1.
Brescia
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Brescia is a city and comune in the region of Lombardy in northern Italy. It is situated at the foot of the Alps, a few kilometres from the lakes Garda, with a population of 196,480, it is the second largest city in the region and the fourth of northwest Italy. The urban area of Brescia extends beyond the city limits and has a population of 672,822. The city is the capital of the Province of Brescia, one of the largest in Italy. Founded over 3,200 years ago, Brescia has been an important regional centre since pre-Roman times, Brescia is considered the industrial capital of Italy. The metallurgy and the production of tools and firearms are of particular economic significance, along with mechanical. In addition, Brescia is the setting for most of the action in Alessandro Manzonis 1822 play Adelchi, Brescia and its territory will be the European Region of Gastronomy in 2017. Various myths relate to the founding of Brescia, one assigns it to Hercules while another attributes its foundation as Altilia by a fugitive from the siege of Troy. According to another myth, the founder was the king of the Ligures, Cidnus, colle Cidneo was named after that version, and it is the site of the medieval castle. Others scholars attribute the founding of Brescia to the Etruscans, the Gallic Cenomani, allies of the Insubres, invaded in the 7th century BC, and used the town as their capital. The city became Roman in 225 BC, when the Cenomani submitted to the Romans, during the Carthaginian Wars, Brixia was allied with the Romans. During a Celtic alliance against the city remained fateful to the Romans, with their Roman allies the city remain and attacked and destroyed the Insubres by surprise. Subsequently, the city and the tribe entered the Roman world peacefully as faithful allies, in 89 BC, Brixia was recognized as civitas and in 41 BC, its inhabitants received Roman citizenship. Augustus founded a colony there in 27 BC, and he. Roman Brixia had at least three temples, an aqueduct, a theatre, a forum with another temple built under Vespasianus, when Constantine advanced against Maxentius in 312, an engagement took place at Brixia in which the enemy was forced to retreat as far as Verona. In 402, the city was ravaged by the Visigoths of Alaric I, during the 452 invasion of the Huns under Attila, the city was besieged and sacked. Forty years later, it was one of the first conquests by the Gothic general Theoderic the Great in his war against Odoacer, in 568, Brescia was taken from the Byzantines by the Lombards, who made it the capital of one of their semi-independent duchies. The first duke was Alachis, who died in 573, later dukes included the future kings of the Lombards Rothari and Rodoald, and Alachis II, a fervent anti-Catholic who was killed in battle at Cornate dAdda in 688
2.
Venice
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Venice is a city in northeastern Italy and the capital of the Veneto region. It is situated across a group of 118 small islands that are separated by canals and these are located in the shallow Venetian Lagoon, an enclosed bay that lies between the mouths of the Po and the Piave Rivers. Parts of Venice are renowned for the beauty of their settings, their architecture, the lagoon and a part of the city are listed as a World Heritage Site. In 2014,264,579 people resided in Comune di Venezia, together with Padua and Treviso, the city is included in the Padua-Treviso-Venice Metropolitan Area, with a total population of 2.6 million. PATREVE is a metropolitan area without any degree of autonomy. The name is derived from the ancient Veneti people who inhabited the region by the 10th century BC, the city was historically the capital of the Republic of Venice. Venice has been known as the La Dominante, Serenissima, Queen of the Adriatic, City of Water, City of Masks, City of Bridges, The Floating City, and City of Canals. The City State of Venice is considered to have been the first real international financial center which gradually emerged from the 9th century to its peak in the 14th century and this made Venice a wealthy city throughout most of its history. It is also known for its several important artistic movements, especially the Renaissance period, Venice has played an important role in the history of symphonic and operatic music, and it is the birthplace of Antonio Vivaldi. Venice has been ranked the most beautiful city in the world as of 2016, the name Venetia, however, derives from the Roman name for the people known as the Veneti, and called by the Greeks Eneti. The meaning of the word is uncertain, although there are other Indo-European tribes with similar-sounding names, such as the Celtic Veneti, Baltic Veneti, and the Slavic Wends. Linguists suggest that the name is based on an Indo-European root *wen, so that *wenetoi would mean beloved, lovable, a connection with the Latin word venetus, meaning the color sea-blue, is also possible. The alternative obsolete form is Vinegia, some late Roman sources reveal the existence of fishermen on the islands in the original marshy lagoons. They were referred to as incolae lacunae, the traditional founding is identified with the dedication of the first church, that of San Giacomo on the islet of Rialto — said to have taken place at the stroke of noon on 25 March 421. Beginning as early as AD166 to 168, the Quadi and Marcomanni destroyed the center in the area. The Roman defences were again overthrown in the early 5th century by the Visigoths and, some 50 years later, New ports were built, including those at Malamocco and Torcello in the Venetian lagoon. The tribuni maiores, the earliest central standing governing committee of the islands in the Lagoon, the traditional first doge of Venice, Paolo Lucio Anafesto, was actually Exarch Paul, and his successor, Marcello Tegalliano, was Pauls magister militum. In 726 the soldiers and citizens of the Exarchate rose in a rebellion over the controversy at the urging of Pope Gregory II
3.
Mathematician
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A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems. Mathematics is concerned with numbers, data, quantity, structure, space, models, one of the earliest known mathematicians was Thales of Miletus, he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, the number of known mathematicians grew when Pythagoras of Samos established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was All is number. It was the Pythagoreans who coined the term mathematics, and with whom the study of mathematics for its own sake begins, the first woman mathematician recorded by history was Hypatia of Alexandria. She succeeded her father as Librarian at the Great Library and wrote works on applied mathematics. Because of a dispute, the Christian community in Alexandria punished her, presuming she was involved, by stripping her naked. Science and mathematics in the Islamic world during the Middle Ages followed various models and it was extensive patronage and strong intellectual policies implemented by specific rulers that allowed scientific knowledge to develop in many areas. As these sciences received wider attention from the elite, more scholars were invited and funded to study particular sciences, an example of a translator and mathematician who benefited from this type of support was al-Khawarizmi. A notable feature of many working under Muslim rule in medieval times is that they were often polymaths. Examples include the work on optics, maths and astronomy of Ibn al-Haytham, the Renaissance brought an increased emphasis on mathematics and science to Europe. As time passed, many gravitated towards universities. Moving into the 19th century, the objective of universities all across Europe evolved from teaching the “regurgitation of knowledge” to “encourag productive thinking. ”Thus, seminars, overall, science became the focus of universities in the 19th and 20th centuries. Students could conduct research in seminars or laboratories and began to produce doctoral theses with more scientific content. According to Humboldt, the mission of the University of Berlin was to pursue scientific knowledge. ”Mathematicians usually cover a breadth of topics within mathematics in their undergraduate education, and then proceed to specialize in topics of their own choice at the graduate level. In some universities, a qualifying exam serves to test both the breadth and depth of an understanding of mathematics, the students, who pass, are permitted to work on a doctoral dissertation. Mathematicians involved with solving problems with applications in life are called applied mathematicians. Applied mathematicians are mathematical scientists who, with their knowledge and professional methodology. With professional focus on a variety of problems, theoretical systems
4.
Engineer
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Engineers design materials, structures, and systems while considering the limitations imposed by practicality, regulation, safety, and cost. The word engineer is derived from the Latin words ingeniare and ingenium, the work of engineers forms the link between scientific discoveries and their subsequent applications to human and business needs and quality of life. His/her work is predominantly intellectual and varied and not of a mental or physical character. It requires the exercise of original thought and judgement and the ability to supervise the technical, he/she is thus placed in a position to make contributions to the development of engineering science or its applications. In due time he/she will be able to give authoritative technical advice, much of an engineers time is spent on researching, locating, applying, and transferring information. Indeed, research suggests engineers spend 56% of their time engaged in various information behaviours, Engineers must weigh different design choices on their merits and choose the solution that best matches the requirements. Their crucial and unique task is to identify, understand, Engineers apply techniques of engineering analysis in testing, production, or maintenance. Analytical engineers may supervise production in factories and elsewhere, determine the causes of a process failure and they also estimate the time and cost required to complete projects. Supervisory engineers are responsible for major components or entire projects, Engineering analysis involves the application of scientific analytic principles and processes to reveal the properties and state of the system, device or mechanism under study. Most engineers specialize in one or more engineering disciplines, numerous specialties are recognized by professional societies, and each of the major branches of engineering has numerous subdivisions. Civil engineering, for example, includes structural and transportation engineering and materials engineering include ceramic, metallurgical, mechanical engineering cuts across just about every discipline since its core essence is applied physics. Engineers also may specialize in one industry, such as vehicles, or in one type of technology. Several recent studies have investigated how engineers spend their time, that is, research suggests that there are several key themes present in engineers’ work, technical work, social work, computer-based work, information behaviours. Amongst other more detailed findings, a recent work sampling study found that engineers spend 62. 92% of their time engaged in work,40. 37% in social work. The time engineers spend engaged in activities is also reflected in the competencies required in engineering roles. There are many branches of engineering, each of which specializes in specific technologies, typically engineers will have deep knowledge in one area and basic knowledge in related areas. When developing a product, engineers work in interdisciplinary teams. For example, when building robots an engineering team will typically have at least three types of engineers, a mechanical engineer would design the body and actuators
5.
Topography
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Topography is the study of the shape and features of the surface of the Earth and other observable astronomical objects including planets, moons, and asteroids. The topography of an area could refer to the shapes and features themselves. This field of geoscience and planetary science is concerned with detail in general, including not only relief but also natural and artificial features. This meaning is common in the United States, where topographic maps with elevation contours have made topography synonymous with relief. The older sense of topography as the study of place still has currency in Europe, topography in a narrow sense involves the recording of relief or terrain, the three-dimensional quality of the surface, and the identification of specific landforms. This is also known as geomorphometry, in modern usage, this involves generation of elevation data in digital form. It is often considered to include the representation of the landform on a map by a variety of techniques, including contour lines, hypsometric tints. The term topography originated in ancient Greece and continued in ancient Rome, the word comes from the Greek τόπος and -γραφία. In classical literature this refers to writing about a place or places, in Britain and in Europe in general, the word topography is still sometimes used in its original sense. Detailed military surveys in Britain were called Ordnance Surveys, and this term was used into the 20th century as generic for topographic surveys, the earliest scientific surveys in France were called the Cassini maps after the family who produced them over four generations. The term topographic surveys appears to be American in origin, the earliest detailed surveys in the United States were made by the “Topographical Bureau of the Army, ” formed during the War of 1812, which became the Corps of Topographical Engineers in 1838. In the 20th century, the term started to be used to describe surface description in other fields where mapping in a broader sense is used. An objective of topography is to determine the position of any feature or more generally any point in terms of both a horizontal coordinate system such as latitude, longitude, and altitude, identifying features, and recognizing typical landform patterns are also part of the field. There are a variety of approaches to studying topography, which method to use depend on the scale and size of the area under study, its accessibility, and the quality of existing surveys. Work on one of the first topographic maps was begun in France by Giovanni Domenico Cassini, in areas where there has been an extensive direct survey and mapping program, the compiled data forms the basis of basic digital elevation datasets such as USGS DEM data. This data must often be cleaned to eliminate discrepancies between surveys, but it forms a valuable set of information for large-scale analysis. The original American topographic surveys involved not only recording of relief, remote sensing is a general term for geodata collection at a distance from the subject area. Besides their role in photogrammetry, aerial and satellite imagery can be used to identify and delineate terrain features, certainly they have become more and more a part of geovisualization, whether maps or GIS systems
6.
Republic of Venice
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It was based in the lagoon communities of the historically prosperous city of Venice. It was a leading European economic and trading power during the Middle Ages, the Venetian city state was founded as a safe haven for people escaping persecution in mainland Europe after the fall of the Roman Empire. In its early years, it prospered on the salt trade, in subsequent centuries, the city state established a thalassocracy. It dominated trade on the Mediterranean Sea, including commerce between Asia, Europe and North Africa, the Venetian navy was used in the Crusades. Venice achieved territorial conquests along the Adriatic Sea, the city became home to an extremely wealthy merchant class, who patronized renowned art and architecture along the citys lagoons. Venetian merchants were influential financiers in Europe, the city was also the birthplace of great European explorers, including Marco Polo, as well as the classical music composer Vivaldi. The republic was ruled by the Doge, who was elected by members of the Great Council of Venice, the ruling class was an oligarchy of merchants and aristocrats. Venice and other Italian maritime republics played a key role in fostering capitalism, Venetian citizens generally supported the system of governance. The city-state enforced strict laws and employed ruthless tactics in its prisons, the opening of new trade routes to the Americas and the East Indies via the Atlantic Ocean marked the beginning of Venices decline as a maritime republic. The city state suffered defeats from the navy of the Ottoman Empire, in 1797, the country was colonized by Austria and France, following an invasion by Napoleon Bonaparte. Venice became a part of a unified Italy in the 19th century and it was formally known as the Most Serene Republic of Venice and is often referred to as La Serenissima, in reference to its title as one of the Most Serene Republics. He was the first historical Doge of Venice, whichever the case, the first doges had their power base in Heraclea. Ursuss successor, Deusdedit, moved his seat from Heraclea to Malamocco in the 740s and he was the son of Ursus and represented the attempt of his father to establish a dynasty. Such attempts were more commonplace among the doges of the first few centuries of Venetian history. They desired to remain well-connected to the Empire, another faction, republican in nature, believed in continuing along a course towards practical independence. The other main faction was pro-Frankish, supported mostly by clergy, they looked towards the new Carolingian king of the Franks, Pepin the Short, as the best provider of defence against the Lombards. A minor, pro-Lombard faction was opposed to close ties with any of these further-off powers, the successors of Obelerio inherited a united Venice. By the Pax Nicephori, the two emperors had recognised that Venice belonged to the Byzantine sphere of influence, many centuries later, the Venetians claimed that the treaty had recognised Venetian de facto independence, but the truth of this claim is doubted by modern scholars
7.
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 France, Switzerland, Austria, Slovenia, San Marino, Italy covers an area of 301,338 km2 and has a largely temperate seasonal climate and Mediterranean climate. Due to its shape, it is referred to in Italy as lo Stivale. With 61 million inhabitants, it is the fourth most populous EU member state, the Italic tribe known as the Latins formed the Roman Kingdom, which eventually became a republic that conquered and assimilated other nearby civilisations. The legacy of the Roman Empire is widespread and can be observed in the distribution of civilian law, republican governments, Christianity. The Renaissance began in Italy and spread to the rest of Europe, bringing a renewed interest in humanism, science, exploration, Italian culture flourished at this time, producing famous scholars, artists and polymaths such as Leonardo da Vinci, Galileo, Michelangelo and Machiavelli. The weakened sovereigns soon fell victim to conquest by European powers such as France, Spain and Austria. Despite being one of the victors in World War I, Italy entered a period of economic crisis and social turmoil. The subsequent participation in World War II on the Axis side ended in defeat, economic destruction. Today, Italy has the third largest economy in the Eurozone and it has a very high level of human development and is ranked sixth in the world for life expectancy. The country plays a prominent role in regional and global economic, military, cultural and diplomatic affairs, as a reflection of its cultural wealth, Italy is home to 51 World Heritage Sites, the most in the world, and is the fifth most visited country. The assumptions on the etymology of the name Italia are very numerous, according to one of the more common explanations, the term Italia, from Latin, Italia, was borrowed through Greek from the Oscan Víteliú, meaning land of young cattle. The bull was a symbol of the southern Italic tribes and was often depicted goring the Roman wolf as a defiant symbol of free Italy during the Social War. Greek historian Dionysius of Halicarnassus states this account together with the legend that Italy was named after Italus, mentioned also by Aristotle and Thucydides. The name Italia originally applied only to a part of what is now Southern Italy – according to Antiochus of Syracuse, but by his time Oenotria and Italy had become synonymous, and the name also applied to most of Lucania as well. The Greeks gradually came to apply the name Italia to a larger region, 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 ancient Italian peoples of undetermined language families but of possible origins include the Rhaetian people and Cammuni. Also the Phoenicians established colonies on the coasts of Sardinia and Sicily, the Roman legacy has deeply influenced the Western civilisation, shaping most of the modern world
8.
Archimedes
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Archimedes of Syracuse was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the scientists in classical antiquity. He was also one of the first to apply mathematics to physical phenomena, founding hydrostatics and statics and he is credited with designing innovative machines, such as his screw pump, compound pulleys, and defensive war machines to protect his native Syracuse from invasion. Archimedes died during the Siege of Syracuse when he was killed by a Roman soldier despite orders that he should not be harmed. Cicero describes visiting the tomb of Archimedes, which was surmounted by a sphere and a cylinder, unlike his inventions, the mathematical writings of Archimedes were little known in antiquity. Archimedes was born c.287 BC in the city of Syracuse, Sicily, at that time a self-governing colony in Magna Graecia. The date of birth is based on a statement by the Byzantine Greek historian John Tzetzes that Archimedes lived for 75 years, in The Sand Reckoner, Archimedes gives his fathers name as Phidias, an astronomer about whom nothing is known. Plutarch wrote in his Parallel Lives that Archimedes was related to King Hiero II, a biography of Archimedes was written by his friend Heracleides but this work has been lost, leaving the details of his life obscure. It is unknown, for instance, whether he married or had children. During his youth, Archimedes may have studied in Alexandria, Egypt and he referred to Conon of Samos as his friend, while two of his works have introductions addressed to Eratosthenes. Archimedes died c.212 BC during the Second Punic War, according to the popular account given by Plutarch, Archimedes was contemplating a mathematical diagram when the city was captured. A Roman soldier commanded him to come and meet General Marcellus but he declined, the soldier was enraged by this, and killed Archimedes with his sword. Plutarch also gives an account of the death of Archimedes which suggests that he may have been killed while attempting to surrender to a Roman soldier. According to this story, Archimedes was carrying mathematical instruments, and was killed because the thought that they were valuable items. General Marcellus was reportedly angered by the death of Archimedes, as he considered him a valuable asset and had ordered that he not be harmed. Marcellus called Archimedes a geometrical Briareus, the last words attributed to Archimedes are Do not disturb my circles, a reference to the circles in the mathematical drawing that he was supposedly studying when disturbed by the Roman soldier. This quote is given in Latin as Noli turbare circulos meos. The phrase is given in Katharevousa Greek as μὴ μου τοὺς κύκλους τάραττε
9.
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, number theory, Euclid is the anglicized version of the Greek name Εὐκλείδης, which means renowned, glorious. Very few original references to Euclid survive, so little is known about his life, the date, 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 rarely mentioned by name by other Greek mathematicians from Archimedes onward, the few 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, Proclus later retells a story that, when Ptolemy I asked if there was a shorter path to learning geometry than Euclids Elements, Euclid replied there is no royal road to geometry. This anecdote is questionable since it is similar to a story told about Menaechmus, a detailed biography of Euclid is given by Arabian authors, mentioning, for example, a birth town of Tyre. This biography is generally believed to be completely fictitious, however, this hypothesis is not well accepted by scholars and there is little evidence in its favor. The only reference that historians rely on of Euclid having written the Elements was from Proclus, although best known for its geometric results, the Elements also includes number theory. The geometrical system described in the Elements was long known simply as geometry, today, however, that system is often referred to as Euclidean geometry to distinguish it from other so-called non-Euclidean geometries that mathematicians discovered in the 19th century. In addition to the Elements, at least five works of Euclid have survived to the present day and they follow the same logical structure as Elements, with definitions and proved propositions. Data deals with the nature and implications of information in geometrical problems. On Divisions of Figures, which only partially in Arabic translation. It is similar to a first-century AD work by Heron of Alexandria, catoptrics, which concerns the mathematical theory of mirrors, particularly the images formed in plane and spherical concave mirrors. The attribution is held to be anachronistic however by J J OConnor, phaenomena, a treatise on spherical astronomy, survives in Greek, it is quite similar to On the Moving Sphere by Autolycus of Pitane, who flourished around 310 BC. Optics is the earliest surviving Greek treatise on perspective, in its definitions Euclid follows the Platonic tradition that vision is caused by discrete rays which emanate from the eye. One important definition is the fourth, Things seen under a greater angle appear greater, proposition 45 is interesting, proving that for any two unequal magnitudes, there is a point from which the two appear equal. Other works are attributed to Euclid, but have been lost
10.
Mathematics
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Mathematics is the study of topics such as quantity, structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope, Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or 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 abstraction and logic, mathematics developed from counting, calculation, measurement, practical mathematics has been a human activity from as 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 Euclids Elements. Galileo Galilei said, The universe cannot be read until we have learned the language and it is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth, carl Friedrich Gauss referred to mathematics 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, rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise. Albert Einstein stated that as far as the laws of mathematics refer to reality, they are not certain, Mathematics is essential in many fields, including natural science, engineering, medicine, finance and the social sciences. Applied mathematics has led to entirely new mathematical disciplines, such as statistics, Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, the history of mathematics can be seen as an ever-increasing series of abstractions. The earliest uses of mathematics were in trading, land measurement, painting and weaving patterns, in Babylonian mathematics elementary arithmetic first appears in the archaeological record. Numeracy pre-dated writing and numeral systems have many and diverse. Between 600 and 300 BC the Ancient Greeks began a study of mathematics in its own right with Greek mathematics. Mathematics has since been extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries continue to be made today, the overwhelming majority of works in this ocean contain new mathematical theorems and their proofs. The word máthēma is derived from μανθάνω, while the modern Greek equivalent is μαθαίνω, in Greece, the word for mathematics came to have the narrower and more technical meaning mathematical study even in Classical times
11.
Ballistics
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A ballistic body is a body with momentum which is free to move, subject to forces, such as the pressure of gases in a gun or a propulsive nozzle, by rifling in a barrel, by gravity, or by air drag. The earliest known ballistic projectiles were stones and spears, and the throwing stick. The oldest evidence of stone-tipped projectiles, which may or may not have been propelled by a bow, dating to c.64,000 years ago, were found in Sibudu Cave, present day-South Africa. The oldest evidence of the use of bows to shoot arrows dates to about 10,000 years ago and they had shallow grooves on the base, indicating that they were shot from a bow. The oldest bow so far recovered is about 8,000 years old, archery seems to have arrived in the Americas with the Arctic small tool tradition, about 4,500 years ago. The first devices identified as guns appeared in China around 1000 AD, and by the 12th century the technology was spreading through the rest of Asia, the word ballistics comes from the Greek βάλλειν ballein, meaning to throw. A projectile is any object projected into space by the exertion of a force, although any object in motion through space is a projectile, the term most commonly refers to a ranged weapon. Mathematical equations of motion are used to analyze projectile trajectory, examples of projectiles include balls, arrows, bullets, artillery shells, rockets, etc. Throwing is the launching of a projectile by hand, although some other animals can throw, humans are unusually good throwers due to their high dexterity and good timing capabilities, and it is believed that this is an evolved trait. Evidence of human throwing dates back 2 million years, the 90 mph throwing speed found in many athletes far exceeds the speed at which chimpanzees can throw things, which is about 20 mph. This ability reflects the ability of the shoulder muscles and tendons to store elasticity until it is needed to propel an object. A sling is a projectile weapon used to throw a blunt projectile such as a stone. A sling has a cradle or pouch in the middle of two lengths of cord. The sling stone is placed in the pouch, the middle finger or thumb is placed through a loop on the end of one cord, and a tab at the end of the other cord is placed between the thumb and forefinger. The sling is swung in an arc, and the tab released at a precise moment and this frees the projectile to fly to the target. A bow is a piece of material which shoots aerodynamic projectiles called arrows. A string joins the two ends and when the string is drawn back, the ends of the stick are flexed, when the string is released, the potential energy of the flexed stick is transformed into the velocity of the arrow. Archery is the art or sport of shooting arrows from bows, a catapult is a device used to launch a projectile a great distance without the aid of explosive devices — particularly various types of ancient and medieval siege engines
12.
Galileo Galilei
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Galileo Galilei was an Italian polymath, astronomer, physicist, engineer, philosopher, and mathematician. He played a role in the scientific revolution of the seventeenth century. Galileo also worked in applied science and technology, inventing an improved military compass, Galileos 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 a stellar parallax. He was tried by the Inquisition, found vehemently suspect of heresy and he spent the rest of his life under house arrest. He has been called the father of observational astronomy, the father of modern physics, the father of scientific method, and the father of science. Galileo was born in Pisa, Italy, on 15 February 1564, the first of six children of Vincenzo Galilei, a famous lutenist, composer, and music theorist, and Giulia, three of Galileos five siblings survived infancy. The youngest, Michelangelo, also became a noted lutenist and composer although he contributed to financial burdens during Galileos young adulthood, Michelangelo was unable to contribute his fair share of their fathers promised dowries to their brothers-in-law, who would later attempt to seek legal remedies for payments due. Michelangelo would also occasionally have to borrow funds from Galileo to support his musical endeavours and these financial burdens may have contributed to Galileos early fire to develop inventions that would bring him additional income. When Galileo Galilei was eight, his family moved to Florence and he then was educated in the Vallombrosa Abbey, about 30 km southeast of Florence. Galileo Bonaiuti was buried in the church, the Basilica of Santa Croce in Florence. It was common for mid-sixteenth century Tuscan families to name the eldest son after the parents surname, hence, Galileo Galilei was not necessarily named after his ancestor Galileo Bonaiuti. The Italian male given name Galileo derives from the Latin Galilaeus, meaning of Galilee, the biblical roots of Galileos name and surname were to become the subject of a famous pun. In 1614, during the Galileo affair, one of Galileos opponents, in it he made a point of quoting Acts 1,11, Ye men of Galilee, why stand ye gazing up into heaven. Despite being a genuinely pious Roman Catholic, Galileo fathered three children out of wedlock with Marina Gamba and they had two daughters, Virginia and Livia, and a son, Vincenzo. Their only worthy alternative was the religious life, both girls were accepted by the convent of San Matteo in Arcetri and remained there for the rest of their lives. Virginia took the name Maria Celeste upon entering the convent and she died on 2 April 1634, and is buried with Galileo at the Basilica of Santa Croce, Florence. Livia took the name Sister Arcangela and was ill for most of her life, Vincenzo was later legitimised as the legal heir of Galileo and married Sestilia Bocchineri
13.
War of the League of Cambrai
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The War of the League of Cambrai, sometimes known as the War of the Holy League and by several other names, was a major conflict in the Italian Wars. Although the League was initially successful, friction between Julius and Louis caused it to collapse by 1510, Julius then allied himself with Venice against France. In the aftermath of the First Italian War, Pope Alexander VI had, with French assistance, in 1507, Julius returned to the question of the cities in Venetian hands, once again rebuffed by the Senate, he encouraged Emperor Maximilian I to attack the Republic. Julius, humiliated by the failure of the Imperial invasion, turned to Louis XII of France with an offer of alliance. On 10 December 1508, representatives of the Papacy, France, on 15 April 1509, Louis left Milan at the head of a French army and moved rapidly into Venetian territory. Consequently, when Louis crossed the Adda River in early May and Alviano advanced to him, Pitigliano, believing it best to avoid a pitched battle. Alviano, disregarding the new orders, continued the engagement, his army was surrounded and destroyed. DEste, having joined the League and been appointed Gonfalonier on 19 April, the newly arrived Imperial governors, however, quickly proved to be unpopular. In mid-July, the citizens of Padua, aided by detachments of Venetian cavalry under the command of the proveditor Andrea Gritti, the landsknechts garrisoning the city were too few in number to mount effective resistance, and Padua was restored to Venetian control on 17 July 1509. The success of the revolt finally pushed Maximilian into action, in early August, a massive Imperial army, accompanied by bodies of French and Spanish troops, set out from Trento into the Veneto. In mid-November, Pitigliano returned to the offensive, Venetian troops easily defeated the remaining Imperial forces, capturing Vicenza, Este, Feltre, although a subsequent attack on Verona failed, Pitigliano destroyed a Papal army under Francesco II of Gonzaga in the process. Francesco Guicciardini credited the victory to Alfonso himself. A new French advance soon forced Pitigliano to withdraw to Padua once again, faced with a shortage of both funds and men, the Senate decided to send an embassy to Julius in order to negotiate a settlement. The Senate argued over the terms for two months, but finally accepted them on February 24,1510 and this apparent reconciliation between Venice and the Pope did not stop the French from again invading the Veneto in March. Gritti garrisoned Padua for an attack by a combined Franco-Imperial army, but Louis, more concerned by the death of his advisor. His own forces being inadequate for the venture, the Pope hired an army of Swiss mercenaries, ordering them to attack the French in Milan, the Republic, facing a renewed French onslaught, readily accepted the offer. By July 1510, the new Veneto-Papal alliance was on the offensive, Julius now excommunicated Alfonso dEste, thus justifying an attack on the Duchy itself, in anticipation of his coming victory, the Pope traveled to Bologna, so as to be nearby when Ferrara was taken. The French army, however, had been left unopposed by the Swiss and was free to march south into the heart of Italy
14.
Alphabet
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An alphabet is a standard set of letters that is used to write one or more languages based upon the general principle that the letters represent phonemes of the spoken language. This is in contrast to other types of writing systems, such as syllabaries and logographies, the Proto-Canaanite script, later known as the Phoenician alphabet, is the first fully phonemic script. Thus the Phoenician alphabet is considered to be the first alphabet, the Phoenician alphabet is the ancestor of most modern alphabets, including Arabic, Greek, Latin, Cyrillic, Hebrew, and possibly Brahmic. Under a terminological distinction promoted by Peter T. Daniels, an alphabet is a script that represents both vowels and consonants as letters equally. In this narrow sense of the word the first true alphabet was the Greek alphabet, in other alphabetic scripts such as the original Phoenician, Hebrew or Arabic, letters predominantly or exclusively represent consonants, such a script is also called an abjad. A third type, called abugida or alphasyllabary, is one where vowels are shown by diacritics or modifications of consonantal letters, as in Devanagari. The Khmer alphabet is the longest, with 74 letters, there are dozens of alphabets in use today, the most popular being the Latin alphabet. Many languages use modified forms of the Latin alphabet, with additional letters formed using diacritical marks, while most alphabets have letters composed of lines, there are also exceptions such as the alphabets used in Braille. Alphabets are usually associated with an ordering of letters. This makes them useful for purposes of collation, specifically by allowing words to be sorted in alphabetical order and it also means that their letters can be used as an alternative method of numbering ordered items, in such contexts as numbered lists and number placements. The English word alphabet came into Middle English from the Late Latin word alphabetum, the Greek word was made from the first two letters, alpha and beta. The names for the Greek letters came from the first two letters of the Phoenician alphabet, aleph, which also meant ox, and bet, in the alphabet song in English, the term ABCs is used instead of the word alphabet. Knowing ones ABCs, in general, can be used as a metaphor for knowing the basics about anything, the history of the alphabet started in ancient Egypt. These glyphs were used as guides for logograms, to write grammatical inflections. Based on letter appearances and names, it is believed to be based on Egyptian hieroglyphs and this script had no characters representing vowels, although originally it probably was a syllabary, but unneeded symbols were discarded. An alphabetic cuneiform script with 30 signs including three that indicate the vowel was invented in Ugarit before the 15th century BC. This script was not used after the destruction of Ugarit, the Proto-Sinaitic script eventually developed into the Phoenician alphabet, which is conventionally called Proto-Canaanite before ca.1050 BC. The oldest text in Phoenician script is an inscription on the sarcophagus of King Ahiram and this script is the parent script of all western alphabets
15.
Euclid's Elements
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Euclids 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, propositions, the books cover Euclidean geometry and the ancient Greek version of elementary number theory. Elements is the second-oldest extant Greek mathematical treatise after Autolycus On the Moving Sphere and it has proven instrumental in the development of logic and modern science. According to Proclus, the element was used to describe a theorem that is all-pervading. The word element in the Greek language is the same as letter and this suggests that theorems in the Elements should be seen as standing in the same relation to geometry as letters to language. Euclids Elements has been referred to as the most successful and influential textbook ever written, for centuries, when the quadrivium was included in the curriculum of all university students, knowledge of at least part of Euclids Elements was required of all students. Not until the 20th century, by which time its content was taught through other school textbooks. Scholars believe that the Elements is largely a collection of theorems proven by other mathematicians, the Elements may have been based on an earlier textbook by Hippocrates of Chios, who also may have originated the use of letters to refer to figures. This manuscript, the Heiberg manuscript, is from a Byzantine workshop around 900 and is the basis of modern editions, papyrus Oxyrhynchus 29 is a tiny fragment of an even older manuscript, but only contains the statement of one proposition. Although known to, for instance, Cicero, no record exists of the text having been translated into Latin prior to Boethius in the fifth or sixth century. The Arabs received the Elements from the Byzantines around 760, this version was translated into Arabic under Harun al Rashid circa 800, the Byzantine scholar Arethas commissioned the copying of one of the extant Greek manuscripts of Euclid in the late ninth century. Although known in Byzantium, the Elements was lost to Western Europe until about 1120, the first printed edition appeared in 1482, and since then it has been translated into many languages and published in about a thousand different editions. Theons Greek edition was recovered in 1533, in 1570, John Dee provided a widely respected Mathematical Preface, along with copious notes and supplementary material, to the first English edition by Henry Billingsley. Copies of the Greek text still exist, some of which can be found in the Vatican Library, the manuscripts available are of variable quality, and invariably incomplete. By careful analysis of the translations and originals, hypotheses have been made about the contents of the original text, ancient texts which refer to the Elements itself, and to other mathematical theories that were current at the time it was written, are also important in this process. Such analyses are conducted by J. L. Heiberg and Sir Thomas Little Heath in their editions of the text, also of importance are the scholia, or annotations to the text. These additions, which distinguished themselves from the main text. The Elements is still considered a masterpiece in the application of logic to mathematics, in historical context, it has proven enormously influential in many areas of science
16.
Latin
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Latin is a classical language belonging to the Italic branch of the Indo-European languages. The Latin alphabet is derived from the Etruscan and Greek alphabets, Latin was originally spoken in Latium, in the Italian Peninsula. Through the power of the Roman Republic, it became the dominant language, Vulgar Latin developed into the Romance languages, such as Italian, Portuguese, Spanish, French, and Romanian. Latin, Italian and French have contributed many words to the English language, Latin and Ancient Greek roots are used in theology, biology, and medicine. By the late Roman Republic, Old Latin had been standardised into Classical Latin, Vulgar Latin was the colloquial form spoken during the same time and attested in inscriptions and the works of comic playwrights like Plautus and Terence. Late Latin is the language from the 3rd century. Later, Early Modern Latin and Modern Latin evolved, Latin was used as the language of international communication, scholarship, and science until well into the 18th century, when it began to be supplanted by vernaculars. Ecclesiastical Latin remains the language of the Holy See and the Roman Rite of the Catholic Church. Today, many students, scholars and members of the Catholic clergy speak Latin fluently and it is taught in primary, secondary and postsecondary educational institutions around the world. The language has been passed down through various forms, some inscriptions have been published in an internationally agreed, monumental, multivolume series, the Corpus Inscriptionum Latinarum. Authors and publishers vary, but the format is about the same, volumes detailing inscriptions with a critical apparatus stating the provenance, the reading and interpretation of these inscriptions is the subject matter of the field of epigraphy. The works of several hundred ancient authors who wrote in Latin have survived in whole or in part and they are in part the subject matter of the field of classics. The Cat in the Hat, and a book of fairy tales, additional resources include phrasebooks and resources for rendering everyday phrases and concepts into Latin, such as Meissners Latin Phrasebook. The Latin influence in English has been significant at all stages of its insular development. From the 16th to the 18th centuries, English writers cobbled together huge numbers of new words from Latin and Greek words, dubbed inkhorn terms, as if they had spilled from a pot of ink. Many of these words were used once by the author and then forgotten, many of the most common polysyllabic English words are of Latin origin through the medium of Old French. Romance words make respectively 59%, 20% and 14% of English, German and those figures can rise dramatically when only non-compound and non-derived words are included. Accordingly, Romance words make roughly 35% of the vocabulary of Dutch, Roman engineering had the same effect on scientific terminology as a whole
17.
Arithmetic
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Arithmetic is a branch of mathematics that consists of the study of numbers, especially the properties of the traditional operations between them—addition, subtraction, multiplication and division. Arithmetic is an part of number theory, and number theory is considered to be one of the top-level divisions of modern mathematics, along with algebra, geometry. The terms arithmetic and higher arithmetic were used until the beginning of the 20th century as synonyms for number theory and are still used to refer to a wider part of number theory. The earliest written records indicate the Egyptians and Babylonians used all the elementary arithmetic operations as early as 2000 BC and these artifacts do not always reveal the specific process used for solving problems, but the characteristics of the particular numeral system strongly influence the complexity of the methods. The hieroglyphic system for Egyptian numerals, like the later Roman numerals, in both cases, this origin resulted in values that used a decimal base but did not include positional notation. Complex calculations with Roman numerals required the assistance of a board or the Roman abacus to obtain the results. Early number systems that included positional notation were not decimal, including the system for Babylonian numerals. Because of this concept, the ability to reuse the same digits for different values contributed to simpler. The continuous historical development of modern arithmetic starts with the Hellenistic civilization of ancient Greece, prior to the works of Euclid around 300 BC, Greek studies in mathematics overlapped with philosophical and mystical beliefs. For example, Nicomachus summarized the viewpoint of the earlier Pythagorean approach to numbers, Greek numerals were used by Archimedes, Diophantus and others in a positional notation not very different from ours. Because the ancient Greeks lacked a symbol for zero, they used three separate sets of symbols, one set for the units place, one for the tens place, and one for the hundreds. Then for the place they would reuse the symbols for the units place. Their addition algorithm was identical to ours, and their multiplication algorithm was very slightly different. Their long division algorithm was the same, and the square root algorithm that was taught in school was known to Archimedes. He preferred it to Heros method of successive approximation because, once computed, a digit doesnt change, and the square roots of perfect squares, such as 7485696, terminate immediately as 2736. For numbers with a part, such as 546.934. The ancient Chinese used a positional notation. Because they also lacked a symbol for zero, they had one set of symbols for the place
18.
Gerolamo Cardano
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He wrote more than 200 works on science. He made significant contributions to hypocycloids, published in De proportionibus, the generating circles of these hypocycloids were later named Cardano circles or cardanic circles and were used for the construction of the first high-speed printing presses. Today, he is known for his achievements in algebra. He was born in Pavia, Lombardy, the child of Fazio Cardano, a mathematically gifted jurist, lawyer. In his autobiography, Cardano wrote that his mother, Chiara Micheri, had taken various abortive medicines to terminate the pregnancy, he was taken by violent means from my mother and she was in labour for three days. Shortly before his birth, his mother had to move from Milan to Pavia to escape the Plague and his eccentric and confrontational style did not earn him many friends and he had a difficult time finding work after his studies had ended. In 1525, Cardano repeatedly applied to the College of Physicians in Milan and he suffered from impotence throughout the early part of his life, but recovered and married Lucia Banderini in 1531. Before her death in 1546, she bore him three children, Giovanni Battista, Chiara and Aldo, Cardano was the first mathematician to make systematic use of numbers less than zero. He published with attribution the solution of Scipione del Ferro to the cubic equation and the solution of his student Lodovico Ferrari to the quartic equation in his 1545 book Ars Magna. The solution to one case of the cubic equation a x 3 + b x + c =0, had been communicated to him by Niccolò Fontana Tartaglia in the form of a poem. In Opus novum de proportionibus he introduced the binomial coefficients and the binomial theorem, Cardano was notoriously short of money and kept himself solvent by being an accomplished gambler and chess player. He used the game of throwing dice to understand the concepts of probability. He demonstrated the efficacy of defining odds as the ratio of favourable to unfavourable outcomes and he was also aware of the multiplication rule for independent events but was not certain about what values should be multiplied. Cardano made several contributions to hydrodynamics and held that perpetual motion is impossible and he published two encyclopedias of natural science which contain a wide variety of inventions, facts, and occult superstitions. He also introduced the Cardan grille, a tool, in 1550. Someone also assigned to Cardano the credit for the invention of the so-called Cardanos Rings, also called Chinese Rings and he was familiar with a report by Rudolph Agricola about a deaf mute who had learned to write. Two of Cardanos children—Giovanni and Aldo Battista—came to ignoble ends, Giovanni Battista, Cardanos eldest and favorite son, was tried and beheaded in 1560 for poisoning his wife, after he discovered that their three children were not his. Aldo Battista was a gambler, who stole money from his father and was disinherited by him in 1569, Cardano was arrested by the Inquisition in 1570 for unknown reasons, and forced to spend several months in prison and abjure his professorship
19.
Cubic function
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In algebra, a cubic function is a function of the form f = a x 3 + b x 2 + c x + d, where a is nonzero. Setting f =0 produces an equation of the form. The solutions of this equation are called roots of the polynomial f, If all of the coefficients a, b, c, and d of the cubic equation are real numbers then there will be at least one real root. All of the roots of the equation can be found algebraically. The roots can also be found trigonometrically, alternatively, numerical approximations of the roots can be found using root-finding algorithms like Newtons method. The coefficients do not need to be complex numbers, much of what is covered below is valid for coefficients of any field with characteristic 0 or greater than 3. The solutions of the cubic equation do not necessarily belong to the field as the coefficients. For example, some cubic equations with rational coefficients have roots that are complex numbers. Cubic equations were known to the ancient Babylonians, Greeks, Chinese, Indians, Babylonian cuneiform tablets have been found with tables for calculating cubes and cube roots. The Babylonians could have used the tables to solve cubic equations, the problem of doubling the cube involves the simplest and oldest studied cubic equation, and one for which the ancient Egyptians did not believe a solution existed. Methods for solving cubic equations appear in The Nine Chapters on the Mathematical Art, in the 3rd century, the Greek mathematician Diophantus found integer or rational solutions for some bivariate cubic equations. In the 11th century, the Persian poet-mathematician, Omar Khayyám, in an early paper, he discovered that a cubic equation can have more than one solution and stated that it cannot be solved using compass and straightedge constructions. He also found a geometric solution, in the 12th century, the Indian mathematician Bhaskara II attempted the solution of cubic equations without general success. However, he gave one example of an equation, x3 + 12x = 6x2 +35. He used what would later be known as the Ruffini-Horner method to approximate the root of a cubic equation. He also developed the concepts of a function and the maxima and minima of curves in order to solve cubic equations which may not have positive solutions. He understood the importance of the discriminant of the equation to find algebraic solutions to certain types of cubic equations. Leonardo de Pisa, also known as Fibonacci, was able to approximate the positive solution to the cubic equation x3 + 2x2 + 10x =20
20.
Tetrahedron
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In geometry, a tetrahedron, also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the ordinary convex polyhedra, the tetrahedron is the three-dimensional case of the more general concept of a Euclidean simplex. The tetrahedron is one kind of pyramid, which is a polyhedron with a polygon base. In the case of a tetrahedron the base is a triangle, like all convex polyhedra, a tetrahedron can be folded from a single sheet of paper. For any tetrahedron there exists a sphere on which all four vertices lie, a regular tetrahedron is one in which all four faces are equilateral triangles. It is one of the five regular Platonic solids, which have known since antiquity. In a regular tetrahedron, not only are all its faces the same size and shape, regular tetrahedra alone do not tessellate, but if alternated with regular octahedra they form the alternated cubic honeycomb, which is a tessellation. The regular tetrahedron is self-dual, which means that its dual is another regular tetrahedron, the compound figure comprising two such dual tetrahedra form a stellated octahedron or stella octangula. This form has Coxeter diagram and Schläfli symbol h, the tetrahedron in this case has edge length 2√2. Inverting these coordinates generates the dual tetrahedron, and the together form the stellated octahedron. In other words, if C is the centroid of the base and this follows from the fact that the medians of a triangle intersect at its centroid, and this point divides each of them in two segments, one of which is twice as long as the other. The vertices of a cube can be grouped into two groups of four, each forming a regular tetrahedron, the symmetries of a regular tetrahedron correspond to half of those of a cube, those that map the tetrahedra to themselves, and not to each other. The tetrahedron is the only Platonic solid that is not mapped to itself by point inversion, the regular tetrahedron has 24 isometries, forming the symmetry group Td, isomorphic to the symmetric group, S4. The first corresponds to the A2 Coxeter plane, the two skew perpendicular opposite edges of a regular tetrahedron define a set of parallel planes. When one of these intersects the tetrahedron the resulting cross section is a rectangle. When the intersecting plane is one of the edges the rectangle is long. When halfway between the two edges the intersection is a square, the aspect ratio of the rectangle reverses as you pass this halfway point. For the midpoint square intersection the resulting boundary line traverses every face of the tetrahedron similarly, if the tetrahedron is bisected on this plane, both halves become wedges
21.
Volume
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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 SI derived unit, the cubic metre, three dimensional mathematical shapes are also assigned volumes. Volumes of some simple shapes, such as regular, straight-edged, Volumes of a complicated shape can be calculated by integral calculus if a formula exists for the shapes boundary. Where a variance in shape and volume occurs, such as those that exist between different human beings, these can be calculated using techniques such as the Body Volume Index. One-dimensional figures and 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 other and the volume is not additive. In differential geometry, volume is expressed by means of the volume form, in thermodynamics, volume is a fundamental parameter, and is a conjugate variable to pressure. Any unit of length gives a 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. The metric system also includes the litre as a unit of volume, thus 1 litre =3 =1000 cubic centimetres =0.001 cubic metres, so 1 cubic metre =1000 litres. Small amounts of liquid are often measured in millilitres, where 1 millilitre =0.001 litres =1 cubic centimetre. Capacity is defined by the Oxford English Dictionary as the applied to the content of a vessel, and to liquids, grain, or the like. Capacity is not identical in meaning to volume, though closely related, Units of capacity are the SI litre and its derived units, and Imperial units such as gill, pint, gallon, and others. Units of volume are the cubes of units of length, in SI the units of volume and capacity are closely related, one litre is exactly 1 cubic decimetre, the capacity of a cube with a 10 cm side. In other systems the conversion is not trivial, the capacity of a fuel tank is rarely stated in cubic feet, for example. The density of an object is defined as the ratio of the mass to the volume, the inverse of density is specific volume which is defined as volume divided by mass. Specific volume is an important in thermodynamics where the volume of a working fluid is often an important parameter of a system being studied
22.
Distance
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Distance is a numerical description of how far apart objects are. In physics or everyday usage, distance may refer to a physical length, in most cases, distance from A to B is interchangeable with distance from B to A. In mathematics, a function or metric is a generalization of the concept of physical distance. A metric is a function that behaves according to a set of rules. The circumference of the wheel is 2π × radius, and assuming the radius to be 1, in engineering ω = 2πƒ is often used, where ƒ is the frequency. Chessboard distance, formalized as Chebyshev distance, is the number of moves a king must make on a chessboard to travel between two squares. Distance measures in cosmology are complicated by the expansion of the universe, the term distance is also used by analogy to measure non-physical entities in certain ways. In computer science, there is the notion of the distance between two strings. For example, the dog and dot, which vary by only one letter, are closer than dog and cat. In this way, many different types of distances can be calculated, such as for traversal of graphs, comparison of distributions and curves, distance cannot be negative, and distance travelled never decreases. Distance is a quantity or a magnitude, whereas displacement is a vector quantity with both magnitude and direction. Directed distance is a positive, zero, or negative scalar quantity, the distance covered by a vehicle, person, animal, or object along a curved path from a point A to a point B should be distinguished from the straight-line distance from A to B. For example, whatever the distance covered during a trip from A to B and back to A. In general the straight-line distance does not equal distance travelled, except for journeys in a straight line, directed distances are distances with a directional sense. They can be determined along straight lines and along curved lines, for instance, just labelling the two endpoints as A and B can indicate the sense, if the ordered sequence is assumed, which implies that A is the starting point. A displacement is a kind of directed distance defined in mechanics. A directed distance is called displacement when it is the distance along a line from A and B. This implies motion of the particle, the distance traveled by a particle must always be greater than or equal to its displacement, with equality occurring only when the particle moves along a straight path
23.
Heron's formula
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Herons formula states that the area of a triangle whose sides have lengths a, b, and c is A = s, where s is the semiperimeter of the triangle, that is, s = a + b + c 2. Herons formula can also be written as A =14 A =142 − A =142 −2 A =144 a 2 b 2 −2. Let △ABC be the triangle sides a =4, b =13. The semiperimeter is s = 1/2 = 1/2 =16, in this example, the side lengths and area are all integers, making it a Heronian triangle. However, Herons formula works well in cases where one or all of these numbers is not an integer. The formula is credited to Heron of Alexandria, and a proof can be found in his book, Metrica, written c. A formula equivalent to Herons, namely A =12 a 2 c 2 −2 and it was published in Shushu Jiuzhang, written by Qin Jiushao and published in 1247. Herons original proof made use of quadrilaterals, while other arguments appeal to trigonometry as below, or to the incenter. A modern proof, which uses algebra and is quite unlike the one provided by Heron, 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 b2 = h2 + d2, subtracting these yields a2 − b2 = c2 − 2cd. Herons formula as given above is numerically unstable for triangles with a small angle when using floating point arithmetic. A stable alternative involves arranging the lengths of the sides so that a ≥ b ≥ c, the brackets in the above formula are required in order to prevent numerical instability in the evaluation. Three other area formulas have the structure as Herons formula but are expressed in terms of different variables. First, denoting the medians from sides a, b, and c respectively as ma, mb, Herons formula is a special case of Brahmaguptas formula for the area of a cyclic quadrilateral. Herons formula and Brahmaguptas formula are both special cases of Bretschneiders formula for the area of a quadrilateral, Herons formula can be obtained from Brahmaguptas formula or Bretschneiders formula by setting one of the sides of the quadrilateral to zero. Herons formula is also a case of the formula for the area of a trapezoid or trapezium based only on its sides. Herons formula is obtained by setting the smaller parallel side to zero, another generalization of Herons formula to pentagons and hexagons inscribed in a circle was discovered by David P. Robbins
24.
Triangle
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A triangle is a polygon with three edges and three vertices. It is one of the shapes in geometry. A triangle with vertices A, B, and C is denoted △ A B C, in Euclidean geometry any three points, when non-collinear, determine a unique triangle and 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 all sides the same length. An equilateral triangle is also a 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 triangles isosceles triangles, the 45–45–90 right triangle, which appears in the tetrakis 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, a side can be marked with a pattern of ticks, short line segments in the form of tally marks, two sides have equal lengths if they are both marked with the same pattern. In a triangle, the pattern is no more than 3 ticks. Similarly, patterns of 1,2, or 3 concentric arcs inside the angles are used to indicate equal angles, triangles can also be classified according to their internal angles, measured here in degrees. A right triangle has one of its interior angles measuring 90°, the side opposite to the right angle is the hypotenuse, the longest side of the triangle. The other two sides are called the legs or catheti of the triangle, special right triangles are right triangles with additional properties that make calculations involving them easier. One of the two most famous is the 3–4–5 right triangle, where 32 +42 =52, in this situation,3,4, and 5 are a Pythagorean triple. The other one is a triangle that has 2 angles that each measure 45 degrees. Triangles that do not have an angle measuring 90° are called oblique triangles, a triangle with all interior angles measuring less than 90° is an acute triangle or acute-angled triangle. If c is the length of the longest side, then a2 + b2 > c2, a triangle with one interior angle measuring more than 90° is an obtuse triangle or obtuse-angled triangle. If c is the length of the longest side, then a2 + b2 < c2, a triangle with an interior angle of 180° is degenerate
25.
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 edition and variation of a book, for example, an e-book, a paperback and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, the method of assigning an ISBN is nation-based and 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 in 1967 based upon the 9-digit Standard Book Numbering created in 1966, the 10-digit ISBN format was developed by the International Organization for Standardization and was published in 1970 as international standard ISO2108. Occasionally, a book may appear without a printed ISBN if it is printed privately or the author does not follow the usual ISBN procedure, however, this can be rectified later. Another identifier, the International Standard Serial Number, identifies periodical publications such as magazines, the ISBN configuration of recognition was generated in 1967 in the United Kingdom by David Whitaker and in 1968 in the US by Emery Koltay. The 10-digit ISBN format was developed by the International Organization for Standardization and was published in 1970 as international standard ISO2108, 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 to an ISBN by prefixing the digit 0. For example, the edition of Mr. J. G. Reeder Returns, published by Hodder in 1965, has SBN340013818 -340 indicating the publisher,01381 their serial number. This can be converted to ISBN 0-340-01381-8, the check digit does not need to be re-calculated, since 1 January 2007, ISBNs have contained 13 digits, a format that is compatible with Bookland European Article Number EAN-13s. An ISBN is assigned to each edition and variation of a book, for example, an ebook, a paperback, and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, a 13-digit ISBN can be separated into its parts, and when this is done it is customary to separate the parts with hyphens or spaces. Separating the parts of a 10-digit ISBN is also done with either hyphens or spaces, figuring out how to correctly separate a given ISBN number is complicated, because most of the parts do not use a fixed number of digits. ISBN issuance is country-specific, in that ISBNs are issued by the ISBN registration agency that is responsible for country or territory regardless of the publication language. Some ISBN registration agencies are based in national libraries or within ministries of culture, in other cases, the ISBN registration service is provided by organisations such as bibliographic data providers that are not government funded. In Canada, ISBNs are issued at no cost with the purpose of encouraging Canadian culture. In the United Kingdom, United States, and some countries, where the service is provided by non-government-funded organisations. Australia, ISBNs are issued by the library services agency Thorpe-Bowker
26.
Catholic Encyclopedia
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The first volume appeared in March 1907 and the last three volumes appeared in 1912, followed by a master index volume in 1914 and later supplementary volumes. It was designed to give its readers full and authoritative information on the cycle of Catholic interests, action. The Catholic Encyclopedia was published by the Robert Appleton Company, a company incorporated at New York in February 1905 for the express purpose of publishing the encyclopedia. The five members of the encyclopedias Editorial Board also served as the directors of the company, in 1912 the companys name was changed to The Encyclopedia Press. Publication of the volumes was the sole business conducted by the company during the projects lifetime. The encyclopedia was designed to serve the Roman Catholic Church, concentrating on information related to the Church and it records the accomplishments of Catholics and others in nearly all intellectual and professional pursuits, including artists, educators, poets and scientists. The volumes came out sequentially the first two in 1907 and the last three in 1912, The editors had their first editorial meeting at the office of The Messenger, on West 16th Street, New York City. The text received a nihil obstat from an official censor, Remy Lafort, on November 1,1908 and this review process was presumably accelerated by the reuse of older authorized publications. A first supplement was published in 1922, a supplement in nine loose-leaf sections was published by The Gilmary Society between 1950 and 1958. In 1912, a special completely illustrated commemorative volume was awarded to patrons who contributed to the start of the enterprise by buying multiple encyclopedia sets early on. The encyclopedia was later updated under the auspices of The Catholic University of America and a 17-volume New Catholic Encyclopedia was first published in 1967, and then in 2002. The Catholic Encyclopedia and its makers states that, The work is entirely new, the editors have insisted that the articles should contain the latest and most accurate information to be obtained from the standard works on each subject. Those who wrote new articles in English include Anthony Maas and Herbert Thurston, under United States copyright law, all works published in the United States before 1923 are in the public domain. Knight founded the website New Advent to house the undertaking, volunteers from the United States, Canada, France, and Brazil helped in the transcription of the original material. The site went online in 1995, and transcription work ended in 1997, in 2007, Catholic Answers published a watermarked version derived from page scans. This version has since replaced with a transcription of the Encyclopedia similar to that found at the New Advent website. The Catholic Answers transcription, however, is a transcription of the original text, whereas the New Advent version at times modernizes certain words. Other scanned copies of the 1913 Encyclopedia are available on Google Books, at the Internet Archive, wikisource also hosts a transcription project backed by the scans hosted at Commons
27.
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, St Andrews was founded between 1410 and 1413, when the Avignon Antipope Benedict XIII issued a papal bull to a small founding group of Augustinian clergy. St Andrews is made up from a variety of institutions, including three constituent colleges and 18 academic schools organised into four faculties, the university occupies historic and modern buildings located throughout the town. The academic year is divided into two terms, Martinmas and Candlemas, in term time, over one-third of the towns population is either a staff member or student of the university. It is ranked as the third best university in the United Kingdom in national league tables, the Times Higher Education World Universities Ranking names St Andrews among the worlds 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 many notable alumni and affiliated faculty, including eminent mathematicians, scientists, theologians, philosophers, and politicians. Six Nobel Laureates are among St Andrews alumni and former staff, a charter of privilege was bestowed upon the society of masters and scholars by the Bishop of St Andrews, Henry Wardlaw, on 28 February 1411. Wardlaw then successfully petitioned the Avignon Pope Benedict XIII to grant the university status by issuing a series of papal bulls. 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. A college of theology and arts called St Johns College was founded in 1418 by Robert of Montrose, St Salvators College was established in 1450, by Bishop James Kennedy. St Leonards College was founded in 1511 by Archbishop Alexander Stewart, St Johns College was refounded by Cardinal James Beaton under the name St Marys College in 1538 for the study of divinity and law. Some university buildings that date from this period are still in use today, such as St Salvators Chapel, St Leonards College Chapel, at this time, the majority of the teaching was of a religious nature and was conducted by clerics associated with the cathedral. During the 17th and 18th centuries, the university had mixed fortunes and was beset by civil. He described it as pining in decay and struggling for life, in the second half of the 19th century, pressure was building upon universities to open up higher education to women. In 1876, the University Senate decided to allow women to receive an education at St Andrews at a roughly equal to the Master of Arts degree that men were able to take at the time. The scheme came to be known as the L. L. A and it required women to pass five subjects at an ordinary level and one at honours level and entitled them to hold a degree from the university. In 1889 the Universities Act made it possible to admit women to St Andrews. Agnes Forbes Blackadder became the first woman to graduate from St Andrews on the level as men in October 1894
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Bibsys
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BIBSYS is an administrative agency set up and organized by the Ministry of Education and Research in Norway. They are a provider, focusing on the exchange, storage and retrieval of data pertaining to research. BIBSYS are collaborating with all Norwegian universities and university colleges as well as research institutions, Bibsys is formally organized as a unit at the Norwegian University of Science and Technology, located in Trondheim, Norway. The board of directors is appointed by Norwegian Ministry of Education, BIBSYS offer researchers, students and others an easy access to library resources by providing the unified search service Oria. no and other library services. They also deliver integrated products for the operation for research. As a DataCite member BIBSYS act as a national DataCite representative in Norway and thereby allow all of Norways higher education, all their products and services are developed in cooperation with their member institutions. The purpose of the project was to automate internal library routines, since 1972 Bibsys has evolved from a library system supplier for two libraries in Trondheim, to developing and operating a national library system for Norwegian research and special libraries. The target group has expanded to include the customers of research and special libraries. BIBSYS is an administrative agency answerable to the Ministry of Education and Research. In addition to BIBSYS Library System, the product consists of BISBYS Ask, BIBSYS Brage, BIBSYS Galleri. All operation of applications and databases is performed centrally by BIBSYS, BIBSYS also offer a range of services, both in connection with their products and separate services independent of the products they supply
29.
Integrated Authority File
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The Integrated Authority File or GND is an international authority file for the organisation of personal names, subject headings and corporate bodies from catalogues. It is used mainly for documentation in libraries and increasingly also by archives, the GND is managed by the German National Library in cooperation with various regional library networks in German-speaking Europe and other partners. The GND falls under the Creative Commons Zero license, the GND specification provides a hierarchy of high-level entities and sub-classes, useful in library classification, and an approach to unambiguous identification of single elements. It also comprises an ontology intended for knowledge representation in the semantic web, available in the RDF format
30.
National Library of the Czech Republic
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The National Library of the Czech Republic is the central library of the Czech Republic. It is directed by the Ministry of Culture, the librarys main building is located in the historical Clementinum building in Prague, where approximately half of its books are kept. The other half of the collection is stored in the district of Hostivař, the National Library is the biggest library in the Czech Republic, in its funds there are around 6 million documents. The library has around 60,000 registered readers, as well as Czech texts, the library also stores older material from Turkey, Iran and India. The library also houses books for Charles University in Prague, the library won international recognition in 2005 as it received the inaugural Jikji Prize from UNESCO via the Memory of the World Programme for its efforts in digitising old texts. The project, which commenced in 1992, involved the digitisation of 1,700 documents in its first 13 years, the most precious medieval manuscripts preserved in the National Library are the Codex Vyssegradensis and the Passional of Abbes Kunigunde. In 2006 the Czech parliament approved funding for the construction of a new building on Letna plain. In March 2007, following a request for tender, Czech architect Jan Kaplický was selected by a jury to undertake the project, later in 2007 the project was delayed following objections regarding its proposed location from government officials including Prague Mayor Pavel Bém and President Václav Klaus. Later in 2008, Minister of Culture Václav Jehlička announced the end of the project, the library was affected by the 2002 European floods, with some documents moved to upper levels to avoid the excess water. Over 4,000 books were removed from the library in July 2011 following flooding in parts of the main building, there was a fire at the library in December 2012, but nobody was injured in the event. List of national and state libraries Official website
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National Library of Australia
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In 2012–2013, the National Library collection comprised 6,496,772 items, and an additional 15,506 metres of manuscript material. In 1901, a Commonwealth Parliamentary Library was established to serve the newly formed Federal Parliament of Australia, from its inception the Commonwealth Parliamentary Library was driven to development of a truly national collection. The present library building was opened in 1968, the building was designed by the architectural firm of Bunning and Madden. The foyer is decorated in marble, with windows by Leonard French. In 2012–2013 the Library collection comprised 6,496,772 items, the Librarys collections of Australiana have developed into the nations single most important resource of materials recording the Australian cultural heritage. Australian writers, editors and illustrators are actively sought and well represented—whether published in Australia or overseas, approximately 92. 1% of the Librarys collection has been catalogued and is discoverable through the online catalogue. The Library has digitized over 174,000 items from its collection and, the Library is a world leader in digital preservation techniques, and maintains an Internet-accessible archive of selected Australian websites called the Pandora Archive. A core Australiana collection is that of John A. Ferguson, the Library has particular collection strengths in the performing arts, including dance. The Librarys considerable collections of general overseas and rare materials, as well as world-class Asian. The print collections are further supported by extensive microform holdings, the Library also maintains the National Reserve Braille Collection. The Library has acquired a number of important Western and Asian language scholarly collections from researchers, williams Collection The Asian Collections are searchable via the National Librarys catalogue. The National Library holds a collection of pictures and manuscripts. The manuscript collection contains about 26 million separate items, covering in excess of 10,492 meters of shelf space, the collection relates predominantly to Australia, but there are also important holdings relating to Papua New Guinea, New Zealand and the Pacific. The collection also holds a number of European and Asian manuscript collections or single items have received as part of formed book collections. Examples are the papers of Alfred Deakin, Sir John Latham, Sir Keith Murdoch, Sir Hans Heysen, Sir John Monash, Vance Palmer and Nettie Palmer, A. D. Hope, Manning Clark, David Williamson, W. M. The Library has also acquired the records of many national non-governmental organisations and they include the records of the Federal Secretariats of the Liberal party, the A. L. P, the Democrats, the R. S. L. Finally, the Library holds about 37,000 reels of microfilm of manuscripts and archival records, mostly acquired overseas and predominantly of Australian, the National Librarys Pictures collection focuses on Australian people, places and events, from European exploration of the South Pacific to contemporary events. Art works and photographs are acquired primarily for their informational value, media represented in the collection include photographs, drawings, watercolours, oils, lithographs, engravings, etchings and sculpture/busts
32.
Virtual International Authority File
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The Virtual International Authority File is an international authority file. It is a joint project of national libraries and operated by the Online Computer Library Center. The project was initiated by the US Library of Congress, the German National Library, the National Library of France joined the project on October 5,2007. The project transitions to a service of the OCLC on April 4,2012, the aim is to link the national authority files to a single virtual authority file. In this file, identical records from the different data sets are linked together, a VIAF record receives a standard data number, contains the primary see and see also records from the original records, and refers to the original authority records. The data are available online and are available for research and data exchange. Reciprocal updating uses the Open Archives Initiative Protocol for Metadata Harvesting protocol, the file numbers are also being added to Wikipedia biographical articles and are incorporated into Wikidata. VIAFs clustering algorithm is run every month, as more data are added from participating libraries, clusters of authority records may coalesce or split, leading to some fluctuation in the VIAF identifier of certain authority records
Chisholm, Hugh, ed. (1911). "Tartaglia, Niccolò". Encyclopædia Britannica. 26 (11th ed.). Cambridge University Press.
Chisholm, Hugh, ed. (1911). "