61. PHILOSOPHY OF SCIENCE History of greek mathematics. Basic Ideas in greek mathematics. History of MathematicsHome Page. Basic Ideas in greek mathematics with section on Zeno. http://www.anselm.edu/homepage/dbanach/ph31a.htm

Greek Science and The Golden Section Ancient Science and Mathematics Selections from Julia E. Diggins, String, Straightedge, and Shadow Viking Press, New York , 1965. (Illustrations by Corydon Bell) Chapters 8, 9: Thales Chapters 11, 12: Pythagoras and his Theorem Chapter 13: Platonic Solids Chapter 14: The Irrationals ... History of Mathematics Home Page The Golden Section The Golden Mean An extensive site on the Golden Section in architecture and art. Lots of diagrams and links. A good place to start. The Golden Section in Art and Architecture Jill Britton’s excellent slide show introduction to the Golden Mean. Fibonacci Numbers and The Golden Section One of the best and most extensive sites I’ve found. Ron Knott's Surrey University Site The Golden Proportion Examples of the proportion in nature, art, and architecture. Sacred Geometry Home Page A more general account of the relationship of geometric form to beauty. The page is very well done and gives a good idea of the Neoplatonic view of form and beauty. Mid_Atlantic Geomancy Sacred Geometry Page A very nice simple account of some of the most persistent mathematical forms in Art and Nature. Nice Images!!

62. Greek And Roman Medicine, Science, Mathematics And Industry Science and Technology; Greek Astronomy; greek mathematics and Its ModernHeirs; Greek Science; History of Mathematics; Mathematicians Born http://users.ipa.net/~tanker/science.htm

Catiline's Hard Sciences Page These pages are devoted to medicine, biology, chemistry, physics, engineering, mathematics, industry, etc Archimedes Archimedes Archimedia Bibliographia Archimedeana gone 4/8/01 Ancient Metallurgy Research Group Ancient Navigation and Shipbuilding in the Greek and Roman World Ancient Technology gone 48/01 Antiqua Medicina Catapults in Greek and Roman Antiquity Earliest Uses of Various Mathematical Symbols L'evolution des langues de la communaute scientifique ... Roman Ships gone 4/8/01 Spice Pages A Taste of the Ancient World University Chemistry I: Greek Theory and Roman Practice Return to Bellum Catilinae Home Page

63. ¥j§Æþ¼Æ¾Ç¡]Ancient Greek Mathematics¡^ The summary for this Chinese (Traditional) page contains characters that cannot be correctly displayed in this language/character set. http://www.csjh.tpc.edu.tw/~doing/h-edu-date/edu-d-date/edu-d-2/2-3.htm

¥j§Æ¾¼Æ¾Ç¡] Ancient Greek mathematics¡^ 325¦~¡A¨È¾ú¤s¤j¤j«Ò¡] Alexander the Great¡^©ºªA¤F§Æ¾©MªñªF¡B®J¤Î¡A ¥L¦b¥§¹ªe¤fªþªñ«Ø¥ß¤F¨È¾ú¤s¤j¨½¨È«°¡]Alexandria ¡^¡C¨È¾ú¤s¤j¤j«Ò¦º«á¡]323B.C.¡^¡A¥L³Ð«Øªº«Ò°ê ¤Àµõ¬°¤T­Ó¿W¥ßªº¤ý°ê¡A¦ý¤´Áp¦X¦b¥j§Æ¾¤å¤Æªº¬ù§ô¤U¡A¥vºÙ§Æ¾¤Æ°ê®a¡C²Îªv¤F®J¤Îªº¦«°Ç±K¤@¥@¡] Ptolemy the First¡^¤j¤O´£­Ò¾Ç³N¡A¦h¤èºô¹¤H¤~¡A¦b¨È¾ú¤s¤j¨½¨È«Ø¥ß°_¤@®yªÅ«e§»°¶ªº³Õª«À]©M¹Ï ®ÑÀ]¡A¨Ï³o¸Ì¨ú¥N¶®¨å¡A¤@ÅD¦Ó¦¨¬°¥j¥N¥@¬Éªº¾Ç³N¤å¤Æ¤¤¤ß¡AÁcºa´X¹F¤d¦~¤§¤[¡I ¡@¡@§Æ¾¤Hªº«ä·Q²@µLº°Ý¦a¨ü¨ì¤F®J¤Î©M¤Ú¤ñ­Ûªº¼vÅT¡A¦ý¬O¥L­Ì³Ð¥ßªº¼Æ¾Ç»P«e¤Hªº¼Æ¾Ç¬Û¤ñ¸û¡A«o ¦³µÛ¥»½èªº°Ï§O¡A¨äµo®i¥i¤À¬°¶®¨å®É´Á©M¨È¾ú¤s¤j®É´Á¨â­Ó¶¥¬q¡C ¤@¡B¶®¨å®É´Á¡] 600B.C.-300B.C.¡^ ¡@¡@³o¤@®É´Á©l©ó®õ°Ç´µ¡] ¡@¡@¤½¤¸«e ¡@¡@®J§Q¨È¾Ç¬£ªºªÛ¿Õ¡] ¡@¡@­õ¾Ç®a¬f©Ô¹Ï¡] ¡@ ¤G¡B¨È¾ú¤s¤j®É´Á¡] 300B.C.-641A.D.¡^ ¡@¡@³o¤@¶¥¬q¥H¤½¤¸«e Euclid ¡^¡Bªü°ò¦Ì¼w¡]Archimedes¡^¤Îªüªi¬¥¥§¯Q´µ¡] Appollonius¡^¡C ¡@¡@¼Ú´X¨½±oÁ`µ²¥j¨å§Æ¾¼Æ¾Ç¡A¥Î¤½²z¤èªk¾ã²z´X¦ó¾Ç¡A¼g¦¨ 13¨÷¡m´X¦ó­ì¥»¡n¡]Elements¡^¡C³o³¡¹º ®É¥N¾ú¥v¥¨µÛªº·N¸q¦b©ó¥¦¾ð¥ß¤F¥Î¤½²zªk«Ø¥ß°_ºt¶¼Æ¾ÇÅé¨tªº³Ì¦­¨å½d¡C ¡@¡@ªü°ò¦Ì¼w¬O¥j¥N³Ì°¶¤jªº¼Æ¾Ç®a¡B¤O¾Ç®a©M¾÷±ñ®v¡C¥L±N¹êÅ窺¸gÅç¬ã¨s¤èªk©M´X¦ó¾Çªººt¶±À²z¤è ªk¦³¾÷¦aµ²¦X°_¨Ó¡A¨Ï¤O¾Ç¬ì¾Ç¤Æ¡A¬J¦³©w©Ê¤ÀªR¡A¤S¦³©w¶q­pºâ¡Cªü°ò¦Ì¼w¦b¯Â¼Æ¾Ç»â°ì¯A¤Îªº½d³ò¤] «Ü¼s¡A¨ä¤¤¤@¶µ­«¤j°^Äm¬O«Ø¥ß¦hºØ¥­­±¹Ï§Î­±¿n©M±ÛÂàÅéÅé¿nªººë±K¨D¿nªk¡AÄ­§tµÛ·L¿n¤Àªº«ä·Q¡C ¡@¡@¨È¾ú¤s¤j¹Ï®ÑÀ]À]ªø®J©Ô¦«¶ë¥§¡] Eratosthenes¡^¤]¬O³o¤@®É´Á¦³¦W±æªº¾ÇªÌ¡Cªüªi¬¥¥§¯Q´µªº¡m¶êÀ@ ¦±½u½×¡n¡]Conic Sections¡^§â«e½ú©Ò±o¨ìªº¶êÀ@¦±½uª¾Ñ¡A¤©¥HÄY®æªº¨t²Î¤Æ¡A¨°µ¥X·sªº°^Äm¡A¹ï17 ¥@¬ö¼Æ¾Çªºµo®i¦³µÛ¥¨¤jªº¼vÅT¡C

64. Mathematics (Rome Reborn: The Vatican Library & Renaissance Culture) greek mathematics and its Modern Heirs. For over a thousand yearsfromthe fifth century BC to the fifth century ADGreek mathematicians http://www.loc.gov/exhibits/vatican/math.html

The Library of Congress Exhibitions HOME Exhibition Sections: Introduction The Vatican Library Archaeology Humanism ... Credits MATHEMATICS Greek Mathematics and its Modern Heirs Ptolemy's Geography Greek Astronomy Greek Mathematics and its Modern Heirs Euclid, Elements In Greek Parchment Ninth century Euclid's Elements, written about 300 B.C., a comprehensive treatise on geometry, proportions, and the theory of numbers, is the most long-lived of all mathematical works. This manuscript preserves an early version of the text. Shown here is Book I Proposition 47, the Pythagorean Theorem: the square on the hypotenuse of a right triangle is equal to the sum of the squares on the sides. This is a famous and important theorem that receives many notes in the manuscript. Archimedes, Works In Latin Translated by Jacobus Cremonensis ca. 1458 In the early 1450s, Pope Nicholas V commissioned Jacobus de Sancto Cassiano Cremonensis to make a new translation of Archimedes with the commentaries of Eutocius. This became the standard version and was finally printed in 1544. This early and very elegant manuscript may have been in the possession of Piero della Francesca before coming to the library of the Duke of Urbino. The pages displayed here show the beginning of Archimedes' On Conoids and Spheroids with highly ornate, and rather curious, illumination.

65. Ken SAITO's Home Page Bibliography of greek mathematics I have revised the greek mathematics section (byLen Berggren) of the socalled Dauben Bibliography, in its revised Edition http://wwwhs.cias.osakafu-u.ac.jp/~ksaito/

Welcome to Ken SAITO's home page Last update 23/Feb/2001 Bibliography of Greek mathematics: I have revised the Greek mathematics section (by Len Berggren) of the so-called Dauben Bibliography, in its revised Edition on CD-ROM appeared in 2000 (ed. Albert C. Lewis). The official name of this bibliography is: The History of Mathematics from Antiquity to the Present: A Selective Annotated Bibliography. You can find and order this CD-ROM from American Mathematical Society. Index of Propositions used in the Conics Index of the Propositions Used in Book 7 of Pappus' Collection List of publication ... Japanese page here

66. A History Of Greek Mathematics, Volume I: From Thales To Euclid Other Editions: A History of greek mathematics, Volume I From Thales to Euclid Other EditionsPaperback Paperback 464 pages Vol 1 (June 1981). http://www.data4all.com/list/500/512000/0486240738

A History of Greek Mathematics, Volume I: From Thales to Euclid Other Editions: Paperback Paperback - 464 pages Vol 1 (June 1981) Information, reviews, pricing for A History of Greek Mathematics, Volume I: From Thales to Euclid Other Editions: Paperback Paperback - 464 pages Vol 1 (June 1981) Greek Astronomy Greek Mathematical Thought and the Origin of Algebra Geometry of Rene Descartes

67. The Ancient World Web: Science/Mathematics greek mathematics This student paper by Chris Weinkopf looks at how the Greeks organizedmathematics into categories Last Site Update 23Nov-1999 Hits 435 http://www.julen.net/ancient/Science/Mathematics/

@import "http://www.julen.net/ancient/ancient-adv.css"; The Science : Mathematics Index The Links Ancient Egypt -Mathematics and the Liberal Arts This is a nicely annotated bibliography of articles. [English] [Last Site Update: 16-Feb-2000 Hits: 812 Rating: 9.00 Votes: 1] Rate It Ancient Mathematics Part of a virtual Vatican exhibit, this site looks at mathematics and astronomy from the point of the Ancients. [English] [Last Site Update: 14-Mar-1999 Hits: 1763 Rating: 5.67 Votes: 3] Rate It Archimedes An extensive collection of Archimedean miscellanea, containing descriptions, sources, and illustrations of all aspects of Archimedes' life, including the siege of Syracuse, the death of Archimedes, Archimedes' tomb, Archimedes' screw, and much more. Entry Added 7-Apr-1999.[English] [Last Site Update: 6-Feb-2002 Hits: 799 Rating: 7.00 Votes: 5] Rate It Babylonian and Egyptian Mathematics Site focuses on the structures of the Math they used. [English] [Last Site Update: 7-Apr-1999 Hits: 1231 Rating: 3.50 Votes: 4] Rate It Egyptian Fractions This site describes how the Egyptians handled fractions, as well as some of the issues surrounding translating them into modern mathematical systems [English]

68. Science Egyptian Mathematics or alternate. greek mathematics its Modern Heirs. ofSt Andrew). Wonders of Ancient greek mathematics (Timothy Reluga). http://pomoerium.com/links/science.htm

Mesopotamian Mathematics History of Mathematics- Babylonia Egyptian Mathematics or alternate Archimedes Chris Rorres ) or alternate or alternate or alternate or alternate or alternate Archimedes page Works of Archimedes Archmede.tm ... Euclid's Elements or alternative Birthplaces of Greek Mathematicians (Univ. of St Andrew) Wonders of Ancient Greek Mathematics (Timothy Reluga) Roman Arithmetic Great mathematicians Library of Alexandria (Ellen N. Brundige) Greek Science History Greek Science (Gregory Crane) Cartography Lexicon of Ancient Geography Ptolemy's Geography Ptolemy's Geography (Library of Congress) Ptolemy (Bill Thayer) Ptolemaeus Weltkarte (Bayerische Staatsbibliothek) Orbis Latinus MapMachine (National Geographic) Fundamentals of Observational Astronomy in Babylonia Ancient Astrology Greek Astronomy Italy's volcanoes ... Fizyka dla wszystkich

69. Wilbur Knorr, Professor Of Philosophy And Classics, Dies At 51 (3/97) professor emeritus at Stanford. He learned Arabic as a way to get additionalinformation about greek mathematics. . . . That's just one http://www.stanford.edu/dept/news/relaged/970319knorr.html

CONTACT: Stanford University News Service (415) 723-2558 Wilbur Knorr, professor of philosophy and classics, dies at 51 Wilbur Richard Knorr, a leading scholar in the field of ancient mathematics, died of melanoma, a form of skin cancer, on March 18 at the Palo Alto Nursing Center. He was 51 and lived in Palo Alto. A memorial service will be held on Monday, March 31, at 4 p.m. in Memorial Church. Knorr came to Stanford in 1979 as an assistant professor in the History of Science program, which he helped to develop. He was promoted to tenure in 1983, holding a joint appointment as an associate professor in the departments of philosophy and classics, and was named a full professor in 1990. "Wilbur was simply one of the world's most distinguished historians of ancient mathematics," said Patrick Suppes, philosophy professor emeritus at Stanford. "He learned Arabic as a way to get additional information about Greek mathematics. . . . That's just one example that illustrates how dedicated he was to the field." Knorr's research over the past several decades was in the study of exact sciences, with special emphasis on the development of classical Greek mathematics and its medieval and modern traditions.

70. Memorial Resolution For Wilbur Knorr Starting in the study of the history of computer science, he soon settled into workon the history of ancient greek mathematics and its medieval continuations. http://www.stanford.edu/dept/facultysenate/archive/1997_1998/reports/105949/1060

MEMORIAL RESOLUTION SenD#4772 =================== Wilbur Richard Knorr

71. Summary: Mathematics In Greek Philosophy Mathematics in Greek Philosophy. Dr. Ess Fall, 1997. Thales Mathematical discoveries Pythagoreansgreek mathematics began in the Milesian school (cf. http://www.drury.edu/ess/philsci/PreSocMath.html

Mathematics in Greek Philosophy Dr. Ess - Fall, 1997 Thales Mathematical discoveries: method for measuring the height of a pyramid (at the time when a person's shadow = his height) "geometry" (Kirk &Raven, 84) Thales generalized these special cases, and in this sense is the father of mathematics as a science, e.g. angles at the base of an isosceles triangle are equal the two sides of an isosceles triangle are equal when two straight lines intersect, opposite angles are equal the angle on the circumference of a circle subtended by the diameter is always a right angle the sum of the angles of a triangle = 2 right angles the sides of triangles with equal angles are always proportional. Simple applications: 1) Using the principle of similar triangles: measuring the distance from shore to ship at sea 2) Measure the height of a pyramid by comparing the length of its shadow with that cast by an object of known height. [Alioto has an interesting quote about the Pythagoreans In other words, with Thales, mathematics became deductive and therefore abstract. The Pythagoreans extended this process of abstraction and in turn infused all of nature with mathematical concepts. It seems that they were the first to stress the idea of number and geometry underlying diverse natural phenomena. The result, adapted and enshrined in Plato's later philosophy along with an ethical, transcendental corollary, was the important recognition that numbers are abstractions, mental concepts, suggested by material things but independent of them. For the early Pythagoreans, however, the physical world was actually constructed from numbers. (36).

72. History Of Mathematics Detailed Syllabus The beginnings of mathematics in Greece, The earliest greek mathematics, the timeof Plato, Aristotle, Euclid and the Elements, Euclid's other works, 3 meetings. http://babbage.clarku.edu/~djoyce/ma105/syll.html

History of Mathematics Detailed Syllabus (For a more general syllabus, see this The chapters refer to our text, A History of Mathematics, an Introduction by Victor J. Katz, Harper Collins College Publishers, New York, second edition, 1998. Other material will be included as appropriate. The actual exercises assigned may not be the ones listed here, but many will. Chapter 1: Ancient mathematics Ancient civilizations, counting, arithmetic computations, Babylonian reciprocal table The Egyptian 2/ n table , linear and equations, simulataneous linear equations , elementary geometry, astronomical calculations, square roots, the Pythagorean theorem, Plimpton 322 tablet 4 meetings. Assignment 1 Asmt. 2: Chap. 1 exercises 5,6,7,10,29,30,33,36. Also tokens of preliterate Mesopotamia. Chapter 2: The beginnings of mathematics in Greece The earliest Greek mathematics, the time of Plato, Aristotle, Euclid and the Elements , Euclid's other works 3 meetings. Exercises: 3-6,10-12,15,20,23,37,41 Euclid's Elements with dragable figures, and a quick trip of the Elements Chapter 3: Archimedes and Apollonius Archimedes and physics, Archimedes and numerical calculations, Archimedes and geometry

73. Euclid (ca. 325-ca. 270 BC) -- From Eric Weisstein's World Of Scientific Biograp BulmerThomas, I. Selections Illustrating the History of greek mathematics, Vol.1 From Thales to Euclid. Heath, T. L. A History of greek mathematics, Vol. http://scienceworld.wolfram.com/biography/Euclid.html

Branch of Science Mathematicians Nationality Greek Euclid (ca. 325-ca. 270 BC) Greek geometer who wrote the Elements , the world's most definitive text on geometry. The book synthesized earlier knowledge about geometry, and was used for centuries in western Europe as a geometry textbook. The text began with definitions, postulates (" Euclid's postulates "), and common opinions, then proceeded to obtain results by rigorous geometric proof. Euclid also proved what is generally known as Euclid's second theorem the number of primes is infinite The beautiful proof Euclid gave of this theorem is still a gem and is generally acknowledged to be one of the "classic" proofs of all times in terms of its conciseness and clarity. In the Elements , Euclid used the method of exhaustion and reductio ad absurdum. He also discussed the so-called Euclidean algorithm for finding the greatest common divisor of two numbers, and is credited with the well-known proof of the Pythagorean theorem Neither the year nor place of his birth have been established, nor the circumstances of his death, although he is known to have lived and worked in Alexandria for much of his life. In addition, no bust which can be verified to be his likeness is known (Tietze 1965, p. 8). Elements Additional biographies: MacTutor (St. Andrews)

74. Expression Calculator Mathematics The spirit of greek mathematics is typified in one of its most lastingachievements, the Elements by Euclid. This is a complete http://excalc.vestris.com/docs/math.html

Software Documentation Chapter 3. Expression Calculator Mathematics Table of Contents Mathematics Algebra Trigonometry Calculus and Analysis ... Functions Mathematics Mathematics is the science of relationships between numbers, between spatial configurations, and abstract structures. The main divisions of pure mathematics include geometry, arithmetic, algebra, calculus, and trigonometry. Mechanics, statistics, numerical analysis, computing, the mathematical theories of astronomy, electricity, optics, thermodynamics, and atomic studies come under the heading of applied mathematics. Prehistoric humans probably learned to count at least up to ten on their fingers. The ancient Egyptians (3rd millennium BC), Sumerians (2000-1500 BC), and Chinese (1500 BC) had systems for writing down numbers and could perform calculations using various types of abacus. They used some fractions. Mathematicians in ancient Egypt could solve simple problems which involved finding a quantity that satisfied a given linear relationship. Sumerian mathematicians knew how to solve problems that involved quadratic equations. The fact that, in a right-angled triangle, the square of the longest side is equal to the sum of the squares of the other two sides (Pythagoras' theorem) was known in various forms in these cultures and also in Vedic India (1500 BC). The first theoretical mathematician is held to be Thales of Miletus (c. 580 BC) who is believed to have proposed the first theorems in plane geometry. His disciple Pythagoras established geometry as a recognized science among the Greeks. Pythagoras began to insist that mathematical statements must be proved using a logical chain of reasoning starting from acceptable assumptions. Undoubtedly the impetus for this demand for logical proof came from the discovery by this group of the surprising fact that the square root of 2 is a number which cannot be expressed as the ratio of two whole numbers. The use of logical reasoning, the methods of which were summarized by Aristotle, enabled Greek mathematicians to make general statements instead of merely solving individual problems as earlier mathematicians had done.

75. History Of Pure Mathematics greek mathematics forms part of the ongoing tradition of Western mathematics, andsome parts of it, notably Euclidean geometry, are still taught in schools. http://www.maths.uwa.edu.au/~schultz/3M3/history.html

A very brief history of pure mathematics The Ishango Bone The very first mathematical document which still survives (in the Institute for Natural Science in Brussels) is the celebrated Ishango bone. This is the 37 000 year-old fibula of a baboon, excavated in central Africa in 1960. It is carved with a curious pattern of grooves and notches, now reliably interpreted to be a diagram representing the moon's phases over a period of several months. One may only speculate on the uses, both rational and religious, of such an object in a huntergatherer society. It has been claimed as evidence that the first mathematicians were women. The clay tablets Much more sophisticated documents are associated with the Mesopotamian societies of some 3 500 years ago. These are numerous baked clay tablets used as astronomical and mathematical tables and school (University?) problem texts. Noteworthy mathematical advances revealed by these texts include linear interpolation to form tables of ephemerides, solution of all quadratic and some cubic equations, construction of "Pythagorean" triples and sophisticated approximations to irrational square roots. The Chinese Civil Service The Han dynasty, (200BC-100AD by our calendar) was a period of remarkable intellectual growth in Ancient China. The only way for the common middle-class youth to advance was by working his (yes, this society had no anti-discrimination laws) way up the ladder of the Civil Service, and the only way to advance from grade to grade was by competitive examination. The four subjects studied were calligraphy, poetry (writing, not reciting), literature and mathematics. If only we were so wise! So remarkably long-lasting texts on arithmetic, geometry and algebra were written. For example an arithmetic text contains the so-called

76. UCLA Distinguished Lecturers Monday, May 21, 2001 MS 6229 400 pm. On the Babylonian Roots of Classicalgreek mathematics . Abstract It is a generally held belief http://www.math.ucla.edu/dls/2001/friberg.html

Distinguished Lecture Series (DLS) People News Media Page UCLA Department of Mathematics Scheduled Lectures Jöran Friberg Professor Emeritus of Mathematics Chalmers University of Technology, Sweden currently visiting Dibner Institute, MIT Monday, May 21, 2001 MS 6229 4:00 p.m. "On the Babylonian Roots of Classical Greek Mathematics" Abstract: It is a generally held belief that classical Greek mathematics arose miraculously out of humble beginnings around 500 BC, invented by a handful of pioneering mathematicians, of which perhaps Pythagoras is the most well known. Recent studies have shown that this view of the origin of mathematics is not correct. Instead, classical Greek mathematics was a more or less direct continuation of the work of many anonymous Mesopotamian mathematicians during the preceding two millennia (Late Babylonian, Old Babylonian, Old Akkadian, Sumerian, and even Proto-Sumerian). This lecture will give a brief and listener-friendly sketch of some popular topics in Mesopotamian mathematics that were taken up and further developed by Greek mathematicians. The lecture begins with a discussion of the incorrectly attributed ^Theorem of Pythagoras^ and its various kinds of known Babylonian predecessors. Other topics mentioned include the Babylonian geometric method of solving quadratic equations, imperfectly copied in Book II of Euclid's Elements, as well as a Babylonian predecessor of Hippocrates' famous squaring of the lune, and various types of Babylonian geometrical constructions related to number theory, perpetuated by Euclid in a book about Division of figures.

77. Euclid Theory (webpage) About greek mathematics RB Jones, Classical GreekMathematics (webpage). back to Books that changed my life . http://www.bayarea.net/~kins/AboutMe/Euclid/EuclidStuff.html

Euclid Sample page from Euclid's Elements ... (Latin translation, 1536) By Euclid Thomas L. Heath, Thirteen Books of Euclid's Elements Ronald Calinger (Editor), Classics of Mathematics David Joyce, Hypertext Version of Euclid's Elements (webpage) About Euclid Thomas L. Heath, History of Greek Mathematics: From Thales to Euclid, Vol 1 Morris Kline, Mathematical Thought from Ancient to Modern Times, Vol 1 Some webpages: (1) Seton Hall University Wolfram Research (WAS a great site) Stockdale H.S. (WAS a great site) Jason H. Martin Univ. of St. Andrews (UK) David Hilbert, Foundations of Geometry Bringing the stuff of Euclid's Elements up to modern standards of rigor, Hilbert's Foundations, like its predecessor in earlier times, served as a model for later efforts of axiomatization. About the axiomatic method Herbert Stachowiak, Rationalismus im Ursprung: Die Genesis des axiomatischen Denkens (Springer Verl., 1971) Stachowiak is professor of philosophy at the University of Berlin. Ian Mueller

78. Archimedes Scholar Finds Something To Holler 'Eureka!' About A scholar of greek mathematics, Netz was hanging out with one of his colleaguesand frequent collaborators, Professor Ken Saito of the Osaka Prefecture http://www.eurekalert.org/pub_releases/2002-11/su-asf110802.php

Public release date: 8-Nov-2002 Contact: John Sanford jsanford@stanford.edu Stanford University Archimedes scholar finds something to holler 'Eureka!' about Reviel Netz, an assistant professor of classics, might not have actually shouted "Eureka!" on a visit last year to the Walters Art Museum in Baltimore, but that's what he was thinking. A scholar of Greek mathematics, Netz was hanging out with one of his colleagues and frequent collaborators, Professor Ken Saito of the Osaka Prefecture University in Japan, when they flew together to Baltimore in January 2001 to look at a recently rediscovered codex of Archimedes treatises. "It was basically just tourism," Netz recalled. On a lark they examined a theretofore unread section of The Method of Mechanical Theorems, which is the book's biggest claim to fame; no other copy of the work is known to exist. What they discovered made their jaws drop. Missing The Archimedes Palimpsest, as the book is called, is in terrible shape. (A palimpsest is a manuscript that has been written on more than once; in this case, a 13th-century Greek prayer book overlays the 10th-century script of the treatises.) The pages have been battered, gouged, scorched by fire and blotched by fungus. Without the use of computer technology, they would be mostly unreadable. But when the palimpsest caught the attention of the great Danish philologist Johan Ludvig Heiberg in 1906, the underlying script was much more legible. At that time, the volume was in a library collection in Constantinople - present-day Istanbul - and, until Heiberg went to examine it, nobody seems to have realized its importance; the book contained the ancient Greek mathematician's previously unknown treatise on The Method of Mechanical Theorems.

79. Myths, Lies, And Truths and other nonEuropean groups. Debate on the Relationship between Egyptianand greek mathematics. OTHER SOURCES. the method of false http://www.math.buffalo.edu/mad/myths_lies.html

MYTHS, LIES, AND TRUTHS ABOUT Third U.S. president Thomas Jefferson in 1792 (when he was Secretary of State): "Comparing them by their faculties of memory, reason, and imagination, it appears to me that in memory [the Negro] are equal to the whites; in reason much inferior, as I think one could scarcely be found capable of tracing and comprehending the investigations of Euclid; and that in imagination they are dull, tasteless, and anomalous." Present day AND ancient achievements contradict such statments. In response, these web page have been created to exhibit accomplishments of the peoples of Africa and the African Diaspora within the Mathematical Sciences. Mathematics Historian W. Rouse Ball : The history of mathematics cannot with certainty be traced back to any school or period before that of the ... Greeks. Mathematician Morris Kline : [The Egyptians] barely recognized mathematics as a distinct discipline ... [Mathematics] finally secured a new grip on life in the highly congenial soil of Greece and waxed strongly for a short period . . . With the decline of Greek civilization the plant remained dormant for a thousand years . . . when he plant was transported to Europe proper and once more imbedded in fertile soil. [Also see Mathematical Thought from Ancient to Modern Times

80. University Of Bristol / Department Of Philosophy / Philosophy Of Mathematics Lecture 1 greek mathematics. greek mathematics Aristotle, Metaphysics, book Mand N, especially ch.3 of M; Fowler, DH, The Mathematics of Plato s Academy; http://www.bris.ac.uk/Depts/Philosophy/UG/ugunits0102/philofmaths.html

PHIL 20020: PHILOSOPHY OF MATHEMATICS Second level unit, Second semester 2001-2002, 10 Credits Lecturer: John Mayberry (Department of Mathematics) Email: j.p.mayberry@bris.ac.uk Unit Instructor and Co-ordinator: Patrick Greenough (Room 1.26, Dept. of Philosophy) Email: Patrick.Greenough@bris.ac.uk, Office Tel: 0117 928 7609 WHAT IS THE PHILOSOPHY OF MATHEMATICS? Many philosophers have taken mathematics to be the paradigm of knowledge, and the reasoning employed in following mathematical proofs is often regarded as the epitome of rational thought. But mathematics is also a rich source of philosophical problems which have been at the centre of epistemology and metaphysics since the beginnings of Western philosophy; among the most important are the following: Do numbers and other mathematical entities exist independently of human cognition? If not then how do we explain the extraordinary applicability of mathematics to science and practical affairs? If so then what kind of things are they and how can we know about them? What is the relationship between mathematics and logic?

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