1.
Book frontispiece
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A frontispiece in books generally refers to a decorative or informative illustration facing a books title page, being the verso opposite the recto title page. While some books depict thematic elements, other books feature the portrait as the frontispiece. In medieval illuminated manuscripts, a miniature showing the book or text being presented was often used as a frontispiece. The word comes from the French frontispice, or the late Latin frontispicium, from the Latin frons, in English, it was originally used as an architectural term, referring to the decorative facade of a building. By then, the English spelling had also morphed, by way of folk etymology, book design Prints & People, A Social History of Printed Pictures, an exhibition catalog from The Metropolitan Museum of Art, which contains material on book frontispieces
2.
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 divided into the Archaic period, Classical period. It is antedated in the second millennium BC by Mycenaean Greek, the language of the Hellenistic phase is known as Koine. Koine is regarded as a historical stage of its own, although in its earliest form it closely resembled Attic Greek. Prior to the Koine period, Greek of the classic and earlier periods included several regional dialects, Ancient Greek was the language of Homer and of fifth-century Athenian historians, playwrights, and philosophers. It has contributed many words to English vocabulary and has been a subject of study in educational institutions of the Western world since the Renaissance. This article primarily contains information about the Epic and Classical phases of the language, Ancient Greek was a pluricentric language, divided into many dialects. The main dialect groups are Attic and Ionic, Aeolic, Arcadocypriot, some dialects are found in standardized literary forms used in literature, while others are attested only in inscriptions. There are also several historical forms, homeric Greek is a literary form of Archaic Greek used in the epic poems, the Iliad and Odyssey, and in later poems by other authors. Homeric Greek had significant differences in grammar and pronunciation from Classical Attic, the origins, early form and development of the Hellenic language family are not well understood because of a lack of contemporaneous evidence. Several theories exist about what Hellenic dialect groups may have existed between the divergence of early Greek-like speech from the common Proto-Indo-European language and the Classical period and they have the same general outline, but differ in some of the detail. The invasion would not be Dorian unless the invaders had some relationship to the historical Dorians. The invasion is known to have displaced population to the later Attic-Ionic regions, the Greeks of this period believed there were three major divisions of all Greek people—Dorians, Aeolians, and Ionians, each with their own defining and distinctive dialects. Often non-west is called East Greek, Arcadocypriot apparently descended more closely from the Mycenaean Greek of the Bronze Age. Boeotian had come under a strong Northwest Greek influence, and can in some respects be considered a transitional dialect, thessalian likewise had come under Northwest Greek influence, though to a lesser degree. Most of the dialect sub-groups listed above had further subdivisions, generally equivalent to a city-state and its surrounding territory, Doric notably had several intermediate divisions as well, into Island Doric, Southern Peloponnesus Doric, and Northern Peloponnesus Doric. The Lesbian dialect was Aeolic Greek and this dialect slowly replaced most of the older dialects, although Doric dialect has survived in the Tsakonian language, which is spoken in the region of modern Sparta. Doric has also passed down its aorist terminations into most verbs of Demotic Greek, by about the 6th century AD, the Koine had slowly metamorphosized into Medieval Greek
3.
Euclidean geometry
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Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry, the Elements. Euclids method consists in assuming a set of intuitively appealing axioms. Although many of Euclids results had been stated by earlier mathematicians, Euclid was the first to show how these propositions could fit into a comprehensive deductive and logical system. The Elements begins with plane geometry, still taught in school as the first axiomatic system. It goes on to the geometry of three dimensions. Much of the Elements states results of what are now called algebra and number theory, for more than two thousand years, the adjective Euclidean was unnecessary because no other sort of geometry had been conceived. Euclids axioms seemed so obvious that any theorem proved from them was deemed true in an absolute, often metaphysical. Today, however, many other self-consistent non-Euclidean geometries are known, Euclidean geometry is an example of synthetic geometry, in that it proceeds logically from axioms to propositions without the use of coordinates. This is in contrast to analytic geometry, which uses coordinates, the Elements is mainly a systematization of earlier knowledge of geometry. Its improvement over earlier treatments was recognized, with the result that there was little interest in preserving the earlier ones. There are 13 total books in the Elements, Books I–IV, Books V and VII–X deal with number theory, with numbers treated geometrically via their representation as line segments with various lengths. Notions such as numbers and rational and irrational numbers are introduced. The infinitude of prime numbers is proved, a typical result is the 1,3 ratio between the volume of a cone and a cylinder with the same height and base. Euclidean geometry is a system, in which all theorems are derived from a small number of axioms. To produce a straight line continuously in a straight line. To describe a circle with any centre and distance and that all right angles are equal to one another. Although Euclids statement of the only explicitly asserts the existence of the constructions. The Elements also include the five common notions, Things that are equal to the same thing are also equal to one another
4.
Number theory
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Number theory or, in older usage, arithmetic is a branch of pure mathematics devoted primarily to the study of the integers. It is sometimes called The Queen of Mathematics because of its place in the discipline. Number theorists study prime numbers as well as the properties of objects out of integers or defined as generalizations of the integers. Integers can be considered either in themselves or as solutions to equations, questions in number theory are often best understood through the study of analytical objects that encode properties of the integers, primes or other number-theoretic objects in some fashion. One may also study real numbers in relation to rational numbers, the older term for number theory is arithmetic. By the early century, it had been superseded by number theory. The use of the arithmetic for number theory regained some ground in the second half of the 20th century. In particular, arithmetical is preferred as an adjective to number-theoretic. The first historical find of a nature is a fragment of a table. The triples are too many and too large to have been obtained by brute force, the heading over the first column reads, The takiltum of the diagonal which has been subtracted such that the width. The tables layout suggests that it was constructed by means of what amounts, in language, to the identity 2 +1 =2. If some other method was used, the triples were first constructed and then reordered by c / a, presumably for use as a table. It is not known what these applications may have been, or whether there could have any, Babylonian astronomy, for example. It has been suggested instead that the table was a source of examples for school problems. While Babylonian number theory—or what survives of Babylonian mathematics that can be called thus—consists of this single, striking fragment, late Neoplatonic sources state that Pythagoras learned mathematics from the Babylonians. Much earlier sources state that Thales and Pythagoras traveled and studied in Egypt, Euclid IX 21—34 is very probably Pythagorean, it is very simple material, but it is all that is needed to prove that 2 is irrational. Pythagorean mystics gave great importance to the odd and the even, the discovery that 2 is irrational is credited to the early Pythagoreans. This forced a distinction between numbers, on the one hand, and lengths and proportions, on the other hand, the Pythagorean tradition spoke also of so-called polygonal or figurate numbers
5.
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
6.
Greek mathematics
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Greek mathematics, as the term is used in this article, is the mathematics written in Greek, developed from the 7th century BC to the 4th century AD around the shores of the Eastern Mediterranean. Greek mathematicians lived in cities spread over the entire Eastern Mediterranean from Italy to North Africa but were united by culture, 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 study of mathematics for its own sake and the use of generalized mathematical theories and proofs is the key difference between Greek mathematics and those of preceding civilizations. 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 possessed writing and were capable of advanced engineering, including four-story palaces with drainage and beehive tombs, 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. Little is known about the life and work of Thales, so little indeed that his date of birth and death are estimated from the eclipse of 585 BC, despite this, it is generally agreed that Thales is the first of the seven wise men of Greece. The two earliest mathematical theorems, Thales theorem and Intercept theorem are attributed to Thales. The former, which states that an angle inscribed in a semicircle is a right angle and it is for this reason that Thales is often hailed as the father of the deductive organization of mathematics and as the first 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, Pythagoras established an order called the Pythagoreans, which held knowledge and property in common and hence all of the discoveries by individual Pythagoreans were attributed to the order. And since in antiquity it was customary to give all credit to the master, aristotle for one refused to attribute anything specifically to Pythagoras as an individual and only discussed the work of the Pythagoreans as a group. One of the most important characteristics of the Pythagorean order was that it maintained that the pursuit of philosophical and mathematical studies was a basis for the conduct of life. Indeed, the philosophy and mathematics are said to have been coined by Pythagoras. From this love of knowledge came many achievements and it has been customarily said that the Pythagoreans discovered most of the material in the first two books of Euclids Elements. The reason it is not clear exactly what either Thales or Pythagoras actually did is that almost no documentation has survived. The only evidence comes from traditions recorded in such as Proclus’ commentary on Euclid written centuries later. Some of these works, such as Aristotle’s commentary on the Pythagoreans, are themselves only known from a few surviving fragments
7.
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
8.
Alexandria
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Alexandria is the second largest city and a major economic centre in Egypt, extending about 32 km along the coast of the Mediterranean Sea in the north central part of the country. Its low elevation on the Nile delta makes it vulnerable to rising sea levels. Alexandria is Egypts largest seaport, serving approximately 80% of Egypts imports and exports and it is an important industrial center because of its natural gas and oil pipelines from Suez. Alexandria is also an important tourist destination, Alexandria was founded around a small Ancient Egyptian town c.331 BC by Alexander the Great. Alexandria was the second most powerful city of the ancient world after Rome, Alexandria is believed to have been founded by Alexander the Great in April 331 BC as Ἀλεξάνδρεια. Alexanders chief architect for the project was Dinocrates, Alexandria was intended to supersede Naucratis as a Hellenistic center in Egypt, and to be the link between Greece and the rich Nile valley. The city and its museum attracted many of the greatest scholars, including Greeks, Jews, the city was later plundered and lost its significance. Just east of Alexandria, there was in ancient times marshland, as early as the 7th century BC, there existed important port cities of Canopus and Heracleion. The latter was rediscovered under water. An Egyptian city, Rhakotis, already existed on the shore also and it continued to exist as the Egyptian quarter of the city. A few months after the foundation, Alexander left Egypt and never returned to his city, after Alexanders departure, his viceroy, Cleomenes, continued the expansion. Although Cleomenes was mainly in charge of overseeing Alexandrias continuous development, the Heptastadion, inheriting the trade of ruined Tyre and becoming the center of the new commerce between Europe and the Arabian and Indian East, the city grew in less than a generation to be larger than Carthage. In a century, Alexandria had become the largest city in the world and and it became Egypts main Greek city, with Greek people from diverse backgrounds. Alexandria was not only a center of Hellenism, but was home to the largest urban Jewish community in the world. The Septuagint, a Greek version of the Tanakh, was produced there, in AD115, large parts of Alexandria were destroyed during the Kitos War, which gave Hadrian and his architect, Decriannus, an opportunity to rebuild it. On 21 July 365, Alexandria was devastated by a tsunami, the Islamic prophet, Muhammads first interaction with the people of Egypt occurred in 628, during the Expedition of Zaid ibn Haritha. He sent Hatib bin Abi Baltaeh with a letter to the king of Egypt and Alexandria called Muqawqis In the letter Muhammad said, I invite you to accept Islam, Allah the sublime, shall reward you doubly. But if you refuse to do so, you bear the burden of the transgression of all the Copts
9.
Ptolemaic Kingdom
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The Ptolemaic Kingdom was a Hellenistic kingdom based in Egypt. Alexandria became the city and a major center of Greek culture. To gain recognition by the native Egyptian populace, they named themselves the successors to the Pharaohs, the later Ptolemies took on Egyptian traditions by marrying their siblings, had themselves portrayed on public monuments in Egyptian style and dress, and participated in Egyptian religious life. The Ptolemies had to fight native rebellions and were involved in foreign and civil wars led to the decline of the kingdom. Hellenistic culture continued to thrive in Egypt throughout the Roman and Byzantine periods until the Muslim conquest. The era of Ptolemaic reign in Egypt is one of the most well documented periods of the Hellenistic Era. In 332 BC, Alexander the Great, King of Macedon invaded the Achaemenid satrapy of Egypt and he visited Memphis, and traveled to the oracle of Amun at the Oasis of Siwa. The oracle declared him to be the son of Amun, the wealth of Egypt could now be harnessed for Alexanders conquest of the rest of the Persian Empire. Early in 331 BC he was ready to depart, and led his forces away to Phoenicia and he left Cleomenes as the ruling nomarch to control Egypt in his absence. Following Alexanders death in Babylon in 323 BC, a crisis erupted among his generals. Perdiccas appointed Ptolemy, one of Alexanders closest companions, to be satrap of Egypt, Ptolemy ruled Egypt from 323 BC, nominally in the name of the joint kings Philip III and Alexander IV. However, as Alexander the Greats empire disintegrated, Ptolemy soon established himself as ruler in his own right, Ptolemy successfully defended Egypt against an invasion by Perdiccas in 321 BC, and consolidated his position in Egypt and the surrounding areas during the Wars of the Diadochi. In 305 BC, Ptolemy took the title of King, as Ptolemy I Soter, he founded the Ptolemaic dynasty that was to rule Egypt for nearly 300 years. All the male rulers of the dynasty took the name Ptolemy, while princesses and queens preferred the names Cleopatra, Arsinoe and Berenice. Because the Ptolemaic kings adopted the Egyptian custom of marrying their sisters, many of the kings ruled jointly with their spouses and this custom made Ptolemaic politics confusingly incestuous, and the later Ptolemies were increasingly feeble. The only Ptolemaic Queens to officially rule on their own were Berenice III, Cleopatra V did co-rule, but it was with another female, Berenice IV. Cleopatra VII officially co-ruled with Ptolemy XIII Theos Philopator, Ptolemy XIV, and Ptolemy XV, upper Egypt, farthest from the centre of government, was less immediately affected, even though Ptolemy I established the Greek colony of Ptolemais Hermiou to be its capital. But within a century Greek influence had spread through the country, nevertheless, the Greeks always remained a privileged minority in Ptolemaic Egypt
10.
Theorem
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In mathematics, a theorem is a statement that has been proved on the basis of previously established statements, such as other theorems, and generally accepted statements, such as axioms. A theorem is a consequence of the axioms. The proof of a theorem is a logical argument for the theorem statement given in accord with the rules of a deductive system. The proof of a theorem is interpreted as justification of the truth of the theorem statement. In light of the requirement that theorems be proved, the concept of a theorem is fundamentally deductive, in contrast to the notion of a scientific law, many mathematical theorems are conditional statements. In this case, the proof deduces the conclusion from conditions called hypotheses or premises, however, the conditional could be interpreted differently in certain deductive systems, depending on the meanings assigned to the derivation rules and the conditional symbol. Although they can be written in a symbolic form, for example, within the propositional calculus. 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 and these subjective judgments vary not only from person to person, but also with time, for example, as a proof is simplified or better understood, a theorem that was once difficult may become trivial. On the other hand, a theorem may be simply stated. Fermats Last Theorem is a particularly well-known example of such a theorem, logically, many theorems are of the form of an indicative conditional, if A, then B. Such a theorem does not assert B, only that B is a consequence of A. In this case A is called the hypothesis of the theorem and B the conclusion. The theorem If n is an natural number then n/2 is a natural number is a typical example in which the hypothesis is n is an even natural number. To be proved, a theorem must be expressible as a precise, nevertheless, theorems are usually expressed in natural language rather than in a completely symbolic form, with the intention that the reader can produce a formal statement from the informal one. It is common in mathematics to choose a number of hypotheses within a given language and these hypotheses form the foundational basis of the theory and are called axioms or postulates. The field of known as proof theory studies formal languages, axioms. Some theorems are trivial, in the sense that they follow from definitions, axioms, a theorem might be simple to state and yet be deep
11.
Compass-and-straightedge construction
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The idealized ruler, known as a straightedge, is assumed to be infinite in length, and has no markings on it and only one edge. The compass is assumed to collapse when lifted from the page, more formally, the only permissible constructions are those granted by Euclids first three postulates. It turns out to be the case that every point constructible using straightedge, the ancient Greek mathematicians first conceived compass-and-straightedge constructions, and a number of ancient problems in plane geometry impose this restriction. The ancient Greeks developed many constructions, but in cases were unable to do so. Gauss showed that some polygons are constructible but that most are not, some of the most famous straightedge-and-compass problems were proven impossible by Pierre Wantzel in 1837, using the mathematical theory of fields. In spite of existing proofs of impossibility, some persist in trying to solve these problems, in terms of algebra, a length is constructible if and only if it represents a constructible number, and an angle is constructible if and only if its cosine is a constructible number. A number is constructible if and only if it can be using the four basic arithmetic operations. Circles can only be starting from two given points, the centre and a point on the circle. The compass may or may not collapse when its not drawing a circle, the straightedge is infinitely long, but it has no markings on it and has only one straight edge, unlike ordinary rulers. It can only be used to draw a segment between two points or to extend an existing segment. The modern compass generally does not collapse and several modern constructions use this feature and it would appear that the modern compass is a more powerful instrument than the ancient collapsing compass. However, by Proposition 2 of Book 1 of Euclids Elements, although the proposition is correct, its proofs have a long and checkered history. Eyeballing it and getting close does not count as a solution and that is, it must have a finite number of steps, and not be the limit of ever closer approximations. One of the purposes of Greek mathematics was to find exact constructions for various lengths, for example. The Greeks could not find constructions for these three problems, among others, Squaring the circle, Drawing a square the same area as a given circle, doubling the cube, Drawing a cube with twice the volume of a given cube. Trisecting the angle, Dividing a given angle into three smaller angles all of the same size, for 2000 years people tried to find constructions within the limits set above, and failed. All three have now been proven under mathematical rules to be generally impossible, the ancient Greek mathematicians first attempted compass-and-straightedge constructions, and they discovered how to construct sums, differences, products, ratios, and square roots of given lengths. They could also construct half of an angle, a square whose area is twice that of another square, a square having the same area as a given polygon
12.
Mathematical proof
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In mathematics, a proof is an inferential argument for a mathematical statement. In the argument, other previously established statements, such as theorems, in principle, a proof can be traced back to self-evident or assumed statements, known as axioms, along with accepted rules of inference. Axioms may be treated as conditions that must be met before the statement applies, Proofs are examples of exhaustive deductive reasoning or inductive reasoning and are distinguished from empirical arguments or non-exhaustive inductive reasoning. A proof must demonstrate that a statement is true, rather than enumerate many confirmatory cases. An unproved proposition that is believed to be true is known as a conjecture, Proofs employ logic but usually include some amount of natural language which usually admits some ambiguity. In fact, the vast majority of proofs in mathematics can be considered as applications of rigorous informal logic. Purely formal proofs, written in language instead of natural language, are considered in proof theory. The distinction between formal and informal proofs has led to examination of current and historical mathematical practice, quasi-empiricism in mathematics. The philosophy of mathematics is concerned with the role of language and logic in proofs, the word proof comes from the Latin probare meaning to test. Related modern words are the English probe, probation, and probability, the Spanish probar, Italian provare, the early use of probity was in the presentation of legal evidence. A person of authority, such as a nobleman, was said to have probity, whereby the evidence was by his relative authority, plausibility arguments using heuristic devices such as pictures and analogies preceded strict mathematical proof. It is likely that the idea of demonstrating a conclusion first arose in connection with geometry, the development of mathematical proof is primarily the product of ancient Greek mathematics, and one of the greatest achievements thereof. Thales proved some theorems in geometry, eudoxus and Theaetetus formulated theorems but did not prove them. Aristotle said definitions should describe the concept being defined in terms of other concepts already known and his book, the Elements, was read by anyone who was considered educated in the West until the middle of the 20th century. Further advances took place in medieval Islamic mathematics, while earlier Greek proofs were largely geometric demonstrations, the development of arithmetic and algebra by Islamic mathematicians allowed more general proofs that no longer depended on geometry. In the 10th century CE, the Iraqi mathematician Al-Hashimi provided general proofs for numbers as he considered multiplication, division and he used this method to provide a proof of the existence of irrational numbers. An inductive proof for arithmetic sequences was introduced in the Al-Fakhri by Al-Karaji, alhazen also developed the method of proof by contradiction, as the first attempt at proving the Euclidean parallel postulate. Modern proof theory treats proofs as inductively defined data structures, there is no longer an assumption that axioms are true in any sense, this allows for parallel mathematical theories built on alternate sets of axioms
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Logic
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Logic, originally meaning the word or what is spoken, is generally held to consist of the systematic study of the form of arguments. A valid argument is one where there is a relation of logical support between the assumptions of the argument and its conclusion. Historically, logic has been studied in philosophy and mathematics, and recently logic has been studied in science, linguistics, psychology. The concept of form is central to logic. The validity of an argument is determined by its logical form, traditional Aristotelian syllogistic logic and modern symbolic logic are examples of formal logic. Informal logic is the study of natural language arguments, the study of fallacies is an important branch of informal logic. Since much informal argument is not strictly speaking deductive, on some conceptions of logic, formal logic is the study of inference with purely formal content. An inference possesses a purely formal content if it can be expressed as an application of a wholly abstract rule, that is. The works of Aristotle contain the earliest known study of logic. Modern formal logic follows and expands on Aristotle, in many definitions of logic, logical inference and inference with purely formal content are the same. This does not render the notion of informal logic vacuous, because no formal logic captures all of the nuances of natural language, Symbolic logic is the study of symbolic abstractions that capture the formal features of logical inference. Symbolic logic is divided into two main branches, propositional logic and predicate logic. Mathematical logic is an extension of logic into other areas, in particular to the study of model theory, proof theory, set theory. Logic is generally considered formal when it analyzes and represents the form of any valid argument type, the form of an argument is displayed by representing its sentences in the formal grammar and symbolism of a logical language to make its content usable in formal inference. Simply put, formalising simply means translating English sentences into the language of logic and this is called showing the logical form of the argument. It is necessary because indicative sentences of ordinary language show a variety of form. Second, certain parts of the sentence must be replaced with schematic letters, thus, for example, the expression all Ps are Qs shows the logical form common to the sentences all men are mortals, all cats are carnivores, all Greeks are philosophers, and so on. The schema can further be condensed into the formula A, where the letter A indicates the judgement all - are -, the importance of form was recognised from ancient times
14.
Science
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Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe. The formal sciences are often excluded as they do not depend on empirical observations, disciplines which use science, like engineering and medicine, may also be considered to be applied sciences. However, during the Islamic Golden Age foundations for the method were laid by Ibn al-Haytham in his Book of Optics. In the 17th and 18th centuries, scientists increasingly sought to formulate knowledge in terms of physical laws, over the course of the 19th century, the word science became increasingly associated with the scientific method itself as a disciplined way to study the natural world. It was during this time that scientific disciplines such as biology, chemistry, Science in a broad sense existed before the modern era and in many historical civilizations. Modern science is distinct in its approach and successful in its results, Science in its original sense was a word for a type of knowledge rather than a specialized word for the pursuit of such knowledge. In particular, it was the type of knowledge which people can communicate to each other, for example, knowledge about the working of natural things was gathered long before recorded history and led to the development of complex abstract thought. This is shown by the construction of calendars, techniques for making poisonous plants edible. For this reason, it is claimed these men were the first philosophers in the strict sense and they were mainly speculators or theorists, particularly interested in astronomy. In contrast, trying to use knowledge of nature to imitate nature was seen by scientists as a more appropriate interest for lower class artisans. A clear-cut distinction between formal and empirical science was made by the pre-Socratic philosopher Parmenides, although his work Peri Physeos is a poem, it may be viewed as an epistemological essay on method in natural science. Parmenides ἐὸν may refer to a system or calculus which can describe nature more precisely than natural languages. Physis may be identical to ἐὸν and he criticized the older type of study of physics as too purely speculative and lacking in self-criticism. He was particularly concerned that some of the early physicists treated nature as if it could be assumed that it had no intelligent order, explaining things merely in terms of motion and matter. The study of things had been the realm of mythology and tradition, however. Aristotle later created a less controversial systematic programme of Socratic philosophy which was teleological and he rejected many of the conclusions of earlier scientists. For example, in his physics, the sun goes around the earth, each thing has a formal cause and final cause and a role in the rational cosmic order. Motion and change is described as the actualization of potentials already in things, while the Socratics insisted that philosophy should be used to consider the practical question of the best way to live for a human being, they did not argue for any other types of applied science
15.
Movable type
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Movable type is the system and technology of printing and typography that uses movable components to reproduce the elements of a document usually on the medium of paper. In 1377, currently the oldest extant movable metal print book, the diffusion of both movable-type systems was, however, limited. Around 1450 Johannes Gutenberg made another version of a metal printing press in Europe, along with innovations in casting the type based on a matrix. The more limited number of characters needed for European languages was an important factor, Gutenberg was the first to create his type pieces from an alloy of lead, tin, and antimony—and these materials remained standard for 550 years. For alphabetic scripts, movable-type page setting was quicker than woodblock printing, the metal type pieces were more durable and the lettering was more uniform, leading to typography and fonts. The high quality and relatively low price of the Gutenberg Bible established the superiority of movable type in Europe, the printing press may be regarded as one of the key factors fostering the Renaissance and due to its effectiveness, its use spread around the globe. The 19th-century invention of hot metal typesetting and its successors caused movable type to decline in the 20th century, the technique of imprinting multiple copies of symbols or glyphs with a master type punch made of hard metal first developed around 3000 BC in ancient Sumer. These metal punch types can be seen as precursors of the letter punches adapted in later millennia to printing with metal type. Cylinder seals were used in Mesopotamia to create an impression on a surface by rolling the seal on wet clay and they were used to sign documents and mark objects as the owners property. By 650 BC the ancient Greeks were using larger diameter punches to imprint small page images onto coins and tokens, seals and stamps may have been precursors to movable type. A few authors even view the disc as technically meeting all definitional criteria to represent an early incidence of movable-type printing, recently it has been alleged by Jerome Eisenberg that the disk is a forgery. The Prüfening dedicatory inscription is medieval example of movable type stamps being used, yet copying books by hand was still labour-consuming. Not until the Xiping Era, towards the end of the Eastern Han Dynasty did sealing print and it was soon used for printing designs on fabrics, and later for printing texts. Woodblock printing, invented by about the 8th century during the Tang Dynasty, then carvers cut away the parts of the board that were not part of the character, so that the characters were cut in relief, completely differently from those cut intaglio. When printing, the characters would have some ink spread on them. With workers’ hands moving on the back of paper gently, characters would be printed on the paper, by the Song Dynasty, woodblock printing came to its heyday. Although woodblock printing played a role in spreading culture, there remained some apparent drawbacks. Firstly, carving the printing plate required considerable time, labour and materials, secondly, it was not convenient to store these plates, with woodblock printing, one printing plate could be used for tens of hundreds of books, playing a magnificent role in spreading culture
16.
Bible
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The Bible is a collection of sacred texts or scriptures that Jews and Christians consider to be a product of divine inspiration and a record of the relationship between God and humans. Many different authors contributed to the Bible, what is regarded as canonical text differs depending on traditions and groups, a number of Bible canons have evolved, with overlapping and diverging contents. The Christian Old Testament overlaps with the Hebrew Bible and the Greek Septuagint, the New Testament is a collection of writings by early Christians, believed to be mostly Jewish disciples of Christ, written in first-century Koine Greek. These early Christian Greek writings consist of narratives, letters, among Christian denominations there is some disagreement about the contents of the canon, primarily the Apocrypha, a list of works that are regarded with varying levels of respect. Attitudes towards the Bible also differ amongst Christian groups and this concept arose during the Protestant Reformation, and many denominations today support the use of the Bible as the only source of Christian teaching. With estimated total sales of over 5 billion copies, the Bible is widely considered to be the book of all time. It has estimated sales of 100 million copies, and has been a major influence on literature and history, especially in the West. The English word Bible is from the Latin biblia, from the word in Medieval Latin and Late Latin. Medieval Latin biblia is short for biblia sacra holy book, while biblia in Greek and it gradually came to be regarded as a feminine singular noun in medieval Latin, and so the word was loaned as a singular into the vernaculars of Western Europe. Latin biblia sacra holy books translates Greek τὰ βιβλία τὰ ἅγια ta biblia ta hagia, the word βιβλίον itself had the literal meaning of paper or scroll and came to be used as the ordinary word for book. It is the diminutive of βύβλος byblos, Egyptian papyrus, possibly so called from the name of the Phoenician sea port Byblos from whence Egyptian papyrus was exported to Greece, the Greek ta biblia was an expression Hellenistic Jews used to describe their sacred books. Christian use of the term can be traced to c.223 CE, bruce notes that Chrysostom appears to be the first writer to use the Greek phrase ta biblia to describe both the Old and New Testaments together. The division of the Hebrew Bible into verses is based on the sof passuk cantillation mark used by the 10th-century Masoretes to record the verse divisions used in oral traditions. The oldest extant copy of a complete Bible is an early 4th-century parchment book preserved in the Vatican Library, the oldest copy of the Tanakh in Hebrew and Aramaic dates from the 10th century CE. The oldest copy of a complete Latin Bible is the Codex Amiatinus and he states that it is not a magical book, nor was it literally written by God and passed to mankind. In Christian Bibles, the New Testament Gospels were derived from traditions in the second half of the first century CE. Riches says that, Scholars have attempted to reconstruct something of the history of the oral traditions behind the Gospels, the period of transmission is short, less than 40 years passed between the death of Jesus and the writing of Marks Gospel. This means that there was time for oral traditions to assume fixed form
17.
Oxyrhynchus Papyri
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The manuscripts date from the 1st to as late as the 7th century AD. They include thousands of Greek and Latin documents, letters and literary works and they also include a few vellum manuscripts, and more recent Arabic manuscripts on paper. The Oxyrhynchus Papyri are currently housed in many institutions all over the world, a substantial number are housed in the Ashmolean Museum at Oxford University. Although the initial hope of finding many of the lost literary works of antiquity at Oxyrhynchus was not realized and these include poems of Pindar, fragments of Sappho and Alcaeus, along with larger pieces of Alcman, Ibycus, and Corinna. There were also remains of the Hypsipyle of Euripides, fragments of the comedies of Menander. Also found were the oldest and most complete diagrams from Euclids Elements, another important find was the historical work known as the Hellenica Oxyrhynchia, whose author is unknown but may be Ephorus or, as many currently think, Cratippus. A life of Euripides by Satyrus the Peripatetic was also unearthed, Menanders plays found in fragments at Oxyrhynchus include Misoumenos, Dis Exapaton, Epitrepontes, Karchedonios, Dyskolos and Kolax. The works found at Oxyrhynchus have greatly raised Menanders status among classicists, there is an on-line table of contents briefly listing the type of contents of each papyrus or fragment. Among the Christian texts found at Oxyrhynchus, were fragments of early non-canonical Gospels, Oxyrhynchus 840, there are many parts of other canonical books as well as many early Christian hymns, prayers, and letters also found among them. All manuscripts classified as theological in the Oxyrhynchus Papyri are listed below, a few manuscripts that belong to multiple genres, or genres that are inconsistently treated in the volumes of the Oxyrhynchus Papyri, are also included. In each volume that contains theological manuscripts, they are listed first, the original Hebrew Bible was translated into Greek between the 3rd and 1st centuries BC. This translation is called the Septuagint, because there is a tradition that seventy Jewish scribes compiled it in Alexandria and it was quoted in the New Testament and is found bound together with the New Testament in the 4th and 5th century Greek uncial codices Sinaiticus, Alexandrinus and Vaticanus. The Septuagint included books, called the Apocrypha or Deuterocanonical by Christians, portions of Old Testament books of undisputed authority found among the Oxyrhynchus Papyri are listed in this section. The first number is the volume of the Oxyrhynchus Papyri in which the manuscript is published, the second number is the overall publication sequence number in Oxyrhynchus Papyri. Standard abbreviated citation of the Oxyrhynchus Papyri is, P. Oxy, <volume in Roman numerals> <publication sequence number>. Context will always make clear whether volume 70 of the Oxyrhynchus Papyri or the Septuagint is intended, VIII1073 is an Old Latin version of Genesis, other manuscripts are probably copies of the Septuagint. Dates are estimated to the nearest 50 year increment, content is given to the nearest verse where known. This name designates several, unique writings or different versions of pre-existing writings found in the canon of the Jewish scriptures
18.
Adelard of Bath
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Adelard of Bath was a 12th-century English natural philosopher. He is known as one of the first to introduce the Hindu–Arabic numeral system to Europe and he stands at the convergence of three intellectual schools, the traditional learning of French schools, the Greek culture of Southern Italy, and the Arabic science of the East. Given the period when he was alive, Adelard’s biography is incomplete in places and leaves some aspects open to interpretation, as a result, much of what is ascribed to Adelard is a product of his own testimony. As his name suggests, he was born in the Roman English city of Bath, despite his extensive travels, by the end of his life he had returned to Bath, where he died. Scholars are hesitant to ascribe definitive parents to the philosopher but Fastred and his name is of Anglo-Saxon origin, which would have placed him in the subordinate class, status wise, in 11th-century England. It is believed that he left England toward the end of the 11th century for Tours, likely on the advice of Bishop John de Villula, during his studies in Tours, an anonymous wise man of Tours inspired Adelard with his interest in astronomy to study the science. Adelard later taught for a time at Laon, leaving Laon for travel no later than 1109, after leaving Laon, he travelled to Southern Italy and Sicily no later than 1116. Adelard also travelled throughout the lands of the Crusades, Greece, West Asia, Sicily, Spain, Tarsus, Antioch. The time spent in these areas would help explain his fascination with mathematics, by 1126, Adelard returned to the West with the intention of spreading the knowledge he had gained about Arab astronomy and geometry to the Latin world. One aspect of particular interest with respect to Adelard, his teachings, and this time of remarkable transition marked an opportunity for someone to gain valuable influence over the evolution of human history. Again, given the 11th-century time period that Adelard was alive, in the absence of a printing press and given the weak public literacy rate, books were rare items in medieval Europe—generally held only by royal courts or Catholic monastic communities. Fittingly, Adelard studied with monks at the Benedictine Monastery at Bath Cathedral, among Adelard of Baths original works is a trio of dialogues, written to mimic the Platonic style, or correspondences with his nephew. The earliest of these is De Eodem et Diverso and it is written in the style of a protreptic, or an exhortation to the study of philosophy. The work is modelled on Boethius Consolation of Philosophy, evident in Adelards vocabulary and it is believed to have been written near Tours after he had already travelled, though there is no indication that he had travelled past Southern Italy and Sicily at the time of writing. The work takes the form of a dialogue between Philocosmia, who advocates worldly pleasures, and Philosophia, whose defence of scholarship leads into a summary of the seven liberal arts. Underlining the entire work is the contrast between Philocosmias res, and Philosophias verba, each section of the liberal arts is divided into two parts. The second of this trio, and arguably Adelards most significant contribution, was his Questiones Naturales or Questions on Natural Science. It can be dated between 1107 and 1133 as, in the text, Adelard himself mentions that seven years have passed since his lecturing in schools at Laon and he chooses to present this work as a forum for Arabic learning, referring often to his experiences in Antioch
19.
Pythagoras
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Pythagoras of Samos was an Ionian Greek philosopher, mathematician, and the putative founder of the movement called Pythagoreanism. Most of the information about Pythagoras was written centuries after he lived. He was born on the island of Samos, and travelled, visiting Egypt and Greece, around 530 BC, he moved to Croton, in Magna Graecia, and there established some kind of school or guild. In 520 BC, he returned to Samos, Pythagoras made influential contributions to philosophy and religion in the late 6th century BC. He is often revered as a mathematician and scientist and 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 colleagues, some accounts mention that the philosophy associated with Pythagoras was related to mathematics and that numbers were important. It was said that he was the first man to himself a philosopher, or lover of wisdom, and Pythagorean ideas exercised a marked influence on Plato. Burkert states that Aristoxenus and Dicaearchus are the most important accounts, Aristotle had written a separate work On the Pythagoreans, which is no longer extant. However, the Protrepticus possibly contains parts of On the Pythagoreans and his disciples Dicaearchus, Aristoxenus, and Heraclides Ponticus had written on the same subject. These writers, late as they are, were among the best sources from whom Porphyry and Iamblichus drew, while adding some legendary accounts. Herodotus, Isocrates, and other writers agree that Pythagoras was the son of Mnesarchus and born on the Greek island of Samos. His father is said to have been a gem-engraver or a wealthy merchant, a late source gives his mothers name as Pythais. As to the date of his birth, Aristoxenus stated that Pythagoras left Samos in the reign of Polycrates, at the age of 40, around 530 BC he arrived in the Greek colony of Croton in what was then Magna Graecia. There he founded his own school the members of which he engaged to a disciplined. He furthermore aquired some political influence, on Greeks and non-Greeks of the region, following a conflict with the neighbouring colony of Sybaris, internal discord drove most of the Pythagoreans out of Croton. Pythagoras left the city before the outbreak of civil unrest and moved to Metapontum, after his death, his house was transformed into a sanctuary of Demeter, out of veneration for the philosopher, by the local population. In ancient sources there was disagreement and inconsistency about the late life of Pythagoras. His tomb was shown at Metapontum in the time of Cicero, according to Walter Burkert, Most obvious is the contradiction between Aristoxenus and Dicaearchus, regarding the catastrophe that overwhelmed the Pythagorean society
20.
Hippocrates of Chios
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Hippocrates of Chios was an ancient Greek mathematician, geometer, and 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 mathematician and astronomer Oenopides of Chios. The reductio ad absurdum argument has been traced to him, only a single, and famous, fragment of Hippocrates Elements is existent, embedded in the work of Simplicius. In this fragment the area is calculated of some so-called Hippocratic lunes — see Lune of Hippocrates. This was part of a programme to achieve the quadrature of the circle. 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, the number π is the ratio of the circumference to the diameter of a circle, and also the ratio of the area to the square of the radius. In the century after Hippocrates at least four other mathematicians wrote their own Elements, steadily improving terminology, in this way Hippocrates pioneering work laid the foundation for Euclids Elements that was to remain the standard geometry textbook for many centuries. Hippocrates is believed to have originated the use of letters to refer to the points and figures in a proposition, e. g. triangle ABC for a triangle with vertices at points A, B. Two other contributions by Hippocrates in the field of mathematics are noteworthy and he found a way to tackle the problem of duplication of the cube, that is, the problem of how to construct a cube root. Like the quadrature of the circle this was another of the three great mathematical problems of Antiquity. Hippocrates also invented the technique of reduction, that is, to transform specific mathematical problems into a general problem that is more easy to solve. The solution to the general problem then automatically gives a solution to the original problem. In the field of astronomy Hippocrates tried to explain the phenomena of comets, ivor Bulmer-Thomas, Hippocrates of Chios, in, Dictionary of Scientific Biography, Charles Coulston Gillispie, ed. pp. 410–418. Björnbo, Hippokrates, in, Paulys Realencyclopädie der Classischen Altertumswissenschaft, G. Wissowa, oConnor, John J. Robertson, Edmund F. Hippocrates of Chios, MacTutor History of Mathematics archive, University of St Andrews. The Quadrature of the Circle and Hippocrates Lunes at Convergence
21.
Hippocrates
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Hippocrates of Kos, also known as Hippocrates II, was a Greek physician of the Age of Pericles, and is considered one of the most outstanding figures in the history of medicine. He is referred to as the Father of Modern Medicine in recognition of his contributions to the field as the founder of the Hippocratic School of Medicine. Hippocrates is commonly portrayed as the paragon of the ancient physician, historians agree that Hippocrates was born around the year 460 BC on the Greek island of Kos, other biographical information, however, is likely to be untrue. Soranus of Ephesus, a 2nd-century Greek gynecologist, was Hippocrates first biographer and is the source of most personal information about him, later biographies are in the Suda of the 10th century AD, and in the works of John Tzetzes, which date from the 12th century AD. Hippocrates is mentioned in passing in the writings of two contemporaries, Plato, in Protagoras and Phaedrus, and, Aristotles Politics, which date from the 4th century BC. Soranus wrote that Hippocrates father was Heraclides, a physician, and his mother was Praxitela, the two sons of Hippocrates, Thessalus and Draco, and his son-in-law, Polybus, were his students. According to Galen, a physician, Polybus was Hippocrates true successor, while Thessalus. Soranus said that Hippocrates learned medicine from his father and grandfather, Hippocrates was probably trained at the asklepieion of Kos, and took lessons from the Thracian physician Herodicus of Selymbria. Hippocrates taught and practiced medicine throughout his life, traveling at least as far as Thessaly, Thrace, several different accounts of his death exist. He died, probably in Larissa, at the age of 83,85 or 90, Hippocrates is credited with being the first person to believe that diseases were caused naturally, not because of superstition and gods. Hippocrates was credited by the disciples of Pythagoras of allying philosophy, indeed there is not a single mention of a mystical illness in the entirety of the Hippocratic Corpus. However, Hippocrates did work with many convictions that were based on what is now known to be incorrect anatomy and physiology, ancient Greek schools of medicine were split on how to deal with disease. The Knidian school of medicine focused on diagnosis, Medicine at the time of Hippocrates knew almost nothing of human anatomy and physiology because of the Greek taboo forbidding the dissection of humans. The Knidian school consequently failed to distinguish when one disease caused many possible series of symptoms, the Hippocratic school or Koan school achieved greater success by applying general diagnoses and passive treatments. Its focus was on patient care and prognosis, not diagnosis and it could effectively treat diseases and allowed for a great development in clinical practice. Hippocratic medicine and its philosophy are far removed from that of modern medicine, now, the physician focuses on specific diagnosis and specialized treatment, both of which were espoused by the Knidian school. S. Houdart called the Hippocratic treatment a meditation upon death, after a crisis, a relapse might follow, and then another deciding crisis. According to this doctrine, crises tend to occur on critical days, if a crisis occurred on a day far from a critical day, a relapse might be expected
22.
Vatican Library
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The Vatican Apostolic Library, more commonly called the Vatican Library or simply the Vat, is the library of the Holy See, located in Vatican City. Formally established in 1475, although it is older, it is one of the oldest libraries in the world. It has 75,000 codices from throughout history, as well as 1.1 million printed books, the Vatican Library is a research library for history, law, philosophy, science and theology. The Vatican Library is open to anyone who can document their qualifications, photocopies for private study of pages from books published between 1801 and 1990 can be requested in person or by mail. In March 2014, the Vatican Library began an initial project of digitising its collection of manuscripts. The Vatican Secret Archives were separated from the library at the beginning of the 17th century, scholars have traditionally divided the history of the library into five periods, Pre-Lateran, Lateran, Avignon, Pre-Vatican and Vatican. The Pre-Lateran period, comprising the initial days of the library, only a handful of volumes survive from this period, though some are very significant. However, in year, the Lateran Palace was burnt. The Avignon period was during the Avignon Papacy, when seven successive popes resided in Avignon and this period saw a great growth in book collection and record keeping by the popes in Avignon, between the death of Boniface and the 1370s when the Papacy returned to Rome. The Pre-Vatican period ranged from about 1370 to 1446, the library was scattered during this time, with parts in Rome, Avignon and elsewhere. In 1451, bibliophile Pope Nicholas V sought to establish a library at the Vatican. Pope Nicholas also expanded his collection by employing Italian and Byzantine scholars to translate the Greek classics into Latin for his library, the knowledgeable Pope already encouraged the inclusion of pagan classics. Nicolas was important in saving many of the Greek works and writings during this period that he had collected while traveling. In 1455, the collection had grown to 1200 books, of which 400 were in Greek language. Nicholas death in 1455 prevented the completion of his vision of a library, but it was finished in 1475 by his successor Pope Sixtus IV. During the papacy of Sixtus IV, acquisitions were made in theology, philosophy, the number of manuscripts is variously counted as 3,500 in 1475 or 2,527 in 1481, when librarian Bartolomeo Platina produced a signed listing. At the time it was the largest collection of books in the Western world, during his reign, Pope Julius II commissioned the expansion of the building. Around 1587, Pope Sixtus V commissioned the architect Domenico Fontana to construct a new building for the library and it was after this the library became known as the Vatican Library
23.
Johan Ludvig Heiberg (historian)
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Johan Ludvig Heiberg was a Danish philologist and historian. He is best known for his discovery of previously unknown texts in the Archimedes Palimpsest and he also published an edition of Ptolemys Almagest. Heiberg was born in Aalborg, the son of Johanne Henriette Jacoba, 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, many of his editions are still in use today. The French Academy of Sciences awarded him the Prix Binoux for 1912 and his sister married biochemist Max Henius. Heiberg inspected the vellum manuscript in Constantinople in 1906, and realized that it contained works by Archimedes that were unknown to scholars at the time. Heibergs examination of the manuscript was with the eye only, while modern analysis of the texts has employed x-ray. The Archimedes Palimpsest is currently stored at the Walters Art Museum in Baltimore, how do we know about Greek mathematicians. 1, 000-year-old text by Greek maths genius Archimedes goes on display Daily Mail, Works by Johan Ludvig Heiberg at Project Gutenberg Works by or about Johan Ludvig Heiberg at Internet Archive
24.
Byzantine Empire
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It survived the fragmentation and fall of the Western Roman Empire in the 5th century AD and continued to exist for an additional thousand years until it fell to the Ottoman Turks in 1453. During most of its existence, the empire was the most powerful economic, cultural, several signal events from the 4th to 6th centuries mark the period of transition during which the Roman Empires Greek East and Latin West divided. Constantine I reorganised the empire, made Constantinople the new capital, under Theodosius I, Christianity became the Empires official state religion and other religious practices were proscribed. Finally, under the reign of Heraclius, the Empires military, 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 Empires eastern frontier was expanded, 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, the Empire recovered again during the Komnenian restoration, such that by the 12th century Constantinople was the largest and wealthiest European city. Despite the eventual recovery of Constantinople in 1261, the Byzantine Empire remained only one of several small states in the area for the final two centuries of its existence. Its remaining territories were 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 Constantines capital. This older name of the city would rarely be used from this point onward except in historical or poetic contexts. The publication in 1648 of the Byzantine du Louvre, and in 1680 of Du Canges Historia Byzantina further popularised the use of Byzantine among French authors, however, it was not until the mid-19th century that the term came into general use in the Western world. The Byzantine Empire was known to its inhabitants as the Roman Empire, the Empire of the Romans, Romania, the Roman Republic, Graikia, and also as Rhōmais. The inhabitants called themselves Romaioi and Graikoi, and even as late as the 19th century Greeks typically referred to modern Greek as Romaika and Graikika. The authority of the Byzantine emperor as the legitimate Roman emperor was challenged by the coronation of Charlemagne as Imperator Augustus by Pope Leo III in the year 800. No such distinction existed in the Islamic and Slavic worlds, where the Empire was more seen as the continuation of the Roman Empire. In the Islamic world, the Roman Empire was known primarily as Rûm, the Roman army succeeded in conquering many territories covering the entire Mediterranean region and coastal regions in southwestern Europe and north Africa. These territories were home to different cultural groups, both urban populations and rural populations. The West also suffered heavily from the instability of the 3rd century AD
25.
Papyrus Oxyrhynchus 29
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Papyrus Oxyrhynchus 29 is a fragment of the second book of the Elements of Euclid in Greek. It was discovered by Grenfell and Hunt in 1897 in Oxyrhynchus, the fragment was originally dated to the end of the third century or the beginning of the fourth century, although more recent scholarship suggests a date of 75–125 CE. It is housed in the library of the University of Pennsylvania, the text was published by Grenfell and Hunt in 1898. The manuscript was written on papyrus in sloping irregular uncial letters, with no iota adscript, the fragment measures 85 by 152 mm. The fragment provides a statement of the 5th proposition of Book 2 of the Elements, together with a diagram. No part of the proof is provided, Oxyrhynchus Papyri Papyrus Oxyrhynchus 28 Papyrus Oxyrhynchus 30 This article incorporates text from a publication now in the public domain, B. P. Grenfell, A. S. Hunt
26.
Cicero
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Marcus Tullius Cicero was a Roman philosopher, politician, lawyer, orator, political theorist, consul, and constitutionalist. He came from a wealthy family of the Roman equestrian order. According to Michael Grant, the influence of Cicero upon the history of European literature, Cicero introduced the Romans to the chief schools of Greek philosophy and created a Latin philosophical vocabulary distinguishing himself as a translator and philosopher. Though he was an orator and successful lawyer, Cicero believed his political career was his most important achievement. During the chaotic latter half of the 1st century BC marked by civil wars, following Julius Caesars death, Cicero became an enemy of Mark Antony in the ensuing power struggle, attacking him in a series of speeches. His severed hands and head were then, as a revenge of Mark Antony. Petrarchs rediscovery of Ciceros letters is often credited for initiating the 14th-century Renaissance in public affairs, humanism, according to Polish historian Tadeusz Zieliński, the Renaissance was above all things a revival of Cicero, and only after him and through him of the rest of Classical antiquity. Cicero was born in 106 BC in Arpinum, a hill town 100 kilometers southeast of Rome and his father was a well-to-do member of the equestrian order and possessed good connections in Rome. However, being a semi-invalid, he could not enter public life, although little is known about Ciceros mother, Helvia, it was common for the wives of important Roman citizens to be responsible for the management of the household. Ciceros brother Quintus wrote in a letter that she was a thrifty housewife, Ciceros cognomen, or personal surname, comes from the Latin for chickpea, cicer. Plutarch explains that the name was given to one of Ciceros ancestors who had a cleft in the tip of his nose resembling a chickpea. However, it is likely that Ciceros ancestors prospered through the cultivation. Romans often chose down-to-earth personal surnames, the family names of Fabius, Lentulus, and Piso come from the Latin names of beans, lentils. Plutarch writes that Cicero was urged to change this name when he entered politics. During this period in Roman history, cultured meant being able to speak both Latin and Greek, Cicero used his knowledge of Greek to translate many of the theoretical concepts of Greek philosophy into Latin, thus translating Greek philosophical works for a larger audience. It was precisely his broad education that tied him to the traditional Roman elite, according to Plutarch, Cicero was an extremely talented student, whose learning attracted attention from all over Rome, affording him the opportunity to study Roman law under Quintus Mucius Scaevola. Ciceros fellow students were Gaius Marius Minor, Servius Sulpicius Rufus, the latter two became Ciceros friends for life, and Pomponius would become, in Ciceros own words, as a second brother, with both maintaining a lifelong correspondence. Cicero wanted to pursue a career in politics along the steps of the Cursus honorum
27.
Boethius
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Anicius Manlius Severinus Boëthius, commonly called Boethius, was a Roman senator, consul, magister officiorum, and philosopher of the early 6th century. Boethius was born in Rome to a family around 480 AD. His family, the Anicii, included emperors Petronius Maximus and Olybrius and his father, Manlius Boethius, who was appointed consul in 487, died while Boethius was young. Another patrician, Quintus Aurelius Memmius Symmachus, adopted and raised Boethius, instilling in him a love for literature and philosophy. Both Memmius Symmachus and Boethius were fluent in Greek, a rare skill at the time in the Western Empire, for this reason. The French scholar Pierre Courcelle has argued that Boethius studied at Alexandria with the Neo-Platonist philosopher Ammonius Hermiae, on account of his erudition, Boethius entered the service of Theodoric the Great at a young age and was already a senator by the age of 25. Boethius married his foster-fathers daughter, Rusticiana, their children included two boys, Symmachus and Boethius. In 522, the year his two sons were appointed joint consuls, Boethius accepted the appointment to the position of magister officiorum. This may have set in place a course of events that would lead to loss of royal favour, five hundred years later, this continuing disagreement led to the East-West Schism in 1054, in which communion between the Catholic Church and Eastern Orthodox Church was broken. In 523 Boethius fell from power, after a period of imprisonment in Pavia for what was deemed a treasonable offence, he was executed in 524. The primary sources are in agreement over the facts of what happened. At a meeting of the Royal Council in Verona, the referandarius Cyprianus accused the ex-consul Caecina Decius Faustus Albinus of treasonous correspondence with Justin I. Boethius leapt to his defense, crying, The charge of Cyprianus is false, but if Albinus did that, so also have I, Cyprianus then also accused Boethius of the same crime, and produced three men who claimed they had witnessed the crime. First the pair were detained in the baptistery of a church, then Boethius was exiled to the Ager Calventianus, a distant country estate, the basic facts in the case are not in dispute, writes Jeffrey Richards. What is disputed about this sequence of events is the interpretation that should be put on them, Boethius claims his crime was seeking the safety of the Senate. He describes the three witnesses against him as dishonorable, Basilius had been dismissed from Royal service for his debts, while Venantius Opilio, however, other sources depict these men in a far more positive light. For example, Cassiodorus describes Cyprianus and Opilio as utterly scrupulous, just and loyal and mentions they are brothers, Theodoric was feeling threatened by international events. The Acacian Schism had been resolved, and the Nicene Christian aristocrats of his kingdom were seeking to renew their ties with Constantinople, the Catholic Hilderic had become king of the Vandals and had put Theodorics sister Amalafrida to death, and Arians in the East were being persecuted
28.
Arabic
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Arabic is a Central Semitic language that was first spoken in Iron Age northwestern Arabia and is now the lingua franca of the Arab world. Arabic is also the language of 1.7 billion Muslims. It is one of six languages of the United Nations. The modern written language is derived from the language of the Quran and it is widely taught in schools and universities, and is used to varying degrees in workplaces, government, and the media. The two formal varieties are grouped together as Literary Arabic, which is the language of 26 states. Modern Standard Arabic largely follows the standards of Quranic Arabic. Much of the new vocabulary is used to denote concepts that have arisen in the post-Quranic era, Arabic has influenced many languages around the globe throughout its history. During the Middle Ages, Literary Arabic was a vehicle of culture in Europe, especially in science, mathematics. As a result, many European languages have borrowed many words from it. Many words of Arabic origin are found in ancient languages like Latin. Balkan languages, including Greek, have acquired a significant number of Arabic words through contact with Ottoman Turkish. Arabic has also borrowed words from languages including Greek and Persian in medieval times. Arabic is a Central Semitic language, closely related to the Northwest Semitic languages, the Ancient South Arabian languages, the Semitic languages changed a great deal between Proto-Semitic and the establishment of the Central Semitic languages, particularly in grammar. Innovations of the Central Semitic languages—all maintained in Arabic—include, The conversion of the suffix-conjugated stative formation into a past tense, the conversion of the prefix-conjugated preterite-tense formation into a present tense. The elimination of other prefix-conjugated mood/aspect forms in favor of new moods formed by endings attached to the prefix-conjugation forms, the development of an internal passive. These features are evidence of descent from a hypothetical ancestor. In the southwest, various Central Semitic languages both belonging to and outside of the Ancient South Arabian family were spoken and it is also believed that the ancestors of the Modern South Arabian languages were also spoken in southern Arabia at this time. To the north, in the oases of northern Hijaz, Dadanitic and Taymanitic held some prestige as inscriptional languages, in Najd and parts of western Arabia, a language known to scholars as Thamudic C is attested
29.
Harun al-Rashid
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Harun al-Rashid (/hɑːˈruːnɑːlrɑːˈʃiːd/ Arabic, هَارُون الرَشِيد, Hārūn Ar-Rašīd, in English, Aaron the Just,17 March 763 or February 766 —24 March 809 was the fifth Abbasid Caliph. His birth date is debated, with sources giving dates from 763 to 766. His surname translates to the Just, the Upright, or the Rightly-Guided, fully translated, Al-Rashid ruled from 786 to 809, during the peak of the Islamic Golden Age. His time was marked by scientific, cultural, and religious prosperity, Islamic art and music also flourished significantly during his reign. He established the legendary library Bayt al-Hikma in Baghdad in present-day Iraq, during his rule, the family of Barmakids, which played a deciding role in establishing the Abbasid Caliphate, declined gradually. In 796, he moved his court and government to Raqqa in present-day Syria, since Harun was intellectually, politically, and militarily resourceful, his life and his court have been the subject of many tales, some factual, but most believed to be fictitious. One factual tale is the story of the clock that was among various presents that Harun sent to Charlemagne, the presents were carried by the returning Frankish mission that came to offer Harun friendship in 799. Charlemagne and his retinue deemed the clock to be a conjuration for the sounds it emanated, among what is known to be fictional is The Book of One Thousand and One Nights, which contains many stories that are fantasized by Haruns magnificent court and even Harun al-Rashid himself. Amongst some of the Twelver sect of Shia Muslims he is disliked for his role in the murder of their 7th Imam, although Sunnis. Hārūn was born in Rey, then part of Jibal in the Abbasid Caliphate, in present-day Tehran Province, the latter expedition was a huge undertaking, and even reached the Asian suburbs of Constantinople. Hārūn became caliph in 786 when he was in his early twenties and he began his reign by appointing very able ministers, who carried on the work of the government so well that they greatly improved the condition of the people. It was under Hārūn ar-Rashīd that Baghdad flourished into the most splendid city of its period, tribute was paid by many rulers to the caliph, and these funds were used on architecture, the arts and a luxurious life at court. In 796, Hārūn decided to move his court and the government to Raqqa at the middle Euphrates, here he spent 12 years, most of his reign. Only once did he return to Baghdad for a short visit, several reasons might have influenced the decision to move to Raqqa. It was close to the Byzantine border, the communication lines via the Euphrates to Baghdad and via the Balikh river to the north and via Palmyra to Damascus were excellent. The agriculture was flourishing to support the new Imperial center, and from Raqqa any rebellion in Syria and the middle Euphrates area could be controlled. Abu al-Faraj al-Isfahani pictures in his anthology of poems the splendid life in his court, in Raqqa the Barmekids managed the fate of the empire, and there both heirs, al-Amin and al-Mamun grew up. For the administration of the empire, he fell back on his mentor
30.
Arethas of Caesarea
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Arethas of Caesarea was Archbishop of Caesarea in Cappadocia early in the 10th century, and is considered one of the most scholarly theologians of the Greek Orthodox Church. The codices produced by him, containing his commentaries are credited with preserving many ancient texts, including those of Plato and he was a disciple of Photius. He studied at the University of Constantinople and he became Deacon of Patrea around 900 and was made Archbishop of Caesarea by Nikolas of Constantinople in 903. Despite Arethas fame as a scholar, Jenkins thinks little of him as a person, when recounting the details of the scandal, Arethas is described as. narrow-minded, bad-hearted. He is the compiler of a Greek commentary on the Apocalypse, for which he made use of the similar work of his predecessor. It was first printed in 1535 as an appendix to the works of Oecumenius, ehrhard inclines to the opinion that he wrote other scriptural commentaries. He is also known as a commentator of Plato and Lucian, other important Greek manuscripts, e. g. of Euclid, the rhetor Aristides, and perhaps of Dio Chrysostom, are owing to him. Not a few of his writings, contained in a Moscow manuscript, are said still to await an editor. Arethas works also contain the oldest known references to the Meditations by the Roman emperor Marcus Aurelius, Arethas admits to holding the work in high regard in letters to the Byzantine emperor Leo VI the Wise and in his comments to Lucian and Dio Chrysostom. Arethas is credited with reintroducing the Meditations to public discourse and this article incorporates text from a publication now in the public domain, Herbermann, Charles, ed. article name needed. Opera Omnia by Migne Patrologia Graeca with analytical indexes Novotny, Frantisek, the Hague, Springer Science & Business Media, Dec 6,2012
31.
John Dee
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John Dee was an English mathematician, astronomer, astrologer, occult philosopher, and advisor to Queen Elizabeth I. He devoted much of his life to the study of alchemy, divination and he was also an advocate of Englands imperial expansion. Dee straddled the worlds of science and magic just as they were becoming distinguishable, one of the most learned men of his age, he had been invited to lecture on the geometry of Euclid at the University of Paris while still in his early twenties. Dee was an ardent promoter of mathematics and an astronomer, as well as a leading expert in navigation. Simultaneously with these efforts, Dee immersed himself in the worlds of magic, astrology, in his lifetime, Dee amassed one of the largest libraries in England. His high status as a scholar also allowed him to play a role in Elizabethan politics and he served as an occasional advisor and tutor to Elizabeth I and nurtured relationships with her ministers Francis Walsingham and William Cecil. Dee also tutored and enjoyed patronage relationships with Sir Philip Sidney, his uncle Robert Dudley, 1st Earl of Leicester and he also enjoyed patronage from Sir Christopher Hatton. Dee was born in Tower Ward, London, to Rowland Dee of Welsh descent and his surname Dee derived from the Welsh du, his grandfather was Bedo Ddu of Nant-y-groes, Pilleth, Radnorshire, and John retained his connection with the locality. His father Roland was a mercer and gentleman courtier to Henry VIII, John Dee claimed to be a descendant of Rhodri the Great, Prince of Wales and constructed a pedigree showing his descent from Rhodri. Dees family arrived in London in the wake of Henry Tudors coronation as Henry VII, Jane Dee was the daughter of William Wild. Dee attended the Chelmsford Chantry School from 1535 to 1542 and he entered St Johns College, Cambridge, in November 1542, aged 15, graduating BA in 1545 or early 1546. His abilities recognised, he became a fellow of Trinity College, Cambridge. At Trinity, the stage effects he produced for a production of Aristophanes Peace procured him the reputation of being a magician that clung to him through life. In the late 1540s and early 1550s, he travelled in Europe, studying at Louvain and Brussels, in 1552, he met Gerolamo Cardano in London, during their acquaintance they investigated a perpetual motion machine as well as a gem purported to have magical properties. Rector at Upton-upon-Severn from 1553, Dee was offered a readership in mathematics at Oxford in 1554, in 1555, Dee became a member of the Worshipful Company of Mercers, as his father had, through the companys system of patrimony. That same year,1555, he was arrested and charged with calculating for having cast horoscopes of Queen Mary and Princess Elizabeth, Dee appeared in the Star Chamber and exonerated himself, but was turned over to the Catholic Bishop Bonner for religious examination. His strong and lifelong penchant for secrecy perhaps worsening matters, this episode was only the most dramatic in a series of attacks. Clearing his name yet again, he became a close associate of Bonner
32.
Henry Billingsley
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Sir Henry Billingsley was an English merchant, Lord Mayor of London and the first translator of Euclid into English. He was a son of Sir William Billingsley, haberdasher and assay master of London and he entered St. Johns College, Cambridge, in 1551, and also studied at Oxford, where, under the tutelage of David Whytehead, he developed an interest in mathematics. He did not take a degree but apprenticed to a London merchant and he became a haberdasher, becoming a freeman of the Worshipful Company of Haberdashers by patrimony in 1560. He was made sheriff of London in 1584 and alderman of Tower Ward in 1585 and he became one of Elizabeths four customs collectors in 1589. In 1596, he succeeded Sir Thomas Skinner as Lord Mayor of London and he was knighted the following year. In 1603, he sat in Parliament for London and he founded three scholarships for poor students at St. Johns College and served as President of St. Thomass Hospital. Though in the introduction of his Euclid he proposed to undertake other translations, in 1570, Billingsley published his translation of Euclids Elements The elements of geometrie of the most ancient philosopher Euclide of Megara. The work included a preface by John Dee, which surveyed all the existing branches of pure. Dee also provided notes and other supplementary material. The work was printed in folio by John Day, and included several three-dimensional fold-up diagrams illustrating solid geometry, though not the very first, it was one of the first books to include such a feature. The translation, renowned for its clarity and accuracy, was made from the Greek rather than the well-known Latin translation of Campanus. Augustus De Morgan has suggested that the translation was solely the work of Dee, but in his correspondence Dee states specifically that only the introduction, anthony Wood asserted that the translation was largely the work of Whytehead, who spent his final years at Billingsleys house. This story passed from Robert Barnes in Oxford to Thomas Allen, Whytehead did apparently provide some assistance, but there is no evidence that the work is all his, Wood frequently reported gossip as fact. The majority of his children were born to his first marriage to Elizabeth Bourne and he purchased, with his son Henry, Siston Court, Gloucestershire c.1598 from Arthur Player of Westerleigh, who had acquired it in 1595. Another child was his daughter Elizabeth who married the cloth merchant, diana M. Simpkins Early editions of Euclid in England, Annals of Science, Volume 22, Number 4, December 1966. George Bruce Halsted, Note on the First English Euclid, American Journal of Mathematics, Vol.2, several pictures of a copy of Billingsleys Euclid
33.
Bodleian Library
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The Bodleian Library, the main research library of the University of Oxford, is one of the oldest libraries in Europe. With over 12 million items, it is the second largest library in Britain after the British Library, known to Oxford scholars as Bodley or the Bod, it operates principally as a reference library and, in general, documents may not be removed from the reading rooms. They do, however, participate in OLIS, the Bodleian Libraries online union catalogue, much of the librarys archives were digitized and put online for public access in 2015. Since the 19th century a number of stores have been built. Before being granted access to the library, new readers are required to agree to a formal declaration and this declaration was traditionally an oral oath, but is now usually made by signing a letter to a similar effect. Ceremonies in which readers recite the declaration are still performed for those who wish to take them, external readers are still required to recite the declaration orally prior to admission. The Bodleian Admissions Office has amassed a collection of translations of the declaration allowing those who are not native English speakers to recite it in their first language. Whilst the Bodleian Library, in its current incarnation, has a history dating back to 1602. The first purpose-built library known to have existed in Oxford was founded in the century under the will of Thomas Cobham. This small collection of chained books was situated above the side of the University Church of St Mary the Virgin on the High Street. A suitable room was built above the Divinity School. This room continues to be known as Duke Humfreys Library, after 1488, the university stopped spending money on the librarys upkeep and acquisitions, and manuscripts began to go unreturned to the library. The late sixteenth century saw the library go through a period of decline, the furniture was sold. During the reign of Edward VI, there was a purge of superstitious manuscripts, six of the Oxford University dons were tasked with helping Bodley in refitting the library in March 1658. Duke Humfrey’s Library was refitted, and Bodley donated a number of his own books to furnish it, the library was formally re-opened on 8 November 1602 under the name “Bodleian Library”. There were around two thousand books in the library at this time, with an ornate Benefactors Register displayed prominently, in 1605, Francis Bacon gave the library a copy of The Advancement of Learning and described the Bodleian as an Ark to save learning from deluge. At this time, there were few books written in English held in the library, Thomas James suggested that Bodley should ask the Stationers Company to provide a copy of all books printed to the Bodleian. In 1610, Bodley made an agreement with the Stationers Company in London to put a copy of every book registered with them in the library, the Bodleian collection grew so fast that the building was expanded between 1610–1612, and again in 1634–1637
34.
Erhard Ratdolt
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Erhard Ratdolt was an early German printer from Augsburg. He was active as a printer in Venice from 1476 to 1486, from 1475 to 1478 he was in partnership with two other German printers. The first book the partnership produced was the Calendarium, written and previously published by Regiomontanus, Ratdolt is also famous for having produced the first known printers type specimen book. His innovations of layout and typography, mixing type and woodcuts, have subsequently been much admired and his graphic choices and technical solutions influenced also those of William Morris
35.
Nicolaus Copernicus
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Copernicus was born and died in Royal Prussia, a region that had been part of the Kingdom of Poland since 1466. A polyglot and polymath, he obtained a doctorate in law and was also a mathematician, astronomer, physician, classics scholar, translator, governor, diplomat. In 1517 he derived a quantity theory of money – a key concept in economics –, Nicolaus Copernicus was born on 19 February 1473 in the city of Toruń, in the province of Royal Prussia, in the Crown of the Kingdom of Poland. His father was a merchant from Kraków and his mother was the daughter of a wealthy Toruń merchant, Nicolaus was the youngest of four children. His brother Andreas became an Augustinian canon at Frombork and his sister Barbara, named after her mother, became a Benedictine nun and, in her final years, prioress of a convent in Chełmno, she died after 1517. His sister Katharina married the businessman and Toruń city councilor Barthel Gertner and left five children, Copernicus fathers family can be traced to a village in Silesia near Nysa. The villages name has been variously spelled Kopernik, Copernik, Copernic, Kopernic, Coprirnik, in the 14th century, members of the family began moving to various other Silesian cities, to the Polish capital, Kraków, and to Toruń. The father, Mikołaj the Elder, likely the son of Jan, Nicolaus was named after his father, who appears in records for the first time as a well-to-do merchant who dealt in copper, selling it mostly in Danzig. He moved from Kraków to Toruń around 1458, Nicolaus father was actively engaged in the politics of the day and supported Poland and the cities against the Teutonic Order. In 1454 he mediated negotiations between Polands Cardinal Zbigniew Oleśnicki and the Prussian cities for repayment of war loans, Copernicuss father married Barbara Watzenrode, the astronomers mother, between 1461 and 1464. The Modlibógs were a prominent Polish family who had been known in Polands history since 1271. The Watzenrode family, like the Kopernik family, had come from Silesia from near Świdnica and they soon became one of the wealthiest and most influential patrician families. Lucas Watzenrode the Elder, a merchant and in 1439–62 president of the judicial bench, was a decided opponent of the Teutonic Knights. In 1453 he was the delegate from Toruń at the Grudziądz conference that planned the uprising against them, Lucas Watzenrode the Younger, the astronomers maternal uncle and patron, was educated at the University of Kraków and at the universities of Cologne and Bologna. He was an opponent of the Teutonic Order, and its Grand Master once referred to him as the devil incarnate. In 1489 Watzenrode was elected Bishop of Warmia against the preference of King Casimir IV, as a result, Watzenrode quarreled with the king until Casimir IVs death three years later. Watzenrode was then able to close relations with three successive Polish monarchs, John I Albert, Alexander Jagiellon, and Sigismund I the Old. He was a friend and key advisor to each ruler, Watzenrode came to be considered the most powerful man in Warmia, and his wealth, connections and influence allowed him to secure Copernicus education and career as a canon at Frombork Cathedral
36.
Johannes Kepler
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Johannes Kepler was a German mathematician, astronomer, and astrologer. A key figure in the 17th-century scientific revolution, he is best known for his laws of motion, based on his works Astronomia nova, Harmonices Mundi. These works also provided one of the foundations for Isaac Newtons theory of universal gravitation, Kepler was a mathematics teacher at a seminary school in Graz, where he became an associate of Prince Hans Ulrich von Eggenberg. Later he became an assistant to the astronomer Tycho Brahe in Prague and he was also a mathematics teacher in Linz, and an adviser to General Wallenstein. Kepler lived in an era when there was no distinction between astronomy and astrology, but there was a strong division between astronomy and physics. Kepler was born on December 27, the feast day of St John the Evangelist,1571 and his grandfather, Sebald Kepler, had been Lord Mayor of the city. By the time Johannes was born, he had two brothers and one sister and the Kepler family fortune was in decline and his father, Heinrich Kepler, earned a precarious living as a mercenary, and he left the family when Johannes was five years old. He was believed to have died in the Eighty Years War in the Netherlands and his mother Katharina Guldenmann, an innkeepers daughter, was a healer and herbalist. Born prematurely, Johannes claimed to have weak and sickly as a child. Nevertheless, he often impressed travelers at his grandfathers inn with his phenomenal mathematical faculty and he was introduced to astronomy at an early age, and developed a love for it that would span his entire life. At age six, he observed the Great Comet of 1577, in 1580, at age nine, he observed another astronomical event, a lunar eclipse, recording that he remembered being called outdoors to see it and that the moon appeared quite red. However, childhood smallpox left him with vision and crippled hands. In 1589, after moving through grammar school, Latin school, there, he studied philosophy under Vitus Müller and theology under Jacob Heerbrand, who also taught Michael Maestlin while he was a student, until he became Chancellor at Tübingen in 1590. He proved himself to be a mathematician and earned a reputation as a skilful astrologer. Under the instruction of Michael Maestlin, Tübingens professor of mathematics from 1583 to 1631 and he became a Copernican at that time. In a student disputation, he defended heliocentrism from both a theoretical and theological perspective, maintaining that the Sun was the source of motive power in the universe. Despite his desire to become a minister, near the end of his studies, Kepler was recommended for a position as teacher of mathematics and he accepted the position in April 1594, at the age of 23. Keplers first major work, Mysterium Cosmographicum, was the first published defense of the Copernican system
37.
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
38.
Isaac Newton
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His book Philosophiæ Naturalis Principia Mathematica, first published in 1687, laid the foundations of classical mechanics. Newton also made contributions to optics, and he shares credit with Gottfried Wilhelm Leibniz for developing the infinitesimal calculus. Newtons Principia formulated the laws of motion and universal gravitation that dominated scientists view of the universe for the next three centuries. Newtons work on light was collected in his influential book Opticks. He also formulated a law of cooling, made the first theoretical calculation of the speed of sound. Newton was a fellow of Trinity College and the second Lucasian Professor of Mathematics at the University of Cambridge, politically and personally tied to the Whig party, Newton served two brief terms as Member of Parliament for the University of Cambridge, in 1689–90 and 1701–02. He was knighted by Queen Anne in 1705 and he spent the last three decades of his life in London, serving as Warden and Master of the Royal Mint and his father, also named Isaac Newton, had died three months before. Born prematurely, he was a child, his mother Hannah Ayscough reportedly said that he could have fit inside a quart mug. When Newton was three, his mother remarried and went to live with her new husband, the Reverend Barnabas Smith, leaving her son in the care of his maternal grandmother, Newtons mother had three children from her second marriage. From the age of twelve until he was seventeen, Newton was educated at The Kings School, Grantham which taught Latin and Greek. He was removed from school, and by October 1659, he was to be found at Woolsthorpe-by-Colsterworth, Henry Stokes, master at the Kings School, persuaded his mother to send him back to school so that he might complete his education. Motivated partly by a desire for revenge against a bully, he became the top-ranked student. In June 1661, he was admitted to Trinity College, Cambridge and he started as a subsizar—paying his way by performing valets duties—until he was awarded a scholarship in 1664, which guaranteed him four more years until he would get his M. A. He set down in his notebook a series of Quaestiones about mechanical philosophy as he found it, in 1665, he discovered the generalised binomial theorem and began to develop a mathematical theory that later became calculus. Soon after Newton had obtained his B. A. degree in August 1665, in April 1667, he returned to Cambridge and in October was elected as a fellow of Trinity. Fellows were required to become ordained priests, although this was not enforced in the restoration years, however, by 1675 the issue could not be avoided and by then his unconventional views stood in the way. Nevertheless, Newton managed to avoid it by means of a special permission from Charles II. A and he was elected a Fellow of the Royal Society in 1672. Newtons work has been said to distinctly advance every branch of mathematics then studied and his work on the subject usually referred to as fluxions or calculus, seen in a manuscript of October 1666, is now published among Newtons mathematical papers
39.
Thomas Hobbes
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Thomas Hobbes, in some older texts Thomas Hobbes of Malmesbury, was an English philosopher who is considered one of the founders of modern political philosophy. Hobbes is best known for his 1651 book Leviathan, which established the social theory that has served as the foundation for most later Western political philosophy. Thomas Hobbes was born at Westport, now part of Malmesbury in Wiltshire, England, born prematurely when his mother heard of the coming invasion of the Spanish Armada, Hobbes later reported that my mother gave birth to twins, myself and fear. His childhood is almost completely unknown, and his mothers name is unknown and his father, Thomas Sr. was the vicar of Charlton and Westport. Thomas Hobbes, the younger, had a brother Edmund, about two years older, and a sister, Thomas Sr. was involved in a fight with the local clergy outside his church, forcing him to leave London and abandon the family. The family was left in the care of Thomas Sr. s older brother, Francis, Hobbes was a good pupil, and around 1603 he went up to Magdalen Hall, the predecessor college to Hertford College, Oxford. The principal John Wilkinson was a Puritan, and he had influence on Hobbes. At university, Hobbes appears to have followed his own curriculum and he did not complete his B. A. Hobbes became a companion to the younger William and they both took part in a grand tour of Europe in 1610. Hobbes was exposed to European scientific and critical methods during the tour and it has been argued that three of the discourses in the 1620 publication known as Horea Subsecivae, Observations and Discourses, also represent the work of Hobbes from this period. Although he associated with figures like Ben Jonson and briefly worked as Francis Bacons amanuensis. His employer Cavendish, then the Earl of Devonshire, died of the plague in June 1628, the widowed countess dismissed Hobbes but he soon found work, again as a tutor, this time to Gervase Clifton, the son of Sir Gervase Clifton, 1st Baronet. This task, chiefly spent in Paris, ended in 1631 when he found work with the Cavendish family, tutoring William. Over the next seven years, as well as tutoring, he expanded his own knowledge of philosophy and he visited Florence in 1636 and was later a regular debater in philosophic groups in Paris, held together by Marin Mersenne. Hobbess first area of study was an interest in the doctrine of motion. Despite his interest in this phenomenon, he disdained experimental work as in physics and he went on to conceive the system of thought to the elaboration of which he would devote his life. He then singled out Man from the realm of Nature and plants, finally he considered, in his crowning treatise, how Men were moved to enter into society, and argued how this must be regulated if Men were not to fall back into brutishness and misery. Thus he proposed to unite the separate phenomena of Body, Man, Hobbes came home, in 1637, to a country riven with discontent which disrupted him from the orderly execution of his philosophic plan. However, by the end of the Short Parliament in 1640, he had written a treatise called The Elements of Law, Natural
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