Scholars are people who devote themselves to study to an area in which they have developed expertise. A scholar may be an academic, a person who works as a teacher or researcher at a university or other higher education institution. An academic holds an advanced degree; the term scholar is sometimes used with equivalent meaning to that of academic and describes in general those who attain mastery in a research discipline. However, it has wider application, with it being used to describe those whose occupation was researched prior to organized higher education. In 1847, minister Emanuel Vogel Gerhart delivered an extensive address on the role of the scholar in society, writing: Who is a scholar? the first reply that must be given is: He is a scholar whose whole inward intellectual and moral being has been symmetrically unfolded and strengthened under the influence of truth. The different mental activities will always be exercised rightly when the proper equilibrium is preserved. No one faculty should be drawn out to the neglect of others.
The whole inner man should be unfolded harmoniously. Gerhart argued that a scholar can not be focused on a single discipline, contending that knowledge of multiple disciplines is necessary to put each into context and to inform the development of each: o be a scholar involves more than mere learning, he may know much about many things and yet know little or nothing right. Knowledge without system or order is of no more service than useless lumber. A genuine scholar possesses something more: he penetrates and understands the principle and laws of the particular department of human knowledge with which he professes acquaintance, he imbibes the life of Science. To know only one thing as it ought to be known constitutes a man more of a scholar than to know many things by rote; the man of one idea may be an object of ridicule, yet if his one idea is apprehended in its proper life and power, he is of far more account than if he had collected a number of notions, all jumbled together in his mind confusedly.
The knowledge of a scholar becomes a part of himself. Yielding himself to the plastic power of truth, as such, his mind is transfused and moulded by its energy and spirit. A more recent examination outlined the following attributes accorded to scholars as "described by many writers, with some slight variations in the definition": The common themes are that a scholar is a person who has a high intellectual ability, is an independent thinker and an independent actor, has ideas that stand apart from others, is persistent in her quest for developing knowledge, is systematic, has unconditional integrity, has intellectual honesty, has some convictions, stands alone to support these convictions. Scholars may rely on the scholarly method or scholarship, a body of principles and practices used by scholars to make their claims about the world as valid and trustworthy as possible, to make them known to the scholarly public, it is the methods that systemically advance the teaching and practice of a given scholarly or academic field of study through rigorous inquiry.
Scholarship is creative, can be documented, can be replicated or elaborated, can be and is peer-reviewed through various methods. Scholars have been upheld as creditable figures engaged in work important to the advance of society. In Imperial China, in the period from 206 BC until AD 1912, the intellectuals were the Scholar-officials, who were civil servants appointed by the Emperor of China to perform the tasks of daily governance; such civil servants earned academic degrees by means of imperial examination, were skilled calligraphers, knew Confucian philosophy. Historian Wing-Tsit Chan concludes that: Generally speaking, the record of these scholar-gentlemen has been a worthy one, it was good enough to be imitated in 18th century Europe. It has given China a tremendous handicap in their transition from government by men to government by law, personal considerations in Chinese government have been a curse. In Joseon Korea, the intellectuals were the literati, who knew how to read and write, had been designated, as the chungin, in accordance with the Confucian system.
They constituted the petite bourgeoisie, composed of scholar-bureaucrats who administered the dynastic rule of the Joseon dynasty. In his 1847 address, Gerhart asserted that scholars have an obligation to continue their studies so as to remain aware of new knowledge being generated, to contribute their own insights to the body of knowledge available to all: The progress of science involves momentous interests, it merits the attention of all sincere lovers of truth. Every one professing to be a scholar is under obligations to contribute towards the ever-progressive unfolding of its riches and power. Not content with what is well known in reference to a great variety of subjects —not content with the imperfect views that have been acquired of many others, all genuine scholars, availing themselves of previous efforts, should combine their energies to bring to view what has eluded the keen vision of those men of noble intellectual stature who have lived and died before them. Many scholars are professors engaged in the teaching of others.
In a number of countries, the title "research professor" refers to a professor, or engaged in research, who has few or no teaching obligations. For example, the title is used in this sense in the United Kingdom (where it is known as research professor at some universities and professorial research fellow at some other institutions
Euclid, sometimes called Euclid of Alexandria to distinguish him from Euclid of Megara, was a Greek mathematician referred to as the "founder of geometry" or the "father of geometry". He was active in Alexandria during the reign of Ptolemy I, his Elements is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics from the time of its publication until the late 19th or early 20th century. In the Elements, Euclid deduced the theorems of what is now called Euclidean geometry from a small set of axioms. Euclid wrote works on perspective, conic sections, spherical geometry, number theory, mathematical rigour; the English name Euclid is the anglicized version of the Greek name Εὐκλείδης, which means "renowned, glorious". Few original references to Euclid survive, so little is known about his life, he was born c. 325 BC, although the place and circumstances of both his birth and death are unknown and may only be estimated relative to other people mentioned with him.
He is mentioned by name by other Greek mathematicians from Archimedes onward, is referred to as "ὁ στοιχειώτης". The few historical references to Euclid were written by Proclus c. 450 AD, centuries after Euclid lived. A detailed biography of Euclid is given by Arabian authors, for example, a birth town of Tyre; this biography is believed to be fictitious. If he came from Alexandria, he would have known the Serapeum of Alexandria, the Library of Alexandria, may have worked there during his time. Euclid's arrival in Alexandria came about ten years after its founding by Alexander the Great, which means he arrived c. 322 BC. Proclus introduces Euclid only in his Commentary on the Elements. According to Proclus, Euclid belonged to Plato's "persuasion" and brought together the Elements, drawing on prior work of Eudoxus of Cnidus and of several pupils of Plato Proclus believes that Euclid is not much younger than these, that he must have lived during the time of Ptolemy I because he was mentioned by Archimedes.
Although the apparent citation of Euclid by Archimedes has been judged to be an interpolation by editors of his works, it is still believed that Euclid wrote his works before Archimedes wrote his. Proclus retells a story that, when Ptolemy I asked if there was a shorter path to learning geometry than Euclid's Elements, "Euclid replied there is no royal road to geometry." This anecdote is questionable since it is similar to a story told about Menaechmus and Alexander the Great. Euclid died c. 270 BC in Alexandria. In the only other key reference to Euclid, Pappus of Alexandria mentioned that Apollonius "spent a long time with the pupils of Euclid at Alexandria, it was thus that he acquired such a scientific habit of thought" c. 247–222 BC. Because the lack of biographical information is unusual for the period, some researchers have proposed that Euclid was not a historical personage, that his works were written by a team of mathematicians who took the name Euclid from Euclid of Megara. However, this hypothesis is not well accepted by scholars and there is little evidence in its favor.
Although many of the results in Elements originated with earlier mathematicians, one of Euclid's accomplishments was to present them in a single, logically coherent framework, making it easy to use and easy to reference, including a system of rigorous mathematical proofs that remains the basis of mathematics 23 centuries later. There is no mention of Euclid in the earliest remaining copies of the Elements, most of the copies say they are "from the edition of Theon" or the "lectures of Theon", while the text considered to be primary, held by the Vatican, mentions no author; the only reference that historians rely on of Euclid having written the Elements was from Proclus, who in his Commentary on the Elements ascribes Euclid as its author. Although best known for its geometric results, the Elements includes number theory, it considers the connection between perfect numbers and Mersenne primes, the infinitude of prime numbers, Euclid's lemma on factorization, the Euclidean algorithm for finding the greatest common divisor of two numbers.
The geometrical system described in the Elements was long known as geometry, was considered to be the only geometry possible. Today, that system is referred to as Euclidean geometry to distinguish it from other so-called non-Euclidean geometries that mathematicians discovered in the 19th century; the Papyrus Oxyrhynchus 29 is a fragment of the second book of the Elements of Euclid, unearthed by Grenfell and Hunt 1897 in Oxyrhynchus. More recent scholarship suggests a date of 75–125 AD; the classic translation of T. L. Heath, reads: If a straight line be cut into equal and unequal segments, the rectangle contained by the unequal segments of the whole together with the square on the straight line between the points of section is equal to the square on the half. In addition to the Elements, at least five works of Euclid have survived to the present day, they follow the same logical structure with definitions and proved propositions. Data deals with the nature and implications of "given" information in geometrical problems.
Agora is a 2009 Spanish English-language historical drama film directed by Alejandro Amenábar and written by Amenábar and Mateo Gil. The biopic stars Rachel Weisz as Hypatia, a female mathematician and astronomer in late 4th-century Roman Egypt, who investigates the flaws of the geocentric Ptolemaic system and the heliocentric model that challenges it. Surrounded by religious turmoil and social unrest, Hypatia struggles to save the knowledge of classical antiquity from destruction. Max Minghella co-stars as Davus, Hypatia's father's slave, Oscar Isaac as Hypatia's student, prefect of Alexandria, Orestes; the story uses historical fiction to highlight the relationship between religion and science at the time amidst the decline of Greco-Roman polytheism and the Christianization of the Roman Empire. The title of the film takes its name from the agora, a public gathering place in ancient Greece, similar to the Roman forum; the film was produced by Fernando Bovaira and shot on the island of Malta from March to June 2008.
Justin Pollard, co-author of The Rise and Fall of Alexandria, was the historical adviser for the film. Agora was screened out of competition at the 2009 Cannes Film Festival in May, opened in Spain on October 9, 2009 becoming the highest-grossing film of the year for that country. Although the film had difficulty finding distribution, it was released country by country throughout late 2009 and early 2010; the film received a 53% overall approval rating from Rotten Tomatoes and seven Goya Awards in Spain, including Best Original Screenplay. It was awarded the Alfred P. Sloan Foundation Feature Film Prize at the Hamptons International Film Festival. In 391 AD, Alexandria is part of the Roman Empire, Greek philosopher Hypatia is a teacher at the Platonic school, where future leaders are educated. Hypatia is the daughter of the director of the Musaeum of Alexandria. Hypatia, her father's slave and two of her pupils and Synesius, are immersed in the changing political and social landscape, she rejects Orestes's love.
Davus is interested in science. He is secretly in love with her. Meanwhile, social unrest begins challenging the Roman rule of the city as Pagans and Christians come into conflict; when the Christians start defiling the statues of the pagan gods, the pagans, including Orestes and Theon, ambush the Christians. However, in the ensuing battle, the pagans unexpectedly find themselves outnumbered by a large Christian mob. Theon is gravely injured, Hypatia and the pagans take refuge in the Library of the Serapeum; the Christian siege of the library ends when an envoy of the Roman Emperor Theodosius I declares that the pagans are pardoned, but the Christians shall be allowed to take possession of the library. Hypatia and the pagans flee while trying to save the most important scrolls before the Christians overtake the library and destroy its contents. Davus chooses to join the Christian forces, he returns with a gladius and sexually assaults her, but he begins to sob and offers his sword to her. However, she tells him that he is free.
Several years Orestes, now converted to Christianity, is prefect of Alexandria. Hypatia continues to investigate the motions of the Sun, the Moon, the five known "wanderers", the stars; some Christians ridicule the thinking that the Earth is a sphere by arguing that people far from the top would fall off the Earth. When they ask Davus what his opinion is, he avoids conflict by saying that only God knows these things. Hypatia investigates the heliocentric model of the solar system proposed by Aristarchus of Samos by having an object dropped from the mast of a moving ship which demonstrates that a possible motion of the Earth would not affect the motion, relative to Earth, of a falling object on Earth. However, due to religious objections against heliocentrism, the Christians have now forbidden Hypatia to teach at the school; the Christians and the Jews come into violent conflict. The leader of the Christians, views Hypatia as having too much influence over Orestes and stages a public ceremony intended to force Orestes to subjugate her.
Hypatia's former pupil, now the Bishop of Cyrene, comes to her rescue as a religious authority counterweight but says he cannot help her unless she accepts Christianity. Hypatia theorizes that the Earth orbits around the Sun in an elliptic orbit, not a circular orbit, with the Sun at one of the foci. Cyril convinces a mob of Christians that Hypatia is a witch, they vow to kill her. Davus tries to run ahead to warn Hypatia, they strip Hypatia and are about to skin her alive until Davus persuades the mob otherwise, they decide to stone her instead. When the mob goes outside to collect stones, Davus suffocates her to spare her the pain of being stoned and tells the mob that she fainted. Davus leaves. Rachel Weisz as Hypatia of Alexandria. Weisz was a fan of Amenábar's work when she received the script, was interested in the role. Although she had not heard of Hypatia before, she felt that her history was still relevant to the contemporary world: "Really, nothing has changed. I mean, we have huge technological advances and medical advances, but in terms of people killing each other in the name of God, fundamentalism still abounds.
And in certain cultures, women are still second-class citizens, they’re denied education." Weisz wanted to delve more into Hypatia's sexuality and her desires. She received science lessons to help inform her depiction of the character. At the 2009 Cannes Film Festival, Weisz spoke about her style and approach: "There's no way we c
The Ancient Greek language includes the forms of Greek used in Ancient Greece and the ancient world from around the 9th century BCE to the 6th century CE. It is roughly divided into the Archaic period, Classical period, Hellenistic period, it is succeeded by medieval Greek. Koine is regarded as a separate historical stage of its own, although in its earliest form it resembled Attic Greek and in its latest form it approaches Medieval 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 and philosophers, it has contributed many words to English vocabulary and has been a standard subject of study in educational institutions of the Western world since the Renaissance. This article contains information about the Epic and Classical periods of the language. Ancient Greek was a pluricentric language, divided into many dialects; the main dialect groups are Attic and Ionic, Aeolic and Doric, many of them with several subdivisions.
Some dialects are found in standardized literary forms used in literature, while others are attested only in inscriptions. There are several historical forms. Homeric Greek is a literary form of Archaic Greek used in the epic poems, the "Iliad" and "Odyssey", in poems by other authors. Homeric Greek had significant differences in grammar and pronunciation from Classical Attic and other Classical-era dialects; 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, they differ in some of the detail. The only attested dialect from this period is Mycenaean Greek, but its relationship to the historical dialects and the historical circumstances of the times imply that the overall groups existed in some form. Scholars assume that major Ancient Greek period dialect groups developed not than 1120 BCE, at the time of the Dorian invasion—and that their first appearances as precise alphabetic writing began in the 8th century BCE.
The invasion would not be "Dorian" unless the invaders had some cultural relationship to the historical Dorians. The invasion is known to have displaced population to the Attic-Ionic regions, who regarded themselves as descendants of the population displaced by or contending with the Dorians; the Greeks of this period believed there were three major divisions of all Greek people—Dorians and Ionians, each with their own defining and distinctive dialects. Allowing for their oversight of Arcadian, an obscure mountain dialect, Cypriot, far from the center of Greek scholarship, this division of people and language is quite similar to the results of modern archaeological-linguistic investigation. One standard formulation for the dialects is: West vs. non-west Greek is the strongest marked and earliest division, with non-west in subsets of Ionic-Attic and Aeolic vs. Arcadocypriot, or Aeolic and Arcado-Cypriot vs. Ionic-Attic. Non-west is called East Greek. Arcadocypriot descended more from the Mycenaean Greek of the Bronze Age.
Boeotian had come under a strong Northwest Greek influence, can in some respects be considered a transitional dialect. Thessalian had come under Northwest Greek influence, though to a lesser degree. Pamphylian Greek, spoken in a small area on the southwestern coast of Anatolia and little preserved in inscriptions, may be either a fifth major dialect group, or it is Mycenaean Greek overlaid by Doric, with a non-Greek native influence. Most of the dialect sub-groups listed above had further subdivisions equivalent to a city-state and its surrounding territory, or to an island. Doric notably had several intermediate divisions as well, into Island Doric, Southern Peloponnesus Doric, Northern Peloponnesus Doric; the Lesbian dialect was Aeolic Greek. All the groups were represented by colonies beyond Greece proper as well, these colonies developed local characteristics under the influence of settlers or neighbors speaking different Greek dialects; the dialects outside the Ionic group are known from inscriptions, notable exceptions being: fragments of the works of the poet Sappho from the island of Lesbos, in Aeolian, the poems of the Boeotian poet Pindar and other lyric poets in Doric.
After the conquests of Alexander the Great in the late 4th century BCE, a new international dialect known as Koine or Common Greek developed based on Attic Greek, but with influence from other dialects. This dialect replaced most of the older dialects, although Doric dialect has survived in the Tsakonian language, spoken in the region of modern Sparta. Doric has passed down its aorist terminations into most verbs of Demotic Greek. By about the 6th century CE, the Koine had metamorphosized into Medieval Greek. Ancient Macedonian was an Indo-European language at least related to Greek, but its exact relationship is unclear because of insufficient data: a dialect of Greek; the Macedonian dialect (or l
Aratus was a Greek didactic poet. His major extant work is his hexameter poem Phenomena, the first half of, a verse setting of a lost work of the same name by Eudoxus of Cnidus, it describes other celestial phenomena. The second half is called the Diosemeia, is chiefly about weather lore. Although Aratus was somewhat ignorant of Greek astronomy, his poem was popular in the Greek and Roman world, as is proved by the large number of commentaries and Latin translations, some of which survive. There are several accounts of Aratus' life by anonymous Greek writers, the Suda and Eudocia mention him. From these it appears, he is known to have studied with Menecrates in Philitas in Cos.. As a disciple of the Peripatetic philosopher Praxiphanes, in Athens, he met the Stoic philosopher Zeno, as well as Callimachus of Cyrene and Menedemus, the founder of the Eretrian school. About 276 BC Aratus was invited to the court of the Macedonian king Antigonus II Gonatas, whose victory over the Gauls in 277 Aratus set to verse.
Here he wrote Phenomena. He spent some time at the court of Antiochus I Soter of Syria, but subsequently returned to Pella in Macedon, where he died sometime before 240/239, his chief pursuits were medicine and philosophy. Several poetical works on various subjects, as well as a number of prose epistles, are attributed to Aratus, but none of them have come down to us, except his two astronomical poems in hexameter; these have been joined together as if parts of the same work. The Phenomena appears to be based on two prose works—Phenomena and Enoptron —by Eudoxus of Cnidus, written about a century earlier. We are told by the biographers of Aratus that it was the desire of Antigonus to have them turned into verse, which gave rise to the Phenomena of Aratus; the purpose of the Phenomena is to give an introduction to the constellations, with the rules for their risings and settings. The positions of the constellations, north of the ecliptic, are described by reference to the principal groups surrounding the north pole, whilst Orion serves as a point of departure for those to the south.
The immobility of the earth, the revolution of the sky about a fixed axis are maintained. The opening of the poem asserts the dependence of all things upon Zeus. From the lack of precision in the descriptions, it would seem that Aratus was neither a mathematician nor observer or, at any rate, that in this work he did not aim at scientific accuracy, he not only represents the configurations of particular groups incorrectly, but describes some phenomena which are inconsistent with any one supposed latitude of the spectator, others which could not coexist at any one epoch. These errors are to be attributed to Eudoxus himself, to the way in which Aratus has used the materials supplied by him. Hipparchus, a scientific astronomer and observer, has left a commentary upon the Phenomenas of Eudoxus and Aratus, accompanied by the discrepancies which he had noticed between his own observations and their descriptions; the Diosemeia consists of forecasts of the weather from astronomical phenomena, with an account of its effects upon animals.
It appears to be an imitation of Hesiod, to have been imitated by Virgil in some parts of the Georgics. The materials are said to be taken wholly from Aristotle's Meteorologica, from the work of Theophrastus, On Weather Signs, from Hesiod. Nothing is said in either poem about Hellenistic astrology; the two poems were popular both in the Greek and Roman world, as is proved by the number of commentaries and Latin translations. He enjoyed immense prestige among Hellenistic poets, including Theocritus and Leonidas of Tarentum; this assessment was picked up including Ovid and Virgil. Latin versions were made by none other than Cicero, the member of the imperial Julio-Claudian dynasty Germanicus, the less-famous Avienus. Quintilian was less enthusiastic. Aratus was cited by the author of Acts, in 17.28, where he relates Saint Paul's address on the Areopagus. Paul, speaking of God, quotes the fifth line of Aratus's Phenomena: Authors of twenty-seven commentaries are known. An Arabic translation was commissioned in the ninth century by the Caliph Al-Ma'mun.
He is cited by Stephanus of Byzantium and Stobaeus. Several accounts of his life are extant, by anonymous Greek writers; the crater Aratus on the Moon and the minor planet 12152 Aratus are named in his honour. The H
An astrolabe is an elaborate inclinometer used by astronomers and navigators to measure the altitude above the horizon of a celestial body, day or night. It can be used to identify stars or planets, to determine local latitude given local time, to survey, or to triangulate, it was used in classical antiquity, the Islamic Golden Age, the European Middle Ages and the Age of Discovery for all these purposes. The astrolabe's importance not only comes from the early development of astronomy, but is effective for determining latitude on land or calm seas. Although it is less reliable on the heaving deck of a ship in rough seas, the mariner's astrolabe was developed to solve that problem. OED gives the translation "star-taker" for the English word astrolabe and traces it through medieval Latin to the Greek word astrolabos, from astron "star" and lambanein "to take". In the medieval Islamic world the Arabic word "al-Asturlāb" was given various etymologies. In Arabic texts, the word is translated as "ākhdhu al-Nujuum", a direct translation of the Greek word.
Al-Biruni quotes and criticizes medieval scientist Hamzah al-Isfahani who stated: "asturlab is an arabization of this Persian phrase". In medieval Islamic sources, there is a folk etymology of the word as "lines of lab", where "Lab" refers to a certain son of Idris; this etymology is mentioned by a 10th-century scientist rejected by al-Khwarizmi. An early astrolabe was invented in the Hellenistic civilization by Apollonius of Perga between 220 and 150 BC attributed to Hipparchus; the astrolabe was a marriage of the planisphere and dioptra an analog calculator capable of working out several different kinds of problems in astronomy. Theon of Alexandria wrote a detailed treatise on the astrolabe, Lewis argues that Ptolemy used an astrolabe to make the astronomical observations recorded in the Tetrabiblos; the invention of the plane astrolabe is sometimes wrongly attributed to Theon's daughter Hypatia, but it is, in fact, known to have been in use at least 500 years before Hypatia was born. The misattribution comes from a misinterpretation of a statement in a letter written by Hypatia's pupil Synesius, which mentions that Hypatia had taught him how to construct a plane astrolabe, but does not state anything about her having invented it herself.
Astrolabes continued in use in the Greek-speaking world throughout the Byzantine period. About 550 AD, Christian philosopher John Philoponus wrote a treatise on the astrolabe in Greek, the earliest extant treatise on the instrument. Mesopotamian bishop Severus Sebokht wrote a treatise on the astrolabe in the Syriac language in the mid-7th century. Sebokht refers to the astrolabe as being made of brass in the introduction of his treatise, indicating that metal astrolabes were known in the Christian East well before they were developed in the Islamic world or in the Latin West. Astrolabes were further developed in the medieval Islamic world, where Muslim astronomers introduced angular scales to the design, adding circles indicating azimuths on the horizon, it was used throughout the Muslim world, chiefly as an aid to navigation and as a way of finding the Qibla, the direction of Mecca. Eighth-century mathematician Muhammad al-Fazari is the first person credited with building the astrolabe in the Islamic world.
The mathematical background was established by Muslim astronomer Albatenius in his treatise Kitab az-Zij, translated into Latin by Plato Tiburtinus. The earliest surviving astrolabe is dated AH 315. In the Islamic world, astrolabes were used to find the times of sunrise and the rising of fixed stars, to help schedule morning prayers. In the 10th century, al-Sufi first described over 1,000 different uses of an astrolabe, in areas as diverse as astronomy, navigation, timekeeping, Salat, etc; the spherical astrolabe was a variation of both the astrolabe and the armillary sphere, invented during the Middle Ages by astronomers and inventors in the Islamic world. The earliest description of the spherical astrolabe dates back to Al-Nayrizi. In the 12th century, Sharaf al-Dīn al-Tūsī invented the linear astrolabe, sometimes called the "staff of al-Tusi", "a simple wooden rod with graduated markings but without sights, it was furnished with a plumb line and a double chord for making angular measurements and bore a perforated pointer".
The geared mechanical astrolabe was invented by Abi Bakr of Isfahan in 1235. Herman Contractus, the abbot of Reichman Abbey, examined the use of the astrolabe in Mensura Astrolai during the 11th century. Peter of Maricourt wrote a treatise on the construction and use of a universal astrolabe in the last half of the 13th century entitled Nova compositio astrolabii particularis. Universal astrolabes can be found at the History of Science Museum in Oxford. English author Geoffrey Chaucer compiled A Treatise on the Astrolabe for his son based on a work by Messahalla or Ibn al-Saffar; the same source was translated by others. The first printed book on the astrolabe was Composition and Use of Astrolabe by Christian of Prachatice using Messahalla, but original. In 1370, the first Indian treatise on the astrolabe was written by the Jain astronomer Mahendra Suri. A simplified astrolabe, known as a balesilha, was used by sailors to get an accurate reading of latitude while out to sea; the use of
The Elements is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC. It is a collection of definitions, postulates and mathematical proofs of the propositions; the books cover plane and solid Euclidean geometry, elementary number theory, incommensurable lines. Elements is the oldest extant large-scale deductive treatment of mathematics, it has proven instrumental in the development of logic and modern science, its logical rigor was not surpassed until the 19th century. Euclid's Elements has been referred to as the most successful and influential textbook written, it was one of the earliest mathematical works to be printed after the invention of the printing press and has been estimated to be second only to the Bible in the number of editions published since the first printing in 1482, with the number reaching well over one thousand. For centuries, when the quadrivium was included in the curriculum of all university students, knowledge of at least part of Euclid's Elements was required of all students.
Not until the 20th century, by which time its content was universally taught through other school textbooks, did it cease to be considered something all educated people had read. Scholars believe that the Elements is a compilation of propositions based on books by earlier Greek mathematicians. Proclus, a Greek mathematician who lived around seven centuries after Euclid, wrote in his commentary on the Elements: "Euclid, who put together the Elements, collecting many of Eudoxus' theorems, perfecting many of Theaetetus', bringing to irrefragable demonstration the things which were only somewhat loosely proved by his predecessors". Pythagoras was the source for most of books I and II, Hippocrates of Chios for book III, Eudoxus of Cnidus for book V, while books IV, VI, XI, XII came from other Pythagorean or Athenian mathematicians; the Elements may have been based on an earlier textbook by Hippocrates of Chios, who may have originated the use of letters to refer to figures. In the fourth century AD, Theon of Alexandria produced an edition of Euclid, so used that it became the only surviving source until François Peyrard's 1808 discovery at the Vatican of a manuscript not derived from Theon's.
This manuscript, the Heiberg manuscript, is from a Byzantine workshop around 900 and is the basis of modern editions. Papyrus Oxyrhynchus 29 is a tiny fragment of an older manuscript, but only contains the statement of one proposition. Although known to, for instance, Cicero, no record exists of the text having been translated into Latin prior to Boethius in the fifth or sixth century; the Arabs received the Elements from the Byzantines around 760. 800. The Byzantine scholar Arethas commissioned the copying of one of the extant Greek manuscripts of Euclid in the late ninth century. Although known in Byzantium, the Elements was lost to Western Europe until about 1120, when the English monk Adelard of Bath translated it into Latin from an Arabic translation; the first printed edition appeared in 1482, since it has been translated into many languages and published in about a thousand different editions. Theon's Greek edition was recovered in 1533. In 1570, John Dee provided a respected "Mathematical Preface", along with copious notes and supplementary material, to the first English edition by Henry Billingsley.
Copies of the Greek text still exist, some of which can be found in the Vatican Library and the Bodleian Library in Oxford. The manuscripts available are of variable quality, invariably incomplete. By careful analysis of the translations and originals, hypotheses have been made about the contents of the original text. Ancient texts which refer to the Elements itself, to other mathematical theories that were current at the time it was written, are important in this process; such analyses are conducted by J. L. Heiberg and Sir Thomas Little Heath in their editions of the text. Of importance are the scholia, or annotations to the text; these additions, which distinguished themselves from the main text accumulated over time as opinions varied upon what was worthy of explanation or further study. The Elements is still considered a masterpiece in the application of logic to mathematics. In historical context, it has proven enormously influential in many areas of science. Scientists Nicolaus Copernicus, Johannes Kepler, Galileo Galilei, Sir Isaac Newton were all influenced by the Elements, applied their knowledge of it to their work.
Mathematicians and philosophers, such as Thomas Hobbes, Baruch Spinoza, Alfred North Whitehead, Bertrand Russell, have attempted to create their own foundational "Elements" for their respective disciplines, by adopting the axiomatized deductive structures that Euclid's work introduced. The austere beauty of Euclidean geometry has been seen by many in western culture as a glimpse of an otherworldly system of perfection and certainty. Abraham Lincoln kept a copy of Euclid in his saddlebag, studied it late at night by lamplight. Edna St. Vincent Millay wrote in her sonnet "Euclid alone has looked on Beauty bare", "O