81. HEATH, Thomas., A History Of Greek Mathematics. Illus. 446 pp.; 586 pp. Two vols. 8vo, wrappers. New York Dover, nd The classic text on the Greek legacy of mathematics. http://www.polybiblio.com/jahill/HillBibl-Selections461.0.html

Jonathan A. Hill, Bookseller Inc. HEATH, Thomas. A History of Greek Mathematics. New York: Dover, n.d. Illus. 446 pp.; 586 pp. Two vols. 8vo, wrappers. New York: Dover, n.d. The classic text on the Greek legacy of mathematics. This item is listed on Bibliopoly by Jonathan A. Hill, Bookseller Inc. ; click here for further details.

82. Plato And Mathematics Plato The Meno as the gateway from Mathematics to Mysticism. this was in all probability the stock example or how not to do rigorous greek mathematics. http://community.middlebury.edu/~harris/Philosophy/Plato.html

PLATO Mathematician or Mystic ? Plato believed at first that Mathematics would be the key to Thought, but in the Meno he abandons hope in the context of a few sentences, which we have constantly misread. This paper examine that crux. No reader of Plato can fail to recognize the important role which mathematics plays in his writing, as would indeed be expected for an author about whom the ancient tradition maintains that he had hung over the entry to his school the words "Let No One Un-versed in Geometry Enter". Presumably it was the level of ability to work with abstract concepts that Plato was interested in primarily, but if the student really had never studied Greek geometric materials there would be many passages in the lectures which would be scarcely intelligible to him. Modern readers, versed in a much higher level of mathematical abstraction which our society can offer, have sometimes felt that Plato's famous "mathematical examples'" were illustrations rather than central to his arguments, and some of Plato's mathematical excursuses have remained obscure to the present time. When Euclid put together his masterful compendium in the 3 rd C. B.C. he was obviously drawing on a legacy of accumulated mathematical research which went back well into the 5th C. B.C. and possibly even further. Activity can be pushed back well into the 5th C. B.C. in view of the quite reasonable ancient assignment of the Pythagorean Theorem of Euclid I 47 to the master himself; this would naturally involve understanding of squares and irrational numbers. And i4 should be noted that well back into that century Iktinos, the architect of the Parthenon was not only considering but actually using in his work the square root of the diagonal of a 1:2 rectangle in the form which later became famous as the Golden Mean, more specifically in the ratio l.6l8 : l

83. History Of Mathematics, Math History University of Illinois, UrbanaChampaign greek mathematics History Guide Examine information regarding Greek ancient mathematics at this website designed http://www.buzzle.com/chapters/education-and-higher-learning_primary-and-seconda

Home Web Directory What's the Buzz? Escape Hatch ... Free Email Friday, September 16, 2005 7:41:54 PM DIRECTORY Primary and Secondary Education Mathematics History of Mathematics Chapter Quicklink What's the Buzz Escape Hatch: Open Mic History of Mathematics Throughout history, the goal of mathematics education has been to develop accurate and logical thinking in individuals so they can apply their newly gained knowledge to solving all kinds of problems. Math is therefore an important course of educational study, especially in preparing college students for careers in business, engineering, medicine, psychology and the various sciences. This section provides math history resources that focus on the history of mathematics and the individuals and groups that have made contributions to this area of study. Advanced Network and Services: Library: Mathematics Historical Time Periods Guide Learn at this site provided by Advanced Network and Services about the history of mathematics that are categorized by various civilizations, time periods and geographical regions. Advanced Network and Services: Think Quest Junior: Ancient Babylonian and Greek Mathematics Guide Go here for various data on the history of mathematics from ancient Babylonian and Greek math to the calculus, geometry and trigonometry used in modern mathematics and physics.

84. Human Activity - Mathematics Knowledge - Read A Biography Of Design a chart of the advancement of greek mathematics and its relationship to preSocratic philosophers. Comprehension Primary - Great Mathematicians site http://departments.cvuhs.org/joe/GreekMathematics.html

Human Activity - Mathematics Knowledge - Read a biography of Euclid, Archimedes and Eratosthenes and describe their most important contributions to mathamatics. Knowledge Primary - The Great Books of the Westen World Vol . 11, The History of Mathematics Knowledge Secondary - Tuft Student Page http://www.perseus.tufts.edu/GreekScience/Students/Mike/geometry.html http://www.perseus.tufts.edu/GreekScience/Students/Tim/Contents.html Knowledge Other - Clark University History of Mathematics http://aleph0.clarku.edu/~djoyce/mathhist/greece.html Comprehension Review architecture used in the temples of Ancient Greece e.g. Artemis at Eleusis, the Temple of Zeus at Olympus or the Parthanon and explain the geometric principles used. Design a chart of the advancement of Greek mathematics and its relationship to pre-Socratic philosophers. Comprehension Primary - Great Mathematicians site 1. http://sunsite.unc.edu/expo/vatican.exhibit/exhibit/d-mathematics/Greek_math.html 2. http://www-adm.pdx.edu/user/sinq/greekciv/science/mathematics/IT.html Ancient Science, History of Architecture

85. ¥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.edp.ust.hk/math/history/2/2_4.htm

¥j§Æ¾¼Æ¾Ç¡]Ancient Greek mathematics¡^ ¡@¡@§Æ¾¤Hªº«ä·Q²@µLº°Ý¦a¨ü¨ì¤F®J¤Î©M¤Ú¤ñ­Ûªº ¼vÅT¡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.¡^ ¡@ ¤G¡B¨È¾ú¤s¤j®É´Á¡]300B.C.-641A.D.¡^ ¡@¡@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 ¡@¡@¤½¤¸529¦~¡AªF¹°¨«Ò°ê¬Ó«Ò¬d¤h¤B¥§¡]Justinian ¡^¤U¥Oö³¬¶®¨åªº¾Ç®Õ¡AÄY¸T¬ã¨s©M¶Ç¼½¼Æ¾Ç¡A¼Æ¾Ç µo®i¦A¦¸¨ü¨ì­P©Rªº¥´À»¡C ¡@¡@¤½¤¸641¦~¡Aªü©Ô§B¤H§ð¦û¨È¾ú¤s¤j¨½¨È«°¡A¹Ï ®ÑÀ]¦A«×³QµI¡]²Ä¤@¦¸¬O¦b¤½¤¸«e46¦~¡^¡A§Æ¾¼Æ¾Ç ±y¤[ÀéÄꪺ¾ú¥v¡A¦Ü¦¹²×µ²¡C

86. Other Topics In Greek Mathematics Other Topics in greek mathematics. _. Commensurability. Choose One of the Following, Commensurate Lines Measured by http://math.furman.edu/~jpoole/mth15hp/othertopicsgk/othertopicsgk.htm

Other Topics in Greek Mathematics Commensurability Choose One of the Following: Commensurate Lines Measured by the Greatest Common Measure A Geometric Proof Assuming all Lines are Commensurable Back to Mth 15 Home Page

87. BEING AND SIGN II Axiomatic-deductive Method And Infinite In Thus we are going to deal with greek mathematics till Euclid, and hence to ignore in This report deals with the evolution of classic greek mathematics. http://www.dm.uniba.it/~psiche/bas2/node1.html

Next: 1. Mesopotamian and Up: No Title Previous: No Title BEING AND SIGN II: Axiomatic-deductive method and infinite in greek mathematics. Luigi Borzacchini Department of Mathematics University of Bari, Italy Knowledge representation and formal thinking have 'ancient roots', deeply embedded in our modern culture. This has been analyzed in the first report, in the Platonic and Aristotelian foundation of the syntactic paradigm, against Sophists' 'negative judgement paradox' and beyond the Parmenidean 'being' philosophy. In this report we extend the analysis to the evolution of greek mathematics, dealing with incommensurability's discovery and Zeno's paradoxes, from Pythagoras till the Aristotelian foundation of the axiomatic-deductive method and the continuous/discrete idea of infinite. The core of this analysis is in Euclid's Elements where we can acknowledge the passage from an ancient non-syntactic proof-theory to the axiomatic-deductive method. (In geometry) the elements are prior to propositions or problems. And likewise in what we call grammar the letters are prior to the syllables (Aristotle, Categoriae 14 a36-b14 2) This is the second report of a series of four about the genesis of the formal and/or syntactic thinking. In this context we use ''formal'', in a broader sense, as manipulating signs by rules, and ''syntactic'', in a more restricted sense, as manipulating string of signs by rules. Here ''manipulating'' means that signs' usage is intersubjective, i.e. all the people or a social class, to this aim recognised by all the people, agree on the manipulation rules and on the 'meaning' of the signs. Roughly speaking, syntactic thinking concerns with arithmetic and writing, formal thinking comprehends pictograms, games and icons too. Regarding geometric graphical symbols, we shall use the term ''figure''. Intersubjectivity thus entails that, dealing with the signs, the single ''interpreter'' vanishes and is substituted by a ''social'' one.

88. Myths, Lies, And Truths The argument goes pregreek mathematics had neither a well-defined idea of proof nor Debate on the Relationship between Egyptian and greek mathematics 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

89. Science - Mathematics: History BRIEF HISTORY OF greek mathematics. Numbers are undoubtedly an indispensable part of our daily lives and essential to the preservation of human civilization http://www.archaeonia.com/science/mathematics/history.htm

BRIEF HISTORY OF GREEK MATHEMATICS N umbers are undoubtedly an indispensable part of our daily lives and essential to the preservation of human civilization as we know it. We all use numbers to identify our residence, conduct purchases of food and clothes, communicate through the phone, and keep track of just how many items (CDs, books, pets, etc) we own, just to mention a few. Human beings are so dependent on numbers and counting that, in fact, one of the first things we teach young children to do is how to count to ten. What the ancient Greeks did to contribute to our modern world of numbers is absolutely amazing. The great Greek philosopher Plato taught that numbers not only occupy a central role in our world but also even lead us to truth itself . Let us examine the evolution history of ancient Greek counting and some unique contributions with the aim to gain a better understanding and deeper appreciation of something that we so often take for granted It is always hard to say exactly how numbers came into existence , as there is not any definitive record of what person or group of people could have possibly invented them. Numbers seem to be as

90. E-Ren: Student Projects They translated many greek mathematics textbooks. Unsatisfied with existing translations of the great greek mathematics book Almagest, http://www.idbsu.edu/courses/hy309/projects/math.html

Lesson Plan: Renaissance Mathematics by Juan Wang Spring Semester, 1993 I. Thesis of the lesson. This lesson intends to present public school students a brief history of the progress of mathematics during the Renaissance. The lesson will combine an introduction to Renaissance mathematical developments with an explanation of its interactions with social influences of the time. Hopefully students will have a fresh understanding of the Renaissance period from this particular perspective. II. Introduction The development of mathematics almost stopped between the fourteenth century and the first half of the fifteenth century. Many social factors contributed to this situation. The ten years of the dreadful Black Death devastated Europe in the mid- fourteenth century. This caused nearly half of the population to die. The plague greatly distracted peoples' minds from the pursuit of knowledge. The Hundreds Years War between England and France (1337-1453) also created general instability in Europe. Partly because of these tragedies, the earlier Renaissance period suffered a general economic recession. Faced with such an unfavorable social and economic environment, the learned world could hardly devote its energy to intellectual development. The growth of mathematics was not only retarded by war, but also by the injurious influence of traditional scholastic philosophy. The scholastic scholars highly valued studies in the humanities, such as philosophy and literature. Students enthusiastically spent their energies on Aristotle's logic and philosophy. The intellectual leaders of those times also quarrelled over subtle subjects in metaphysics and theology. Useless questions, such as "How many angels can stand on the point of a needle?" was the kind of topic which attracted scholars' interests. The study of mathematics was given minimal attention. Mathematicians could hardly receive respect from scholars of other disciplines. There were few jobs in universities for mathematicians. At some universities, the curriculum requirement of mathematical learning had not changed for almost two centuries since the fourteenth.

91. Greek For Euclid: Contents They do not represent the limits of greek mathematics, only its basis. greek mathematics was further developed by Archimedes, who discussed spirals, http://www.du.edu/~etuttle/classics/nugreek/contents.htm

Reading Euclid This course combines Greek and Geometry to show how to read Euclid's Elements in the original language "I would make them all learn English; and then I would let the clever ones learn Latin as an honour, and Greek as a treat" Sir Winston Churchill Go immediately to Contents Introduction Eu)klei/dou Stoixei~a , Euclid's Elements, the classical textbook in geometry, is easy to read in the original ancient Greek, but its grammar and vocabulary are not those familiar from the usual course in elementary Greek, with peculiarities that make it difficult for the beginner. The text of the Elements that we have is written in the literary koinh/ typical of the 1st century AD. This course concentrates on exactly what is necessary to read Euclid, both in vocabulary and grammar. Its sole aim is to teach how to read this work, and similar texts in Greek mathematics, and not to compose Greek sentences, nor to read the Iliad or Plato. All necessary information is included in the course. A great amount of scholarship has been devoted to Euclid, mainly in Latin or German, and this course may expose some of it to a larger audience, to whom it has been largely inaccessible. For authoritative details, reference must be made to these sources, since the present one claims no expertise. There are many websites with information on Euclid and geometry. For example, look at the link to Euclid in the Seven Wonders website that is referenced in the Classics Index page, under the heading Pharos of Alexandria. As is typical of education on the Internet, many sites are poor, repetitive or childish, however.

92. Arabic Mathematics Explains contributions of Arabian mathematicians by translating early greek texts, developing early algebraic ideas, number theory and astronomical calculations. Includes information about key people during this time period. http://www-history.mcs.st-and.ac.uk/history/HistTopics/Arabic_mathematics.html

Arabic mathematics : forgotten brilliance? Alphabetical list of History Topics History Topics Index Version for printing Recent research paints a new picture of the debt that we owe to Arabic/Islamic mathematics. Certainly many of the ideas which were previously thought to have been brilliant new conceptions due to European mathematicians of the sixteenth, seventeenth and eighteenth centuries are now known to have been developed by Arabic/Islamic mathematicians around four centuries earlier. In many respects the mathematics studied today is far closer in style to that of the Arabic/Islamic contribution than to that of the Greeks. There is a widely held view that, after a brilliant period for mathematics when the Greeks laid the foundations for modern mathematics, there was a period of stagnation before the Europeans took over where the Greeks left off at the beginning of the sixteenth century. The common perception of the period of 1000 years or so between the ancient Greeks and the European Renaissance is that little happened in the world of mathematics except that some Arabic translations of Greek texts were made which preserved the Greek learning so that it was available to the Europeans at the beginning of the sixteenth century. That such views should be generally held is of no surprise. Many leading historians of mathematics have contributed to the perception by either omitting any mention of Arabic/Islamic mathematics in the historical development of the subject or with statements such as that made by Duhem in [3]:-

93. 3.1415926535 - History And Philosophy Of Pi Probably no symbol of infinity in mathematics has evoked as much mystery, romanticism, misconception and human interest as the number and greek letter of Pi. Interesting facts and trivia about Pi. http://briantaylor.com/Pi.htm

Brian Taylor Web Site Developer Search Engine Promoter Changing The World 1 Web Page At A Time FSBi.com History and Philosophy of Pi Pi ( Dictionary.com Definition currently the value of Pi is known to 6.4 billion places Probably no symbol in mathematics has evoked as much mystery, romanticism, misconception and human interest as the number Pi ( Socrates Plato Aristotle Pi 3.14 ... Problems Pi (noun) ... plural = pis. Mathematics. A transcendental number, approximately 3.14159, represented by the symbol , that expresses the ratio of the circumference to the diameter of a circle and appears as a constant in many mathematical expressions. The 16th letter of the Greek alphabet. : BEYOND INFINITY Deep in the nature of man is the will to go further than any human has ever been before. This quest is symbolized by the Greek letter , which evokes infinity. Humans are still in pursuit of the end of its innumerable string of decimals... No number (3.14...) has captured the attention and imagination of number fanatics and nerds throughout the ages as much as the ratio of a circle's circumference to its diameter - a.k.a. Pi. With incisive historical insight and a refreshing sense of humor, this page brings us the story of Pi and humankind's fascination with it, from Archimedes to da Vinci to the modern day Chudnovsky brothers, who holed up in their Manhattan apartment with a homemade supercomputer churning out digits of pi into the billions.

94. Bible Numerics A Study in Biblical mathematics. Numerical analysis of the Hebrew and greek Text. http://biblemaths.com

Last updated 1 May 2005 New DVD A Study in the Deity of the Lord Jesus Christ, the evidence of the book of Genesis, the Shema, John 1.1 and the Extraordinary Messianic prophecy of the 70 Weeks of Daniel and a New Assessment of the Second Advent This book is summarised in two DVD presentations on one DVD. Each presentation is 44 slides and lasts about one hour each. The presentation has synchronized narration with each Presentation. L ecture one - Bible Numerics and Lecture two - The 70 Sevens of Daniel with some aspects of the Second Advent. The DVD can be used in Bible Studies Via the TV or Schools via a PC projector. The presentations Prove that the Bible is the true source of our existence and shows the evidence of how we Prove that Jesus Christ is the Messiah BOOK DVD Only BOOK and DVD 15 Patchcroft Road Peel Hall Wythenshawe Manchester England U.K. 0161 437 7013 E-mail - Peter@biblemaths.com or - lexis2701@ntlworld.com For UK. Chequ e payable to Dr Peter Bluer. Price Includes Postage.

95. Mathematicians Born In Greece Biographies of greek Mathematicians, with supplemental maps and timeline. From the MacTutor, History of mathematics. http://www-gap.dcs.st-and.ac.uk/~history/BirthplaceMaps/Countries/Greece.html

Mathematicians born in Greece Mathematicians' birthplaces are given relative to modern-day boundaries. Click on the name below to go to the biography. Antiphon Arf Aristaeus Aristarchus ... Zenodorus Click HERE to see a clickable map of Greece and Turkey. Places Index Birthplace Maps Index Countries Index Main index ... Societies, honours, etc. JOC/EFR/BS January 1998 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/history/BirthplaceMaps/Greece.html

96. Mathematics, Greek: New & Used Books Category Search Result For Mathematics, Gre mathematics, greek New Used Books Category Search Result for mathematics, greek. Compare new and used books prices among 122 book stores in a click. http://www.fetchbook.info/fwd_topics/id_1520791.html

Bookmark Recommend Us Enhance Your Site Browse Books ... Forums New! Help Keyword Title Author ISBN Welcome Guest [Sign In] Searched in books for Mathematics, Greek More than titles matched your search. Search took seconds. All Categories Mathematics General Mathematics, Greek Add Review Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics By Marcus Du Sautoy Paperback / 335 Pages / Perennial / April 2004 / 0060935588 List Price $13.95 / Similar to Music of the Primes: Searching to... Compare Prices Add To Wish List Details ... Add Review By Edward Fry Dona Lee Fountoukidis (Editor), Jacqueline Kress (Editor) Paperback / 464 Pages / Jossey-Bass Inc Pub / May 2000 / 0130281859 List Price $29.99 / Similar to Compare Prices Add To Wish List Details Add Review Zero: The Biography of a Dangerous Idea By Charles Seife Matt Zimet (Illustrator) Paperback / Penguin USA / September 2000 / 0140296476 List Price $14.00 / Similar to Zero: The Biography of a Dangerous... Compare Prices Add To Wish List Details ... Add Review History of Greek Mathematics: From Thales to Euclid By Thomas L. Heath

97. Bryn Mawr Classical Review 2004.03.47 CJ Tuplin, TE Rihll, Science and mathematics in Ancient greek Culture. Oxford Oxford University Press, 2002. Pp. xvi + 379. ISBN 019-815248-5. $85.00. http://ccat.sas.upenn.edu/bmcr/2004/2004-03-47.html

Bryn Mawr Classical Review 2004.03.47 C.J. Tuplin, T.E. Rihll, Science and Mathematics in Ancient Greek Culture . Oxford: Oxford University Press, 2002. Pp. xvi + 379. ISBN 0-19-815248-5. $85.00. Contributors: T. E. Rihll, A. Barker, J. L. Berggren, H. M. Hine, A. C. Bowen, R. Hannah, L Taub, J. J. Coulton, S. Cuomo, J. R. Milton, R. Netz, E. Hussey, C. M. Taisbak, V. Nutton, T. Tieleman, J. V. Tucker, C. A. Wilson Reviewed by William Wians, Merrimack College (William.wians@merrimack.edu) Word count: 1548 words The excellent collection of essays edited by Tuplin and Rihll (hereafter TR) reflects two major changes that the history of ancient science has experienced in the last thirty years. First is the great broadening of materials considered relevant to the field. Whereas in the not so distant past scholarship would concentrate on a few great works by a few great men, the modern historian of ancient science takes advantage of a much wider range of sources, including, for instance, materials documenting connections between magic and medicine or astrology and astronomy. The second major development has been an increased attention paid to the broader social context out of which scientific practices emerged. Economic and political forces have come to be recognized as important determinants of scientific activities, as have the close connections between practical achievements and theoretical innovation. Both developments are central to the aims and achievements of TR's anthology. Its sixteen papers (and a substantial introduction) arise from a 1996 conference in Liverpool that sought to bring together scholars working in diverse areas of ancient science, including mathematics, astronomy, mechanics, chemistry, medicine, and technology. The aim was not just for participating scholars to share their findings with one another but to demonstrate the relevance and value of historical studies of ancient science to what the editors term "mainstream" classicists and ancient historians. On the whole, the papers succeed in doing this by emphasizing precisely the two trends that have transformed the field. Because so many different and complex papers cannot be adequately treated in a limited review, I shall highlight what seem to me the contributions of greatest interest to the readers for whom the collection is intended.

98. The Research Notebook Of A Beleaguered Hack.: Struik: A Concise History Of Mathe Eudoxus solved the crisis in greek math and determined the course of greek math mathematics is intimately tied to astronomy, which was the science first http://arsenal.media.mit.edu/notebook/archives/000104.html

The research notebook of a beleaguered hack. Struik: A Concise History of Mathematics: Greece As the Mediterranean basin transitioned from the Bronze Age to the Iron Age there were enormous economic and political changes. Iron's introduction changed warfare but also cheapened production, causing a surplus, and allowing more people to be involved in public life. Additionally the introduction of coined money and the alphabet stimulated trade. Culture began to flourish, no longer exclusively the domain of the elite. Sea-raiders upset cultural, scientific, and mathematical progress as they destroyed Minoan civilization, and disrupted Egyptian and Babylonian development. The rise of the Greek city-state in 7th-6th centuries BCE allowed new freedoms to citizens. More leisure (begotten from slavery and wealth) stimulated the growth of rationalism, philosophy, and science. In contrast to oriental approaches, the Greeks did not just "how?" but sought to know "why?" Thales of Milete (who had traveled to Babylon and Egypt) is considered the father of Greek math. In seeking a rational scheme to the universe his tradition added an element of rationalism to mathematics. Only small fragments remain, but through careful analysis a consistent picture of Greek math emerges. The rise of Persia led to conflict and an eventual Greek victory, which expanded the power of Athens. Democratic ideals flourished from 450-400 BCE, paving the path for the Golden Age of Greece. Sophists had greater freedom to examine ideas more abstract than useful. The only complete fragment of this period is written by Hippocrates of Chios. The work shows perfected mathematical reasoning and deals with the impractical: the

99. BBC NEWS | Science/Nature | Greeks 'borrowed Egyptian Numbers' From BBC, The classical pioneers of mathematics, astronomy and physics borrowed their number system from Egypt, research suggests. http://news.bbc.co.uk/1/hi/sci/tech/3109806.stm

Home TV Radio Talk ... Newswatch Last Updated: Monday, 15 September, 2003, 13:31 GMT 14:31 UK E-mail this to a friend Printable version Greeks 'borrowed Egyptian numbers' By Paul Rincon BBC Science The astronomers, physicists and mathematicians of ancient Greece were true innovators. Ancient Greeks used letters and extra symbols to represent digits But one thing it seems the ancient Greeks did not invent was the counting system on which many of their greatest thinkers based their pioneering calculations. New research suggests the Greeks borrowed their system known as alphabetic numerals from the Egyptians, and did not develop it themselves as was long believed. Greek alphabetic numerals were favoured by the mathematician and physicist Archimedes, the scientific philosopher Aristotle and the mathematician Euclid, amongst others. Trade explosion An analysis by Dr Stephen Chrisomalis of McGill University in Montreal, Canada, showed striking similarities between Greek alphabetic numerals and Egyptian demotic numerals, used in Egypt from the late 8th Century BC until around AD 450. Both systems use nine signs in each "base" so that individual units are counted 1-9, tens are counted 10-90 and so on. Both systems also lack a symbol for zero.

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