Geometry.Net - Mathematicians: Greek Mathematics

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 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

Extractions: These pages are devoted to medicine, biology, chemistry, physics, engineering, mathematics, industry, etc 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
¥j§ÆÃ¾¼Æ¾Ç¡]Ancient Greek Mathematics¡^
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http://www.csjh.tpc.edu.tw/~doing/h-edu-date/edu-d-date/edu-d-2/2-3.htm

Extractions: ¥j§ÆÃ¾¼Æ¾Ç¡] Ancient Greek mathematics¡^ 325¦~¡A¨È¾ú¤s¤j¤j«Ò¡] Alexander the Great¡^©ºªA¤F§ÆÃ¾©MªñªF¡B®J¤Î¡A ¥L¦b¥§Ã¹ªe¤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§ÆÃ¾¤å¤Æªº¬ù§ô¤U¡A¥vºÙ§ÆÃ¾¤Æ°ê®a¡C²Îªv¤F®J¤Îªº¦«°Ç±K¤@¥@¡] Ptolemy the First¡^¤j¤O´£Ò¾Ç³N¡A¦h¤èºôÃ¹¤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
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

Extractions: 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 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.
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/

Extractions: 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
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
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/
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

Extractions: 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
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

Extractions: CONTACT: Stanford University News Service (415) 723-2558 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.
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
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

Extractions: 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) Simple applications: [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).
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

Extractions: (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.
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

Extractions: 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
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

Extractions: Software Documentation 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.
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

Extractions: 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. 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 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
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

Extractions: 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.
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
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

Extractions: Stanford University 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.
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

Extractions: 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
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

Extractions: 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 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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