". Dictionary of Greek and Roman Geography. London: John Murray.
Doric hexapolis
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The ruins of the Mausoleum at Halicarnassus, one of the Seven Wonders of the Ancient World
Doric hexapolis
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Greek settlements in western Asia Minor, Doric area in blue.
302.
Ephesus
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Ephesus was an ancient Greek city on the coast of Ionia, three kilometres southwest of present-day Selçuk in İzmir Province, Turkey. It was built by Attic and Greek colonists. During the Classical Greek era it was one of the twelve cities of the Ionian League. The city flourished after it came under the control of the Roman Republic in 129 BC. The city was famed for the nearby Temple of Artemis, one of the Seven Wonders of the Ancient World. Among many other monumental buildings are the Library of Celsus, a theatre capable of holding 25,000 spectators. Ephesus was one of the seven churches of Asia that are cited in the Book of Revelation. The Gospel of John may have been written here. The city was the site of several 5th century Christian Councils. It was partially destroyed by an earthquake in 614 AD. The area surrounding Ephesus was already inhabited during the Neolithic Age, as was revealed by excavations at the nearby höyük of Arvalya and Cukurici. Excavations in recent years have unearthed settlements from the early Bronze Age at Ayasuluk Hill. According to Hittite sources, the capital of the Kingdom of Arzawa was Apasa. Some scholars suggest that this is the later Greek Ephesus. In 1954, a burial ground from the Mycenaean era with ceramic pots was discovered close to the ruins of the basilica of St. John.
Ephesus
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The Library of Celsus in Ephesus
Ephesus
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Site of the Temple of Artemis in the town of Selçuk, near Ephesus.
Ephesus
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Street scene at the archeological excavations at Ephesus.
Ephesus
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Electrum coin from Ephesus, 620-600 BC. Obverse: Forepart of stag. Reverse: Square incuse punch.
303.
Epirus (ancient state)
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Epirus was an ancient Greek state, located in the geographical region of Epirus in the western Balkans. These people buried their leaders in large tumuli containing shaft graves, similar to the Mycenaean tombs, indicating an ancestral link between the Mycenaean civilization. The Dorians invaded Greece at the end of the 2nd millennium BC though the reasons for their migration are obscure. These were the Chaonians of northwestern Epirus, the Thesprotians in the south. She was to become the mother of Alexander the Great. On the death of Arybbas, uncle of Alexander the Great of Macedon, succeeded to the throne with the title King of Epirus. After some successes on the battlefield, he was defeated by a coalition of Italic tribes in 331 BC. Subsequently, a new coinage was issued with the legend Epirotes. After Alexander's death, Aeacides of Epirus, who succeeded him, espoused the cause of Olympias against Cassander, but was dethroned in 313 BC. Aeacides's son Pyrrhus came in 295 BC. Pyrrhus, being a skillful general, was decided to initiate a major offensive in the Italian peninsula and Sicily. Due to its martial abilities, the Epirote army defeated the Romans in the Battle of Heraclea. Subsequently, Pyrrhus's forces had to retreat to avoid an unequal conflict with a more numerous Roman army. In 277 BC, Pyrrhus captured the Carthaginian fortress in Eryx, Sicily. This prompted the rest of the Carthaginian-controlled cities to defect to Pyrrhus.
Epirus (ancient state)
Epirus (ancient state)
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Coin of the Epirote League, depicting Zeus (left) and a lighting bolt with the word "ΑΠΕΙΡΩΤΑΝ", "of the Epirotes" (right).
Epirus (ancient state)
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Political structure of the ancient Greek world (8th–5th centuries BC).
304.
Dardanelles
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Together with the Bosphorus, the Dardanelles forms the Turkish Straits. The Greek name Ἑλλήσποντος means "Sea of Helle", was the ancient name of the narrow strait. It was variously named in classical literature Hellespontium Pelagus, Fretum Hellesponticum. It was so called from the daughter of Athamas, drowned here in the mythology of the Golden Fleece. The Marmara further connects to the Black Sea via the Bosphorus, while the Aegean further links to the Mediterranean. The strait is located at approximately 40 ° 13 ′ N ° 26 ′ E. 1.2 to 6 kilometres wide, averaging 55 metres deep with a maximum depth of 103 metres. The Dardanelles is unique in many respects. The very winding shape of the strait is more akin to that of a river. It is considered one of the difficult and potentially dangerous waterways in the world. It is a major sea access route including Russia and Ukraine. The strait's Asiatic shore was the focus of the Trojan War. Troy was able to control the marine traffic entering this vital waterway. This crossing was named in his tragedy The Persians as the cause of divine intervention against Xerxes. According to Herodotus, Xerxes had those responsible for building the bridges beheaded and the strait itself whipped.
Dardanelles
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An artist's illustration depicting Xerxes' alleged "punishment" of the Hellespont
Dardanelles
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The Dardanelles, a long narrow strait dividing the Balkans (Europe) along the Gallipoli peninsula from Asia Minor
Dardanelles
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Marble plate with 6th century AD law regulating payment of customs in the Dardanelles
Dardanelles
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Historic map of Dardanelles by Piri Reis
305.
Ionia
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Ionia is an ancient region of central coastal Anatolia in present-day Turkey, the region nearest İzmir, historically Smyrna. It consisted of the northernmost territories of the Ionian League of Greek settlements. Never a unified state, it was named after the Ionian tribe who, in the Archaic Period, settled mainly the islands of the Aegean Sea. Ionian states were identified by their use of Eastern Greek. It was bounded by Aeolia to the south. The cities within the region figured large in the strife between Persian Empire and the Greeks. According to Greek tradition, the cities of Ionia were founded from the other side of the Aegean. So intricate is the coastline that the voyage along its shores was estimated at the direct distance. A great part of this area was, moreover, occupied by mountains. None of these mountains attains a height of more than 1,200 metres. The geography of Ionia placed it in a strategic position, both disadvantageous. Ionia was always a maritime power marauding in unsettled times. The arable land slight. The native Luwians for the most part used the rift valleys for wooded pasture. The coastal cities were placed on islands or headlands situated so as to control inland routes up the rift valleys.
Ionia
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Mount Mycale, site of the Panionium
Ionia
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One of the earliest electrum coins struck in Ephesus, 620-600 BC. Obverse: Forepart of stag. Reverse: Square incuse punch.
Ionia
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Northern Ionia, view from space.
Ionia
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The site of Miletus, once coastal, now inland. The plain was a bay in Classical Greece.
306.
Ionian Sea
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The Ionian Sea is an elongated embayment of the Mediterranean Sea, south of the Adriatic Sea. All major islands in the sea belong to Greece. They are collectively referred being Corfu, Zakynthos, Kephalonia, Ithaca, Lefkada. The deepest point in the Mediterranean at − 5,267 m, is located in the Ionian Sea, at 36 ° 34 ′ N 21 ° 8 ′ E. The sea is one of the most seismically active areas in the world. The Ionian comes from the Greek language Ἰόνιον. Its etymology is unknown. Especially Aeschylus, linked it to the myth of Io. In Ancient Greek the adjective Ionios was used because Io swam across it. According to the Oxford Classical Dictionary, the name may derive from Ionians who sailed to the West. The corpse was cast into the sea, which thereafter was called the Ionian Sea. The International Hydrographic Organization defines the limits of the Ionian Sea as follows: On the North. On the East. From the mouth of the Butrinto River in Albania down the coast of the mainland to Cape Matapan. On the South.
Ionian Sea
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The Ionian Sea, view from the island Kefalonia, Greece
Ionian Sea
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Map of the Ionian Sea
Ionian Sea
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The Ionian Sea, as seen from Corfu Island, Greece, and with Saranda, Albania in the background
Ionian Sea
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Gjipe Canyon terminating at the Ionian sea, Albania
307.
Macedonia (ancient kingdom)
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Macedonia or Macedon was an ancient kingdom on the periphery of Classical Greece. And later the dominant state of Hellenistic Greece. It was ruled initially by the founding dynasty of the Argeads, finally the Antigonids. The reign of Philip II saw the rise of Macedonia, when the kingdom rose to control the entire Greek world. Alexander then led this force in retaliation for the invasion of Greece in the 5th BC. In the ensuing wars of Alexander the Great, Alexander overthrew the Achaemenid Empire, conquering a territory that came to stretch as far as the Indus River. Literature flourished in philosophy and science were spread to the ancient world. Of particular importance were the contributions of Aristotle, a teacher to Alexander, whose teachings carried on many centuries past his death. Macedonia's decline began in 168 BC following the Macedonian Wars. The Macedonia comes from the Greek Μακεδόνες, deriving ultimately from the ancient Greek adjective μακεδνός, possibly descriptive of the people. It also shares the same root as the μάκρος, meaning "length" in both modern Greek. The shorter English name variant Macedon developed based on a borrowing from the French form of Macédoine. Today's Vergina, were home to various peoples. Macedonia was at first called Emathia and the city of Aegae was called Edessa, the capital of fabled king Midas in his youth. In approximately 650 BC, an Greek royal house led by Perdiccas I, established their palace-capital at Aegae.
Macedonia (ancient kingdom)
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The entrance to one of the royal tombs at Vergina, a UNESCO World Heritage site.
Macedonia (ancient kingdom)
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The Kingdom of Macedonia in 336 BC.
Macedonia (ancient kingdom)
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Philip II, king of Macedon
Macedonia (ancient kingdom)
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The expansion of ancient Macedon up to the death of Philip II (r. 359–336 BC).
308.
Miletus
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Miletus was an ancient Greek city on the western coast of Anatolia, near the mouth of the Maeander River in ancient Caria. Its ruins are located in Turkey. Before the Persian invasion in the middle of the 6th BC, Miletus was considered the wealthiest of Greek cities. Splendor was reached during later Roman times. Evidence of first settlement at the site has been made inaccessible by the rise of sea level and deposition of sediments from the Maeander. The first available evidence is of the Neolithic. In the middle age the settlement came under Minoan influence. Legend has it that an influx of Cretans occurred displacing the indigenous Leleges. The site was renamed Miletus after a place in Crete. 13th BC, saw the arrival of Luwian language speakers from south central Anatolia calling themselves the Carians. Later in that century other Greeks arrived. The city at that time rebelled against the Hittite Empire. Legend offers an Ionian foundation event sponsored by a founder named Neleus from the Peloponnesus. The Dark Ages were a time of Ionian consolidation in an alliance called the Ionian League. The Archaic Period of Greece began with a sudden and brilliant flash of art and philosophy on the coast of Anatolia.
Miletus
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The theater of Miletus
Miletus
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The Ionic Stoa on the Sacred Way
Miletus
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The plan of Milet in the Classical period
Miletus
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Illustration of Miletus
309.
Peloponnese
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The Peloponnese or Peloponnesus (/ˌpɛləpəˈniːsəs/; Greek: Πελοπόννησος, Pelopónnēsos, is a peninsula and geographic region in southern Greece. It is separated from the central part of the country by the Gulf of Corinth. During the Ottoman era, the peninsula was known still in colloquial use in its demotic form. The peninsula is divided among three administrative regions: most belongs to the Peloponnese region, with smaller parts belonging to the West Greece and Attica regions. It was here that the Greek War of Independence began in 1821. The Peloponnesians have totally dominated politics and government since then. In 2016, Lonely Planet voted the Peloponnese the top spot of their Best in Europe list. The Peloponnese is a peninsula that covers an area of some 21,549.6 square kilometres and constitutes the southernmost part of mainland Greece. It has an artificial one by the Rio-Antirio bridge. The peninsula has a mountainous interior and deeply indented coasts. Mount Taygetus is its highest point, at 2,407 metres. It possesses four south-pointing peninsulas, the Messenian, the Argolid in the far northeast of the Peloponnese. Two groups of islands lie off the Peloponnesian coast: the Argo-Saronic Islands to the east, the Ionian to the west. The island of Kythera, off the Epidaurus Limera peninsula to the south of the Peloponnese, is considered to be part of the Ionian Islands. The peninsula has been inhabited since prehistoric times.
Peloponnese
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The Corinth Canal separates the Peloponnese from mainland Greece.
Peloponnese
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Landscape of Arcadia
Peloponnese
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Map of the Peloponnese of Classical Antiquity.
310.
Pergamon
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Pergamon /ˈpɜːrɡəmən/ or /ˈpɜːrɡəmɒn/ or Pergamum /ˈpɜːrɡəməm/ was a rich and powerful ancient Greek city in Aeolis. Many remains of its impressive monuments can still be seen and especially the outstanding masterpiece of the Pergamon Altar. It became the capital of the Kingdom of Pergamon during the Hellenistic period under the Attalid dynasty in 281–133 BC. Pergamon is cited in the Book of Revelation as one of the seven churches of Asia. Xenophon provides the earliest surviving documentary mention of Pergamon. Captured by Xenophon in 399 BC and immediately recaptured by the Persians, it was severely punished in 362 BC after a revolt. In 261 BC he bequeathed his possessions to his nephew Eumenes I, who increased them greatly, leaving as heir his cousin Attalus I. The Attalids became some of the most loyal supporters of Rome in the Hellenistic world. For their support against the Seleucids, the Attalids were rewarded with all the former Seleucid domains in Asia Minor. As a consequence of its rise to power, the city expanded greatly. Until 188 BC, it had not grown significantly since its founding by Philetaerus, covered circa 21 hectares. After this year, a massive new city wall was constructed, 4 kilometres long and enclosing an area of approximately 90 hectares. The Attalids ruled with intelligence and generosity. Many documents survive showing how the Attalids supported the growth of towns by sending in skilled artisans and by remitting taxes. They allowed the Greek cities in their domains to maintain nominal independence.
Pergamon
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The reconstructed Temple of Trajan at Pergamon
Pergamon
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The Kingdom of Pergamon (colored olive), shown at its greatest extent in 188 BC
Pergamon
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Theatre of Pergamon
Pergamon
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The Great Altar of Pergamon, on display in the Pergamonmuseum in Berlin, Germany
311.
Pontus (region)
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Pontus is a historical Greek designation for a region on the southern coast of the Black Sea, located in modern-day eastern Black Sea Region of Turkey. These Greeks of Pontus are generally referred to as Pontic Greeks. Pontus remained outside the reach of the Bronze Age empires, of which the closest was Great Hatti. The region went further uncontrolled by Hatti's eastern neighbours, Hurrian states like Azzi and Hayasa. In those days, the best any outsider could hope from this region was temporary alliance with a local strongman. The Hittites called the unorganised groups on their northeastern frontier the Kaška. As of 2004 little had been found of them archaeologically. The Greeks, who spoke a related Indo-European tongue, followed them along the coast. The Greeks are the earliest long-term inhabitants of the region from whom written records survive. Since there was little literacy in northeastern Anatolia until the Hellenistic era, one can only speculate as to the other languages spoken here. The earliest written description of Pontus, however, is that of Scylax of Korianda, who in the 7th BC described Greek settlements in the area. When the Athenian Xenophon passed through Pontus in fact, he found no Persians in Pontus. The peoples of this part of northern Asia Minor were incorporated into the third and nineteenth satrapies of the Persian empire. The site flourished and became so important that it was here that the people of Pontus made their most sacred vows. Even in Strabo's day it was still a dynamic center of Persian culture and religion.
Pontus (region)
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Traditional rural Pontic house
Pontus (region)
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The modern definition of the Pontus: the area claimed for the " Republic of Pontus " after World War I, based on the extent of the six local Greek Orthodox bishoprics.
Pontus (region)
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Christian population in 1896
Pontus (region)
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Turkey Black Sea Region
312.
Crimea
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The peninsula is located south of west of the Russian region of Kuban. It is separated from Kuban by the Strait of Kerch. The Arabat Spit is located to a narrow strip of land that separates a system of lagoons named Sivash from the Sea of Azov. Crimea has historically been between the classical world and the Pontic -- Caspian steppe. Adjacent territories were united in the Crimean Khanate during the 15th to 18th century. In 1783, Crimea was annexed by the Russian Empire. Since 1997, after the Peace and Friendship Treaty signed by Russia and Ukraine, Crimea hosts the Black Sea Fleet naval base in Sevastopol. Its facilities were divided between Russia's Black Sea Fleet and the Ukrainian Naval Forces. The two navies co-used some of the city's piers, while others were demilitarised or used by either country. Sevastopol remained the location of the Russian Black Sea Fleet headquarters with the Ukrainian Naval Forces Headquarters also based in the city. The most of the international community do not consider Crimea to be Ukrainian territory. Russia temporarily administers the federal city of Sevastopol. Ukraine continues to assert its right over the peninsula. Taurica is from the Greek Ταυρική, after the peninsula's Scytho-Cimmerian inhabitants, the Tauri. In English usage since the modern period the Crimean Khanate is referred to as Crim Tartary.
Crimea
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Ruins of ancient Greek colony of Chersonesos
Crimea
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Satellite image of the Crimean peninsula
Crimea
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Swallow's Nest, built in 1912 for oil millionaire Baron von Steingel, a landmark of Crimea
Crimea
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Armenian monastery of the Holy Cross (Սուրբ Խաչ), established in 1358
313.
Polis
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Polis, plural poleis literally means city in Greek. It can also mean body of citizens. In modern historiography, polis is normally used to indicate the Greek city-states, like Classical Athens and its contemporaries, thus is often translated as "city-state". The term "city-state", which originated in English, does not fully translate the Greek term. The polis, which in archaic Greece meant "city", changed with the development of the governance center in the city to signify "state". Finally, with the emergence of a notion of citizenship among landowners, it came to describe the entire body of citizens. The body of citizens came to be the most important meaning of the polis in ancient Greece. The Greek term that specifically meant the totality of urban spaces is ἄστυ. Plato analyzes the polis in The Republic, whose Greek title, Πολιτεία, itself derives from the polis. The best form of government of the polis for Plato is the one that leads to the common good. The king is the best ruler because, as a philosopher, he is acquainted with the Form of the Good. In Plato's analogy of the ship of state, the king steers the polis, as if it were a ship, in the best direction. Books II–IV of The Republic are concerned with Plato addressing the makeup of an ideal polis. In The Republic, Socrates is concerned with the two underlying principles of any society: mutual differences in aptitude. Starting from these two principles, Socrates deals with the economic structure of an ideal polis.
Polis
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Acropolis of Athens, a noted polis of classical Greece.
Polis
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Theatre of ancient Syracuse, a classical polis.
314.
Ancient Greek warfare
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Warfare occurred throughout the history of ancient Greece, from the Greek Dark Ages on. These developments ushered in the Archaic period. They also restored the capability of organized warfare between these Poleis. The fractious nature of Greek society seems to have made continuous conflict on this larger scale inevitable. Along with the rise of the city-state evolved a new style of warfare: the hoplite phalanx. The chigi vase, dated to around BC, is the earliest depiction of a hoplite in full battle array. With this evolution in warfare, battles seem to have consisted mostly from the city-states in conflict. Since the soldiers were citizens with other occupations, warfare was limited in distance, scale. Neither side could afford sustained campaigns, so conflicts seem to have been resolved by a single set-piece battle. The scope of warfare in Ancient Greece changed dramatically as a result of the Greco-Persian Wars. To fight the enormous armies of the Achaemenid Empire was effectively beyond the capabilities of a single city-state. The eventual triumph of the Greeks was achieved on a scale never seen before. The rise during this conflict led directly to the Peloponnesian War, which saw diversification of warfare. Emphasis shifted to naval strategies of attrition such as blockades and sieges. Following the defeat of the Athenians in the disbandment of the Athenian-dominated Delian League, Ancient Greece fell under the Spartan hegemony.
Ancient Greek warfare
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Reconstruction of a Hoplite Phalanx formation
Ancient Greek warfare
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A hoplite armed with an aspis and a doru. nb: it is usually agreed that the doru could not be used two-handed with the aspis.
Ancient Greek warfare
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The key actions of each phase
Ancient Greek warfare
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Agrianian peltast holding three javelins, one in his throwing hand and two in his pelte hand as additional ammunition
315.
Classical Athens
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Athenian democracy was established under Cleisthenes following the tyranny of Isagoras. With a few brief interruptions remained in place for 180 years, until 322 BC. The peak of Athenian hegemony was achieved to 430s BC, known as the Age of Pericles. Cleisthenes, then took charge and established democracy in Athens. The tribes each selected fifty members for the Boule, the council which governed Athens on a day-to-day basis. The public opinion of voters could be influenced by the political satires performed in the city theaters. Most offices were filled by lot, although the ten strategoi were elected. Prior to the rise of Athens, a city-state with a militaristic culture, considered itself the leader of the Greeks, enforced a hegemony. In 499 BC Athens sent troops to aid the Ionian Greeks of Asia Minor, who were rebelling against the Persian Empire. This provoked two Persian invasions of Greece, both of which were repelled under the leadership of the soldier-statesmen Themistocles. In 490 the Athenians, led by Miltiades, prevented the first invasion of the Persians, guided by king Darius I, at the Battle of Marathon. In 480 the Persians returned under a new ruler, Xerxes I. Simultaneously the Athenians led an indecisive naval battle off Artemisium. This forced the Athenians to seek the protection of their fleet. Subsequently their allies, led by Themistocles, defeated the Persian navy at sea in the Battle of Salamis.
Classical Athens
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Early Athenian coin, 5th century BC. British Museum.
Classical Athens
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Delian League ("Athenian Empire") shown in yellow, Athenian territory shown in red, situation in 431 BC, before the Peloponnesian War.
Classical Athens
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The modern National Academy in Athens, with Apollo and Athena on their columns, and Socrates and Plato seated in front.
Classical Athens
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Map of the environs of Athens showing Piraeus, Phalerum, and the Long Walls
316.
Byzantium
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Byzantium was an ancient Greek colony on the site that later became Constantinople, later still Istanbul. It was colonised from Megara in c. 657 BC. The etymology of Byzantion is unknown. It has been suggested that the name is of Thraco-Illyrian origin, Byzantium may be derived from Illyrian personal name, Byzas. Greek legend refers to a legendary king Byzas, the leader of the Megarian colonists and founder of the city. The Byzantium is a Latinization of the original name. This usage was introduced only by the historian Hieronymus Wolf, a century after the empire had ceased to exist. During the time of the empire, the Byzantium was restricted to just the city, rather than the empire it ruled. The European side featured only two fishing settlements: Lygos and Semistra. The origins of Byzantium are shrouded in legend. The traditional legend has it that Byzas from Megara founded Byzantium in 667 BC when he sailed northeast across the Aegean Sea. The tradition tells that son of King Nisos, planned to found a colony of the Dorian Greek city of Megara. Byzas consulted the oracle of Apollo at Delphi, which instructed Byzas to settle opposite the "Land of the Blind". He adjudged the Chalcedonians blind not to have recognized the land on the European side of the Bosphorus had over the Asiatic side. In 667 BC he founded Byzantium at their location, thus fulfilling the oracle's requirement.
Byzantium
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O: Head of Alexander the Great with Amun's horns.
Byzantium
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Location of Byzantium
Byzantium
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Byzantine lamellar klivanium (Κλιβάνιον) - a predecessor of ottoman krug mirror armour
317.
Chalcis
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Chalcis or Chalkida is the chief town of the island of Euboea in Greece, situated on the Euripus Strait at its narrowest point. The name is derived from the Greek χαλκός, though there is no trace of any mines in the area. In the late Middle Ages, it was known as a name, applied to the entire island of Euboea as well. The earliest recorded mention of Chalcis is in the Iliad, where it is mentioned in the same line as its rival Eretria. It is also documented that the ships set for the Trojan War gathered at Aulis, the south bank of the strait nearby the city. Chamber tombs at Trypa and Vromousa dated to the Mycenaean period were excavated by Papavasiliou in 1910. Chalcis subsequently became a member of both the Delian Leagues. In the Hellenistic period, it gained importance by which the Macedonian rulers controlled central Greece. It was used as a base for invading Greece. Under Roman rule, Chalcis retained a measure of commercial prosperity. The town survived an naval raid in the 880s and its bishop is attested in the 869 -- 70 Church council held at Constantinople. For Westerners, its common name was Negropont or Negroponte. The town was the Veronese barons of the rest of Euboea, known as the "triarchs", who resided there. The synagogue dated to around 1400. That siege is the subject of the Rossini opera Maometto II.
Chalcis
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Chalcis' seafront
Chalcis
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Exhibits in the archaeological museum of Chalcis.
Chalcis
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View of the Roman aqueduct.
Chalcis
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Venetian map of Chalcis (Negroponte) (1597).
318.
Ancient Corinth
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The modern town of Corinth is located approximately 5 kilometres northeast of the ancient ruins. For Christians, Corinth is well-known from the two letters of Saint Paul in the New Testament, Second Corinthians. Corinth is also mentioned as part of the Apostle Paul's missionary travels. In addition, the second book of Pausanias' Description of Greece is devoted to Corinth. Ancient Corinth was one of the largest and most important cities of Greece, with a population of 90,000 in 400 BC. There is evidence that the city was destroyed around 2000 BC. Some ancient names for the place are derived from a pre-Greek "Pelasgian" language, such as Korinthos. It seems likely that Corinth was also the site of a Bronze Age Mycenaean palace-city, like Mycenae, Tiryns, or Pylos. According to myth, Sisyphus was the founder of a race of ancient kings at Corinth. It was also in Corinth that the leader of the Argonauts, abandoned Medea. During the Trojan War as portrayed in the Iliad, the Corinthians participated under the leadership of Agamemnon. His verdict was that the acropolis of Corinth belonged to Helios. Thus, Greeks of the Classical age accounted in the highest part of the site. The Upper Peirene spring is located within the walls of the acropolis. "The spring, behind the temple, they say was the gift of Asopus to Sisyphus.
Ancient Corinth
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Apollo Temple has been built in Doric style on the ruins of earlier temple, being a good example of peripteral temple, supported by 38 columns, only 7 of which are still in place.
Ancient Corinth
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Archeological site located close to Temple of Apollo.
Ancient Corinth
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Archeological site of Ancient Theater first built in Corinth in 5th c. BC. The Theater could seat around 15000 spectators.
Ancient Corinth
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Temple of Apollo, Ancient Corinth.
319.
Kerkyra
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Corfu is a Greek island in the Ionian Sea. And, including its small satellite islands, forms the northwesternmost part of Greece. The municipality has an area of the island proper 592.877 km2. The principal city of the seat of the municipality is also named Corfu. It is home to the Ionian University. The island is bound up from the beginnings of Greek mythology. Its history is full of conquests. Castles punctuating strategic locations across the island are a legacy of these struggles. Two of these castles enclose its capital, the only city in Greece to be surrounded in such a way. As a result, Corfu's capital has been officially declared a Kastropolis by the Greek government. The fortifications of the island were used by the Venetians to defend into the Adriatic. It repulsed several Ottoman sieges, before falling under British rule following the Napoleonic Wars. In 2007, the city's old quarter was added following a recommendation by ICOMOS. It is a very popular destination. The island was the location of the 1994 European Union summit.
Kerkyra
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Pontikonisi (background) and Vlacherna Monastery (foreground) seen from the hilltops of Kanoni
Kerkyra
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Bay of Agios Georgios in northwestern Corfu
Kerkyra
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Lazaretto Island
Kerkyra
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A relief of Dionysus Bacchus at the Archaeological Museum of Corfu.
320.
Larissa
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It is the capital and largest city of the Thessaly region, the fifth most populous in Greece and capital of the Larissa regional unit. It, within its municipality, has 162,591 inhabitants, while the regional unit of Larissa reached a population of 284,325. Larissa is a major commercial and industrial centre in Greece. Legend has it that Hippocrates, the Father of Medicine, died here. The region is directly linked through the International Airport of Central Greece located in Nea Anchialos a short distance from Larissa. It lies on the river Pineios. A deep gash in the surface of Dione, a natural satellite of Saturn, was named after Larissa. The climate of Larissa is transitional. Some snowstorms may occur. Temperatures of 40 ° C may occur. Heavy rain may cause agricultural damage. It receives 450 mm of rain per year. According to Greek mythology Larissa is said that the city was founded by Acrisius, killed accidentally by Perseus. There lived Peleus, his son Achilles. In mythology, the nymph Larissa was a daughter of the primordial man Pelasgus.
Larissa
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The first ancient theatre of Larissa
Larissa
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Seal
Larissa
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Mount Ossa viewed from Pineios river in Larissa.
321.
Megara
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Megara is a historic town and a municipality in West Attica, Greece. Megara was also its people using their ships and wealth as a way to gain leverage on armies of neighboring poleis. Megara specialized in the exportation of wool and other animal products including livestock such as horses. It possessed two harbors, Pegae, to the west to the east on the Saronic Gulf of the Aegean Sea. Megara then afterwards founded Chalcedon in 685 BC, as well as Byzantium. Megara is known to have early ties with Miletos, in the region of Caria in Asia Minor. According to some scholars, they had built up a “colonisation alliance”. In the century BCE these two cities acted in accordance with each other. Both cities acted under the sanction of an Apollo oracle. Megara cooperated with that of Delphi. Miletos had her own oracle of Apollo Didymeus Milesios in Didyma. Also, there are many parallels in the political organisation of both cities. In the 7th century BC Theagenes established himself as tyrant of Megara by slaughtering the cattle of the rich to win over the poor. During the Persian invasion of Greece Megara fought alongside the Spartans and Athenians at crucial battles such as Salamis and Plataea. Megara's defection from the Spartan-dominated Peloponnesian League became one of the causes of the First Peloponnesian War.
Megara
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Megara Μέγαρα
322.
Rhodes
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Rhodes is the largest of the Dodecanese islands in terms of land area and also the island group's historical capital. Administratively the island forms a separate municipality within the regional unit, part of the South Aegean administrative region. The principal town of the seat of the municipality is Rhodes. The city of Rhodes had 50,636 inhabitants in 2011. It is located northeast of southeast of Athens and just off the Anatolian coast of Turkey. Rhodes' nickname is The island of the Knights, named after the Knights of Saint John of Jerusalem, who once conquered the land. Historically, Rhodes was famous worldwide for the Colossus of Rhodes, one of the Seven Wonders of the Ancient World. The Medieval Old Town of the City of Rhodes has been declared a World Heritage Site. It is one of the most popular tourist destinations in Europe. The island has been known in Greek throughout its history. In addition, the island has been called Italian: Turkish: Rodos, Ladino: Rodi or Rodes. Limestone is the main bedrock. The city of Rhodes is located at the northern tip of the island, well as the site of the ancient and modern commercial harbours. The main gateway is located 14 km to the southwest of the city in Paradisi. The network radiates from the city along the east and west coasts.
Rhodes
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Palace of the Grand Master in the city of Rhodes
Rhodes
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Akramitis mountain
Rhodes
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Ixia beach
323.
Samos
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Samos is also the only municipality of the regional unit. In ancient times it was an powerful city-state, particularly known for its vineyards and wine production. Samos is the Heraion of Samos, a UNESCO World Heritage Site that includes the Eupalinian aqueduct, a marvel of ancient engineering. Wine was well known in antiquity, is still produced on the island. The island was governed under Ottoman suzerainty from 1835 until it joined Greece in 1912. It is 43 km long and 13 km wide. Samos is separated by the approximately 1-mile-wide Mycale Strait. While largely mountainous, it has several relatively fertile plains. A great portion of the island is covered with vineyards, from which wine is made. The island's population is 33,814, the 9th most populous of the Greek islands. The Samian climate is typically Mediterranean, with mild rainy winters, warm summers. Samos' relief is dominated by Ampelos and Kerkis. The Ampelos massif occupies the center of the island, rising to 1,095 metres. Mt. Kerkis, though smaller in area is the taller of the two and its summit is the island's highest point, at 1,434 metres. The mountains are a continuation of the Mycale range on the Anatolian mainland.
Samos
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Vathy, capital of Samos
Samos
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Psalida Beach. At the distant background Mount Kerketeas.
Samos
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Kouros of Samos, the largest surviving Kouros in Greece (Archaeological Museum of Samos).
Samos
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Inside the Eupalinian aqueduct.
324.
Sparta
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Sparta was a prominent city-state in ancient Greece. Around 650 BC, it rose to become the military land-power in ancient Greece. Given its military pre-eminence, Sparta was recognized during the Greco-Persian Wars. Sparta's defeat by Thebes in the Battle of Leuctra in 371 BC ended Sparta's prominent role in Greece. However, it maintained its political independence in 146 BC. It then underwent a long period of decline, especially in the Middle Ages, when many Spartans moved to live in Mystras. Modern Sparta is the capital of a center for the processing of goods such as citrus and olives. Sparta was unique in ancient Greece for its social constitution, which completely focused on military training and excellence. Its inhabitants were classified as Spartiates, mothakes, helots. Spartan phalanges were widely considered to be among the best in battle. Spartan women enjoyed considerably more rights and equality in the classical world. Sparta was the subject following the revival of classical learning. This admiration of Sparta is known as Laconism or Laconophilia. At its peak around 500 BC the size of the city would have been some 20,000 -- 35,000 free residents, perioikoi. Ollier's theory of the "Spartan mirage" has been widely accepted by scholars.
Sparta
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Territory of ancient Sparta
Sparta
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Hollow Lacedaemon. Site of the Menelaion, the ancient shrine to Helen and Menelaus constructed in the Bronze Age cit