21. Greek Mathematics greek mathematics. Greeks borrowed Egyptian numbers MORE greek mathematics Elsewhere Greek Language Instruction and Pronunciation. http://ancienthistory.about.com/b/a/026618.htm

zJs=10 zJs=11 zJs=12 zJs=13 zc(5,'jsc',zJs,9999999,'') About History Ancient / Classical History Home ... Trojan War Hero Achilles - Troy zau(256,152,145,'gob','http://z.about.com/5/ad/go.htm?gs='+gs,''); Atlas and Places - Where? Ancient Greece - Greek Ancient Rome - Romans ANE Egypt Persia Israel... ... Help zau(256,138,125,'el','http://z.about.com/0/ip/417/0.htm','');w(xb+xb); Stay Current Subscribe to the About Ancient / Classical History newsletter. Search Ancient / Classical History Greek Mathematics Ancient/Classical History Blog Main September 16, 2003 Greek Mathematics Instead of using the numerals 1, 2, 3, etc., the Greeks used the letters of the alphabet, so they represented one with their first letter, alpha; 2 with their second letter, beta, etc. BBC News reports that the Greek alphabetic numeral system may not have been invented by the Greeks. Instead, the Greeks may have borrowed it from the Egyptians. Greeks 'borrowed Egyptian numbers' MORE: Greek Mathematics Elsewhere: Greek Language Instruction and Pronunciation Email a Friend Display Latest Headlines Read Archives Most Popular Achilles - Greek Hero Achilles The Trojan War Who's Who in Greek Legend - Ancient Greek Heroes - Mythology...

22. A History Of Greek Mathematics, Vol. 2 Click to enlarge A History of greek mathematics, Vol. 2 Sir Thomas Heath. Our Price, $14.95. Availability In Stock. (Usually ships in 24 to 48 hours). Format Book. http://store.doverpublications.com/0486240746.html

American History, American...... American Indians Anthropology, Folklore, My...... Antiques Architecture Art Bridge and Other Card Game...... Business and Economics Chess Children Clip Art and Design on CD-...... Cookbooks, Nutrition Crafts Detective, Ghost , Superna...... Dover Patriot Shop Ethnic Interest Features Gift Certificates Gift Ideas History, Political Science...... Holidays Humor Languages and Linguistics Literature Magic, Legerdemain Military History, Weapons ...... Music Nature Performing Arts, Drama, Fi...... Philosophy and Religion Photography Posters Puzzles, Amusement, Recrea...... Science and Mathematics Sociology, Anthropology, M...... Sports, Out-of-Door Activi...... Stationery, Gift Sets Stationery, Seasonal Books...... Summer Fun Shop Summer Reading Shop Travel and Adventure Women's Studies By Subject Science and Mathematics General Science A History of Greek Mathematics, Vol. 2 Sir Thomas Heath Our Price Availability: In Stock (Usually ships in 24 to 48 hours) Format: Book ISBN: Page Count: Dimensions: 5 3/8 x 8 1/2 Volume 2 of an authoritative coverage of essentials of mathematics, every important innovation, every important figure-Euclid, Apollonius, others. Total in set: 262 illustrations. Buy Now!

23. A History Of Greek Mathematics, Vol. 1 Click to enlarge A History of greek mathematics, Vol. 1 Sir Thomas Heath. Our Price, $17.95. Availability In Stock. (Usually ships in 24 to 48 hours). Format Book. http://store.doverpublications.com/0486240738.html

American History, American...... American Indians Anthropology, Folklore, My...... Antiques Architecture Art Bridge and Other Card Game...... Business and Economics Chess Children Clip Art and Design on CD-...... Cookbooks, Nutrition Crafts Detective, Ghost , Superna...... Dover Patriot Shop Ethnic Interest Features Gift Certificates Gift Ideas History, Political Science...... Holidays Humor Languages and Linguistics Literature Magic, Legerdemain Military History, Weapons ...... Music Nature Performing Arts, Drama, Fi...... Philosophy and Religion Photography Posters Puzzles, Amusement, Recrea...... Science and Mathematics Sociology, Anthropology, M...... Sports, Out-of-Door Activi...... Stationery, Gift Sets Stationery, Seasonal Books...... Summer Fun Shop Summer Reading Shop Travel and Adventure Women's Studies By Subject Science and Mathematics General Science A History of Greek Mathematics, Vol. 1 Sir Thomas Heath Our Price Availability: In Stock (Usually ships in 24 to 48 hours) Format: Book ISBN: Page Count: Dimensions: 5 3/8 x 8 1/2 Volume 1 of an authoritative coverage of essentials of mathematics, every important innovation, every important figure-Euclid, Apollonius, others. Total in set: 262 illustrations. Buy Now!

24. Aristotle And Greek Mathematics: A Supplement To Aristotle And Mathematics Aristotle and greek mathematics. greek mathematics in Aristotle s Works. Here are twentyfive of his favorite propositions (the list is not exhaustive). http://plato.stanford.edu/entries/aristotle-mathematics/supplement4.html

Stanford Encyclopedia of Philosophy Supplement to Aristotle and Mathematics Citation Information Aristotle and Greek Mathematics This supplement provides some general indications of Aristotle's awareness and participation in mathematical activities of his time. Greek mathematics in Aristotle's Works Here are twenty-five of his favorite propositions (the list is not exhaustive). Where a proposition occurs in Euclid's Elements , the number is given, * indicates that we can reconstruct from what Aristotle says a proof different from that found in Euclid). Where the attribution is in doubt, I cite the scholar who endorses it. In many cases, the theorem is inferred from the context. In a given circle equal chords form equal angles with the circumference of the circle ( Prior Analytics i.24; not at all Euclidean in conception) The angles at the base of an isosceles triangle are equal ( Prior Analytics i.24; Eucl. i.5*). The angles about a point are two right angles ( Metaphysics ix 9; Eucl. follows from i def. 10). If two straight-lines are parallel and a straight-line intersects them, the interior angle is equal to the exterior angle (

25. Aristotle And First Principles In Greek Mathematics: A Supplement To Aristotle A Stanford Encyclopedia of Philosophy Supplement to Aristotle and Mathematics Citation Information. Aristotle and First Principles in greek mathematics. http://plato.stanford.edu/entries/aristotle-mathematics/supplement1.html

Stanford Encyclopedia of Philosophy Supplement to Aristotle and Mathematics Citation Information Aristotle and First Principles in Greek Mathematics It has long been a tradition to read Aristotle's treatment of first principles as reflected in the first principles of Euclid's Elements I. There are similarities and differences. Euclid divides his principles into Definitions horoi Postulates ), and Common Notions koinai ennoiai Elements i is tenuous at best. Elsewhere in Greek mathematics, and even in the Elements , we find other treatments first principles, some of which are closer in other ways to Aristotle's conceptions. For example, Archimedes' On the Sphere and Cylinder opens with existence hypotheses (that certain lines exist) and stipulations (that they should be called such-and-such). A more fundamental distinction between Aristotle's treatment of first principles and those found in Greek mathematics is that Aristotle seems to think that each first principle has both a logical and an explanatory role in a treatise. Yet it is typical, especially in treatises which are introductory to a topic, to have principles which serve a logical and explanatory role, but also to have principles whose only explicit role is pedagogical. For they serve no obvious role in the demonstrations. Such might be the definitions of point and line in Elements i. Hence, if there is a relation between Aristotle's conception of first principles and those of the mathematicians, Aristotle provides an ideal framework based on contemporary mathematical practice and which may or may not have been noticed by authors such as Euclid.

26. A Journey To The World Of Greek Mathematics The exhibition spans the whole period of greek mathematics from the 6th century BC to the 4th century AD, and covers the most important events and people in http://www.fhw.gr/exhibitions/math/en/

The Foundation of the Hellenic World's exhibition on the development of mathematics and mathematical thought in the ancient Greek world, a period in which the foundations of science were established, attempts to demonstrate one of the most important aspects of ancient Greek culture. In accordance with the Foundation's general policy and vision, the exhibition targeted from the beginning two basic objectives or messages: To demonstrate that the mathematics of the ancient Greeks was the foundation stone of scientific thought. To emphasize that mathematics is for everyone, since: it contributes to the personal growth of each individual it is an intellectual challenge it can help us in many activities and it is an essential part of the history and culture of the society that creates and uses it The exhibition spans the whole period of Greek mathematics from the 6th century BC to the 4th century AD, and covers the most important events and people in the history of Greek mathematics. Pre-Hellenic mathematics, that of the Egyptians and the Babylonians, is also dealt with briefly, as is the story of the Greek texts themselves from the end of the ancient world as they passed from Byzantine monks and Arab copyists to the European scientists of the Renaissance and the scientific revolution. The basic applications of mathematics to other sciences during this period, with special emphasis on astronomy, mathematical geography and music, complete the picture of Greek mathematics. Furthermore, the exhibition sets out the cultural framework of Greek mathematical thinking, from the Hellenic cities of Asia Minor and southern Italy to Classical Athens and the Alexandria of the Hellenistic Period.

27. A Journey To The World Of Greek Mathematics types of exhibit bring to life the way in which the concept of mathematical proof was born, during this second period of the history of greek mathematics. http://www.fhw.gr/exhibitions/math/en/station3.html

The second half of the 5th and 4th centuries BC. This is the period of Plato, Euclid and Aristotle, the age of Classical Athens. Various types of exhibit bring to life the way in which the concept of mathematical proof was born, during this second period of the history of Greek mathematics. Mathematical proof was of paramount importance to the development of the science of mathematics.

28. The Golden Age Of Greek Mathematics THE GOLDEN AGE OF greek mathematics. The Death of Alexander the Grat led to internal strife but by 306BC control of the Egyptian http://www.scit.wlv.ac.uk/university/scit/modules/mm2217/gagm.htm

THE GOLDEN AGE OF GREEK MATHEMATICS The Death of Alexander the Grat led to internal strife but by 306BC control of the Egyptian portion of the empire was in the hands of Ptolemy 1. He established a school at Alexandria and Euclid became a teacher there. 5 works of Euclid have survived ' Elements ', 'Data', 'Division of Figures', Phaenomena' and 'Optics'. Euclid was a good teacher - no new discovery is attributed to him, he just wrote 'Elements' as a textbook. University students were being presented with a textbook ('Elements') which gave them the fundamentals of elementary mathematics (geometry and algebra). 'Elements' is divided into 13 books of which the first half dozen were at elementary plane geometry next 3 on numbers, book X on incommensurables and the last 3 on solid geometry. Euclid's 'Elements' - Book 1 The book opens with a list of 23 definitions. Definitions do not really define because they use words which are no better known than the word being defined. eg. The Euclidean definition of a plane angle as "the inclination to one another of 2 lines in a plane which meet one another and do not lie in a straight line" is not very good because inclination has not being previously defined and is not better known than the word "angle". Following the definitions Euclid listed 5 postulates and 5 common notions (axioms).

29. Read This: The Shaping Of Deduction In Greek Mathematics Read This! The MAA Online book review column review of The Shaping of Deduction in greek mathematics, by Reviel Netz. Read This! http://www.maa.org/reviews/netz.html

Read This! The MAA Online book review column The Shaping of Deduction in Greek Mathematics A study in cognitive history by Reviel Netz Reviewed by Christian Marinus Taisbak Reviel Netz has written an stimulating book about diagrams and mathematics, telling us facts that we all know, but hardly ever thought of. Thus he sets himself in the best of company, for isn't that what Euclid did from the very first proposition in the Elements? "The diagram is the metonym of mathematics" is RN's main claim. To understand what he means by that, think of two typical situations in the circus of conferences: if a philosopher or historian gives a talk, he will read aloud for half an hour, facing his audience without moving from his chair. If a mathematician gives a talk, he will dance around the platform talking to the blackboard while writing figures and letters on it, most of the time ignoring his audience and concentrating on his written deductions as they emerge out of sheer necessity. Years ago David Fowler (of Plato's Academy ) coined a motto: "Greek mathematics is to draw a figure and tell a story about it." RN has widened and deepened this into "Deductive mathematics grew out of the Greeks drawing lettered diagrams and telling stories by means of them, not only about them." The diagram and the argument live in such a close symbiosis that one cannot be understood without the other. The diagram is the metonym of mathematics.

30. Read This: The Mathematics Of Plato's Academy Reviewed by Fernando Q. Gouvêa. Most mathematicians who know anything about the history of their subject know the standard story about greek mathematics. http://www.maa.org/reviews/mpa.html

Read This! The MAA Online book review column The Mathematics Of Plato's Academy: A New Reconstruction (Second Edition) by David Fowler Reviewed by Fernando Q. Gouvêa Most mathematicians who know anything about the history of their subject know the standard story about Greek mathematics. David Fowler describes that story like this: The early Pythagoreans based their mathematics on commensurable magnitudes (or on rational numbers, or on common fractions m/n), but their discovery of the phenomenon of incommensurability (or the irrationality of the square root of 2) showed that this was inadequate. This provoked problems in the foundation of mathematics that were not resolved before the discovery of the proportion theory that we find in Book V of Euclid's Elements (p. 356). As he points out, we have all heard, and some of us have told, that story. It may be somewhat surprising, then, to discover that many, if not most, historians of ancient mathematics disbelieve some or all of this story. In The Mathematics of Plato's Academy , David Fowler gives a convincing account of the reasons for rejecting the standard story, and offers a very interesting alternative reconstruction of the history of early Greek mathematics.

31. ISHM | Articles greek mathematics. by Maria Fragoulopoulou. There are three important periods in the development of greek mathematics. http://www.indianshm.com/articles/show.php?id=000065

32. ThinkQuest : Library : Go Forth & Multiply: A Mathematics Adventure greek mathematics preEuclidean period. The Greeks not only made significant advancements in geometry, but also changed the way mathematicians think. http://library.thinkquest.org/C0110248/geometry/history2.htm

Index Education Want to learn more about the world of mathematics? Then go forth, and enter the wildest math adventure you've ever been! Learn new math concepts and refresh your knowledge for those you've already known. Understand how the formulae you use were derived from. Or, you can take a step back into the past and read about how mathematics and its concepts originated. Go forth and multiply! Visit Site 2001 ThinkQuest Internet Challenge Awards Achievement Award Students Teow Lim Raffles Junior College, Singapore, Singapore Vee San Raffles Girls' School (Secondary), Singapore, Singapore Coaches Poh Kheng Pioneer Junior College, Singapore, Singapore Jee Wah Raffles Girls' School (Sec), Hougang, Singapore Want to build a ThinkQuest site? The ThinkQuest site above is one of thousands of educational web sites built by students from around the world. Click here to learn how you can build a ThinkQuest site. Privacy Policy

33. ThinkQuest : Library : Mathematics History ¥±. The greek mathematics Demonstrative Geometry. ßCharacteristic of greek mathematics In the 600 BC Mathematics was focused http://library.thinkquest.org/22584/emh1200.htm

Index Math Mathematics History An extensive history of mathematics is at your fingertips, from Babylonian cuneiforms to advances in Egyptian geometry, from Mayan numbers to contemporary theories of axiomatical mathematics. You will find it all here. Biographical information about a number of important mathematicians is included at this excellent site. Visit Site 1998 ThinkQuest Internet Challenge Languages English Korean Students Hyun-jin Jae-yun Hwang(Seoul Yo Sang), Kwan-ak Gu, Korea, South Kyung-sun Jae-yun Hwang(Seoul Yo Sang), Kwan-ak Gu, Korea, South So-young Jae-yun Hwang(Seoul Yo Sang), Kwan-ak Gu, Korea, South Coaches Jae-yun Jae-yun Hwang(Seoul Yo Sang), Kwan-ak Gu, Korea, South Jong-hyun Jong-hyun Lee(Seoul Yo Sang), Kwan-ak Gu, Korea, South Dea-won Dea-won Ko (Seoul Yo Sang), Kwan-ak Gu, Korea, South Want to build a ThinkQuest site? The ThinkQuest site above is one of thousands of educational web sites built by students from around the world. Click here to learn how you can build a ThinkQuest site.

34. Ancient Greek Mathematics Ancient greek mathematics. LINKS. The Science of Magnitudes. The Beginnings The Greeks, Scientists and Artists. See some beautiful http://www.mlahanas.de/Greeks/MathLinks.htm

Ancient Greek Mathematics LINKS The Science of Magnitudes. The Beginnings: The Greeks, Scientists and Artists See some beautiful Proofs of Ancient Greek Mathematicians http://www.calstatela.edu/faculty/hmendel/Ancient%20Mathematics/VignettesAncientMath.html Read Euclid Elements and learn ancient Greek to read the original text http://www.du.edu/~etuttle/classics/nugreek/contents.htm Euclid Elements, a well known Website http://aleph0.clarku.edu/~djoyce/java/elements/toc.html Ancient Mathematicians (French Language with links) http://perso.wanadoo.fr/jean-paul.davalan/hist/ Geometric Problems of Antiquity Eric W. Weisstein. "Geometric Problems of Antiquity." From MathWorld A Wolfram Web Resource. http://mathworld.wolfram.com/GeometricProblemsofAntiquity.html University of St. Andrews (Includes an extensive list with biographies of Greek mathematicians and from all other countries ) The classic Greek mathematic Problems Squaring the circle Doubling the cube Trisecting an angle The teaching of mathematics in Ancient Greece ... Enquiries about the genesis of formal thinking and about syntactic knowledge representation Various mathematical problems The Ten Means of Ancient Greece When is a Triangle Not a Triangle?

35. MODERN GREEK MATHEMATICS (Web Pages) By Antreas P. Hatzipolakis MODERN greek mathematics (Web Pages) by Antreas P. Hatzipolakis. reply to this message post a message on a new topic Back to mathhistory-list http://mathforum.org/epigone/math-history-list/dwehblaxsmeld

MODERN GREEK MATHEMATICS (Web Pages) by Antreas P. Hatzipolakis reply to this message post a message on a new topic Back to math-history-list Subject: MODERN GREEK MATHEMATICS (Web Pages) Author: xpolakis@hol.gr Date: Fri, 29 May 1998 20:31:05 +0200 Hellenomnimon Web Pages Note: Since the name "Hellenomnimon" is latinized has lost its Greek spelling. In Greek: E(LLHNOMNH/MWN = E(/LLHN [:Greek] + MNH/MWN [from MNH/MH: memory] * Hellenomnimon Project Page URL: http://sat1.space.noa.gr/hellinomnimon/index.html Excerpt from the Project's About Page: URL: http://sat1.space.noa.gr/hellinomnimon/project.htm http://sat1.space.noa.gr/hellinomnimon/public_1.htm * On-line Paper: ISSUES IN THE HISTORIOGRAPHY OF POST - BYZANTINE SCIENCE. appeared in "Trends in the Historiography of Science", edited by Kostas Gavroglu, Jean Christianidis and Eythymios Nicolaidis, Boston Studies in the Philosophy of Science, vol. 151, 1994, Kluwer Academic Publishers. Dimitris Dialetis and Efthymios Nicolaidis URL: http://sat1.space.noa.gr/hellinomnimon/public_3.htm

36. [HM] Is Greek Mathematics The *real* Thing? a topic from HistoriaMatematica Discussion Group HM Is greek mathematics the *real* thing? post a message on this topic post a message on a new topic http://mathforum.org/epigone/historia_matematica/fringblingshu/

a topic from Historia-Matematica Discussion Group [HM] Is Greek mathematics the *real* thing? post a message on this topic post a message on a new topic 2 Nov 1998 [HM] Is Greek mathematics the *real* thing? , by Julio Gonzalez Cabillon 2 Nov 1998 Re: [HM] Is Greek mathematics the *real* thing? , by barnabas hughes 2 Nov 1998 Re: [HM] Is Greek mathematics the *real* thing? , by Glen Van Brummelen 3 Nov 1998 Re: [HM] Is Greek mathematics the *real* thing? , by Gordon Fisher 3 Nov 1998 Re: [HM] Is Greek mathematics the *real* thing? , by George Gheverghese Joseph 6 Nov 1998 [HM] Is Greek mathematics the *real* thing? , by Moshe' Machover 6 Nov 1998 Re: [HM] Is Greek mathematics the *real* thing? , by Jeremy Smith 9 Nov 1998 Re: [HM] Is Greek mathematics the *real* thing? , by kermit@polaris.net 9 Nov 1998 Re: [HM] Is Greek mathematics the *real* thing? , by Jeremy Smith 3 Nov 1998 Re: [HM] Is Greek mathematics the *real* thing? , by Daryn Lehoux 3 Nov 1998 Re: [HM] Is Greek mathematics the *real* thing? , by Roger Cooke 3 Nov 1998 Re: [HM] Is Greek mathematics the *real* thing?

37. Science Awakening I: Egyptian, Babylonian & Greek Mathematics Science Awakening I Egyptian, Babylonian greek mathematics Search for books at mathematicsbooks.org. mathematicsbooks.org. Home, http://mathematicsbooks.org/0945726058.html

Home Search High Volume Orders Links ... Philosophy of Mathematics Additional Subjects No more excuses: 2002001698) Death Dying History of Mathematics A Diplomatic History of the American People ... Brothers It Written by B. L. Van Der Waerden Published by Scholars Book Shelf (August 1988) ISBN 0945726058 Price $6.95 Look for related books on other categories Science/Mathematics Still didn't find what you want? Try Amazon search Search: All Products Books Magazines Popular Music Classical Music Video DVD Baby Electronics Software Outdoor Living Wireless Phones Keywords: Or try to look for at Fetch Used Books, at or at CampusI See Also Namibia's Post-Apartheid Regional Institutions: The Founding Year The Ecstasies of Roland Barthes Motel of the Mysteries Nursing I.V. Drug Handbook ... Elementary Statistics, Ninth Edition Our Bookstores Cooking Books Games Books Computer Books Health Books ... Music Books Web Resources Amazon Australian Mathematics Trust European Mathematical Society (EMS) Kappa Mu Epsilon - Official Site ... Exchange links with us

38. A History Of Greek Mathematics, Vol. 1 A History of greek mathematics, Vol. 1 Search for books at mathematicsbooks.org. mathematicsbooks.org. A History of greek mathematics, Vol. 1. http://mathematicsbooks.org/0486240738.html

Home Search High Volume Orders Links ... Philosophy of Mathematics Additional Subjects No more excuses: 2002001698) Death Dying History of Mathematics A Diplomatic History of the American People ... Brothers It A History of Greek Mathematics, Vol. 1 Written by Sir Thomas Heath Published by Dover Pubns (May 1981) ISBN 0486240738 Price $17.95 Customer Reviews It should be noted that this is one of a two volume set. This author also compiled and commented upon The Elements of Euclid in three volumes [also available here].These works were first brought to my attention by my Greek language professor nearly 40 years ago as the best English language source on Greek Mathematics.Just as the Greeks did not view 'pure' mathematics or geometry as a lifes-work so to younger readers [through collage] the methods of logic may prove most useful.For we retired 'geezers' not quite ready for Oprah reruns and made for T.V. 'romances' it may be the stimulation of the brain by the problems [which are documented and solved in full], the history and the 'awe' of how much these did 'without computers'; This is not a terribly exciting book to read, but it is a superior reference for looking up Greek mathematicians. It is apparent that the author is partial to Euclid, as his section is close to a third of the book, (see the author's version of the Elements)but being a Euclid fan myself I can forgive this easily. Even the most obscure mathematicians are covered in good detail along with what they proved, as well as how they proved it. For those interested in historical mathematics, this book is invaluable. Note: This is a two volume set. I thought it was only one and I only purchased the second. Be sure to get both.

39. Nardia Symonds : Greek Mathematics Nardia Symonds gives a survey of the history of greek mathematics as part of the assessment for the Honours Pure Mathematics subject History of Mathematics http://www.maths.adelaide.edu.au/people/pscott/history/nardia/symonds1.htm

History of Greek Mathematics Thales Pythagoras Zeno Euclid ... Archimedes Timeline All dates are BCE INDEX Links to related sites

40. Nardia Symonds : Greek Mathematics Archimedes. Links on the History of greek mathematics. The greek mathematics Demonstrative Geometry. greek mathematics Index, University of St Andrews, Scotland. http://www.maths.adelaide.edu.au/people/pscott/history/nardia/symonds8.htm

Thales Pythagoras Zeno Euclid ... Archimedes Links on the History of Greek Mathematics The Greek Mathematics : Demonstrative Geometry Archimedes' Approximation of Pi Greek Mathematics Index, University of St Andrews, Scotland History of Greek Mathematics, University of Utah ... Greek Mathematics home page

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