41. Malaspina.com - Hippocrates (ca. 460-377 BC) Works by Hippocrates HTML, Internet Classics Archive. Oath and Law ofHippocrates Text, Wiretap; On Airs, MacTutor Entry on hippocrates of chios http://www.mala.bc.ca/~mcneil/hippo1.htm

Hippocrates (ca. 460-377 B.C.) [Biography, SFU] Etexts by this Author [Athena] Great Books Biography [Malaspina] Amazon Search Form] Library of Canada Online Citations [NLC] Library of Congress Online Citations [LC] Library of Congress Offline Citations [MGB] COPAC UK Online Citations [COPAC] Free Online Practice Exams [Grad Links] Canadian Book Orders! Chapters-Indigo Save on Textbooks! [Study Abroad] Used Books Search Form Alibris Dummies Books Amazon Books from Amazon Amazon EBay! Ebay Books from Amazon UK Amazon UK Books from Chapters Canada Chapters Amazon's 100 Hot Books Amazon Hippocrates Amazon Greek Medicine Amazon Hippocrates in a World of Pagans and Christians Amazon Works by Hippocrates [HTML, Internet Classics Archive] Oath and Law of Hippocrates [Text, Wiretap] On Airs, Waters, and Places [HTML, Internet Classics Archive] On Ancient Medicine [HTML, Internet Classics Archive] Aphorisms [HTML, Internet Classics Archive] On the Articulations [HTML, Internet Classics Archive] The Book of Prognostics [HTML, Internet Classics Archive] On Fistulae [HTML, Internet Classics Archive]

42. Malaspina.com - Hippocrates (ca. 460-377 BC) Oath and Law of Hippocrates Text, Wiretap; On Airs, Waters, and Places HTML,Internet Classics Archive MacTutor Entry on hippocrates of chios http://www.mala.bc.ca/~mcneil/thippo1.htm

Hippocrates (ca. 460-377 B.C.) [Biography] Etexts by this Author [Athena] Great Books Biography [Malaspina] Amazon Search Form] Library of Canada Online Citations [NLC] Library of Congress Online Citations [LC] Library of Congress Offline Citations [MGB] COPAC UK Online Citations [COPAC] Free Online Practice Exams [Grad Links] Canadian Book Orders! Chapters-Indigo Save on Textbooks! [Study Abroad] Used Books Search Form Alibris Dummies Books Amazon Books from Amazon Amazon EBay! Ebay Books from Amazon UK Amazon UK Books from Chapters Canada Chapters Amazon's 100 Hot Books Amazon Hippocrates Amazon Greek Medicine Amazon Hippocrates in a World of Pagans and Christians Amazon Works by Hippocrates [HTML, MIT] Oath and Law of Hippocrates [Text, Wiretap] On Airs, Waters, and Places [HTML, Internet Classics Archive] On Ancient Medicine [HTML, Internet Classics Archive] Aphorisms [HTML, Internet Classics Archive] On the Articulations [HTML, Internet Classics Archive] The Book of Prognostics [HTML, Internet Classics Archive] On Fistulae [HTML, Internet Classics Archive]

43. HISTORY OF MATHEMATICS IN THE LAST 25 YEARS: NEW DEPARTURES, NEW QUESTIONS, NEW of difficult geometrical propositions was hippocrates of chios . gives amathematical example that reminds the squarings of hippocrates of chios. http://www.tau.ac.il/humanities/cohn/activities/international_work/workshop2001/

Annual International Workshop History of Mathematics in the Last 25 Years New Departures, New Questions, New Ideas May 14-17, 2001 Tel-Aviv and Jerusalem Abstracts The emergence of the set-theoretical approach in mathematics The talk will explore the gradual rise of a set-theoretical approach to mathematical problems in German authors of the period 1850–1914. This includes Dirichlet’s work on real functions, Riemann’s work on function theory and differential geometry, Dedekind’s work on algebra and algebraic number theory, the work of Cantor and others on real functions and point-sets, attempts to bring to completion the arithmetization of mathematics, and many other later contributions (most notably, those of Hilbert). As can easily be seen from this list, set theory did not just emerge from the field of analysis, as used to be the opinion of historians on the basis of their study of Cantor’s career. In the talk we shall likewise consider the broad diffusion of set theory as the preferred language for modern mathematics around 1900, and the leading role played by Hilbert in this episode. Also present will be the emergence of logicism, which we shall understand as a result of the rise of set-theoretical mathematics, coupled with an old, “logical” conception of sets; and the problems posed by the set-theoretical paradoxes, showing that this “logical” conception was untenable and calling for axiomatization and formalization.

44. 430s BC: Information From Answers.com hippocrates of chios b. Chios (Greek island), c. 470 bce, dc 410 bce writeshis Elements of Geometry, which predates Euclid s more famous Elements by more http://www.answers.com/topic/430s-bc

showHide_TellMeAbout2('false'); Business Entertainment Games Health ... More... On this page: Wikipedia Mentioned In Or search: - The Web - Images - News - Blogs - Shopping 430s BC In the year bce Communication An optical telegraph using torches to signal from hilltop to hilltop operates in Greece. It uses combinations of 5 torches to indicate each letter of the Greek alphabet. See also ce Communication Earth science Democritus of Abdera [b. Abdera, Thrace, c. 470 bce , d. c. 380 bce ] is reputed to be able to predict the weather. See also bce Earth science Mathematics Hippocrates of Chios [b. Chios (Greek island), c. 470 bce , d. c. 410 bce ] writes his Elements of Geometry, which predates Euclid's more famous Elements by more than a century. Since the work has been lost, it is not clear what it contained. However, his most famous discovery is the method of squaring a figure with two sides that are each segments of circles. The figure is called the lune because of its resemblance to the crescent Moon. He is also credited with introducing indirect proof, a method in which the opposite of what is to be proved is shown to be impossible. See also bce Mathematics bce Mathematics . (See essay Physics Democritus of Abdera expands the concept, introduced by his teacher Leucippus, of the atom as an indivisible body and shows how every form of matter can be explained by his version of the atom.

45. Archytas: Information From Answers.com hippocrates of chios before reduced this problem to finding mean proportionals.Archytas theory of proportions is treated in the book VIII. of Euclid s http://www.answers.com/topic/archytas

showHide_TellMeAbout2('false'); Business Entertainment Games Health ... More... On this page: Wikipedia Mentioned In Or search: - The Web - Images - News - Blogs - Shopping Archytas Wikipedia @import url(http://content.answers.com/main/content/wp/css/common.css); @import url(http://content.answers.com/main/content/wp/css/gnwp.css); Archytas Archytas 428 BC 347 BC ), was a Greek philosopher mathematician astronomer ... strategist and commander-in-chief Archytas was born in Tarentum Magna Graecia (now Italy ) and was the son of Mnesagoras or Histiaeus. He was taught for a while by Philolaus and he was a teacher of mathematics to Eudoxus of Cnidus . He was scientist of the Pythagorean school, famous as the intimate friend of Plato . His and Eudoxus' student was Menaechmus Sometimes he is believed to be the founder of mathematical mechanics According to Eutocius Archytas solved the problem of duplicating the cube in his manner with a geometric construction. Hippocrates of Chios before reduced this problem to finding mean proportionals . Archytas' theory of proportions is treated in the book VIII. of Euclid 's Elements The Archytas curve , which he used in his solution of the doubling the cube problem, is named after him.

46. Antiphon.html hippocrates of chios was a merchant who came across a pirate ship and lost everything.He came to Athens to fill out a writ against the pirates. http://www.calstatela.edu/faculty/hmendel/Ancient Mathematics/Philosophical Text

Antiphon's Squaring of the Circle by Henry Mendell (Cal. State U., L.A.) Return to Vignettes of Ancient Mathematics In the text in Aristotle discussed by Simplicius, Aristotle claims that he does not have to refute Parmenides' view that what is is just one and unchangeable. In a book on nature, he does not have to concern himself with hypotheses which reject nature altogether. He then draws a contrast between two attempts to square the circle, one through segments, and one by Antiphon. The mathematician needs to concern himself with a refutation of squaring by segments, but does not need to be concerned with refuting Antiphon's, which rejects mathematical principles. Elsewhere, in Met . K 1 (assuming Aristotle to be the author), he appears to hold that such a refutation belongs to first philosophy. Simplicius identifies the squaring through segments with the construction of lunules by Hippocrates of Chios, as suggested by Aristotle, Sophistical Refutations b Characters of the Drama Antiphon lived in the late 5th century B.C.E. He may or not be the Athenian orator of that name. Fragments of his work on nature as well as another comment in Aristotle's Physics a Simplicius wrote his commentary on the Physics sometime around the 540's.

47. Archytas We are told that the mathematician, hippocrates of chios, who was active in thesecond half of the fifth century, had already confronted the problem and had http://plato.stanford.edu/entries/archytas/

version history HOW TO CITE THIS ENTRY Stanford Encyclopedia of Philosophy A ... Z This document uses XHTML/Unicode to format the display. If you think special symbols are not displaying correctly, see our guide Displaying Special Characters last substantive content change JUN The Encyclopedia Now Needs Your Support Please Read How You Can Help Keep the Encyclopedia Free Archytas Archytas of Tarentum was a Greek mathematician, political leader and philosopher, active in the first half of the fourth century BC (i.e., during Plato's lifetime). He was the last prominent figure in the early Pythagorean tradition and the dominant political figure in Tarentum, being elected general seven consecutive times. He sent a ship to rescue Plato from the clutches of the tyrant of Syracuse, Dionysius II, in 361, but his personal and philosophical connections to Plato are complex, and there are many signs of disagreement between the two philosophers. A great number of works were forged in Archytas' name starting in the first century BC, and only four fragments of his genuine work survive, although these are supplemented by a number of important testimonia. Archytas was the first to solve one of the most celebrated mathematical problems in antiquity, the duplication of the cube. We also have his proof showing that ratios of the form ( n n , which are important in music theory, cannot be divided by a mean proportional. He was the most sophisticated of the Pythagorean harmonic theorists and provided mathematical accounts of musical scales used by the practicing musicians of his day. He was the first to identify the group of four canonical sciences (logistic [arithmetic], geometry, astronomy and music), which would become known as the

48. Aristotle And Greek Mathematics: A Supplement To Aristotle And Mathematics Sophistici Elenchi 11, Physics i.2; this is a problem of hippocrates of chios,whom Aristotle claims thought that he could thus square a circle). 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 (

49. Ancient Greek Philosophy: Additional Search Terms HIPPIAS hippocrates of chios HYPATIA ION OF CHIOS LEUCIPPUS LYCOPHRON LYSISMELISSUS PANAETIUS PARMENIDES PHAEDO PHILOLANS OF ALEXANDRIA PLATO PLOTINUS http://karn.ohiolink.edu/philosophy/keywords/ast31001.html

OhioLINK History of Philosophy Website Ancient Greek Philosophy: Additional Search Terms Contents Figures Titles Terms Search Tools ... About Additional Search Terms Figures Click here to begin an OhioLINK search Click here to begin a KentLINK search Use your "back button" to return to these pages. ANAXGORAS ANAXIMANDER ANAXIMENES ANTIPHON THE SOPHIST ANTITHENES ARCHYTAS ARISTIPPUS OF CYRENE ARISTOTLE CHRYSIPPUS CLEANTHES CRATYLUS CRITIAS DAMON DEMOCRITUS DIODORUS CRONUS DIOGENES LAERTIUS ECHECRATES EMPEDOCLES EPICURUS EPIMENIDES GORGIAS HERACLITUS HESIOD HIPPIAS HIPPOCRATES OF CHIOS HYPATIA ION OF CHIOS LEUCIPPUS LYCOPHRON LYSIS MELISSUS PANAETIUS PARMENIDES PHAEDO PHILOLANS OF ALEXANDRIA PLATO PLOTINUS PORPHYRY PRODICUS PYRRHO PYTHAGORAS SEXTUS EMPIRICUS SOCRATES SPEUSIPPUS THALES THEAGENES THEODORUS THEOPHRASTUS TIMEAUS XENOPHANES XENOPHONE ZENO Back to the Table of Contents Titles Click here to begin an OhioLINK search Click here to begin a KentLINK search Use your "back button" to return to these pages. APOLOGY CATEGORIES CHARMIDES CRATYLUS CRITO DE ANIMA EUTHYPHRO GORGIAS ION LACHES LYSIS MENO METAPHYSICS NICOMACHEAN ETHICS ON INTERPRETAITON PARMENIDES PHAEDO PHAEDRUS PHILEBUS POETICS POLITICS POSTERIOR ANALYTICS PRIOR ANALYTICS PROTAGORAS REPUBLIC RHETORIC SOPHIST SOPHISTICAL REFUTATIONS STATESMAN SYMPOSIUM THEATETUS TIMEAUS TOPICS Back to the Table of Contents Terms Click here to begin an OhioLINK search Click here to begin a KentLINK search Use your "back button" to return to these pages.

50. Compiled List Of Search Terms HIPPIAS Ancient Greek Philosophy; hippocrates of chios Ancient Greek Philosophy;HOBBES Thomas British Empiricism Continental Rationalism http://karn.ohiolink.edu/philosophy/keywords/astglobal.html

OhioLINK History of Philosophy Website Compiled List of Search Terms Contents: Index of Figures A B C D ... Z Index of Titles A B C D ... W Index of Terms A B C D ... To the Search Tools Compiled List of Search Terms: Figures A ABBOT Francis E. American Philosophy ADORNO Theodor Twentieth-Century Philosophy ALLEN Ethan American Philosophy AMBROSE Alice American Philosophy ANAXGORAS Ancient Greek Philosophy ANAXIMANDER Ancient Greek Philosophy ANAXIMENES Ancient Greek Philosophy ANSCOMB Elizabeth Twentieth-Century Philosophy ANSELM Continental Rationalism ANTIPHON THE SOPHIST Ancient Greek Philosophy ANTITHENES Ancient Greek Philosophy APEL Karl Otto Twentieth-Century Philosophy APPIAH Kwame Anthony Twentieth-Century Philosophy ARCHYTAS Ancient Greek Philosophy ARENDT Hannah Twentieth-Century Philosophy ARISTIPPUS OF CYRENE Ancient Greek Philosophy ARISTOTLE Ancient Greek Philosophy German Critical Philosophy ARNAULD Antoine Continental Rationalism AST Friedrich Nineteenth-Century Philosophy AUSTIN J.L. Twentieth-Century Philosophy AYER Alred Jules Twentieth-Century Philosophy To the Search Tools Back to the Table of Contents Compiled List of Search Terms: Figures B BACON Francis British Empiricism German Critical Philosophy BAIN Alexander Nineteenth-Century Philosophy BARTHES Roland Twentieth-Century Philosophy BASEDOW Alexander Joseph German Critical Philosophy BATAILLE Georges Twentieth-Century Philosophy BAUMGARTEN Alexander German Critical Philosophy BENJAMIN Walter Twentieth-Century Philosophy BERGMANN Gustav Twentieth-Century Philosophy BERGSON Henri

51. Hippocrates Hippocrates. hippocrates of chios taught in Athens and worked on the classicalproblems of squaring the circle and duplicating the cube. http://www.palmers.ac.uk/internet/Previous Events/Eric Excellence day/webs2003/J

Hippocrates Hippocrates of Chios taught in Athens and worked on the classical problems of squaring the circle and duplicating the cube . Little is known of his life but he is reported to have been an excellent geometer who, in other respects, was stupid and lacking in sense. Some claim that he was defrauded of a large sum of money because of his naiveté. Back

52. Index Of Ancient Greek Scientists Links Hippocrates, Encyclopedia Britannica; hippocrates of chios. Wrote hisElements almost one century before Euclid s. Hypsicles (180 BC). http://www.ics.forth.gr/~vsiris/ancient_greeks/whole_list.html

not complete Agatharchos. Greek mathematician. Discovered the laws of perspectives. Anaxagoras of Clazomenae (480-430 B.C.). Greek philosopher. Believed that a large number of seeds make up the properties of materials, that heavenly bodies are made up of the same materials as Earth and that the sun is a large, hot, glowing rock. Discovered that the moon reflected light and formulated the correct theory for the eclipses. Erroneously believed that the Earth was flat. Links: Anaxagoras of Clazomenae, MIT Anaximander (610-545 B.C.). Greek astronomer and philosopher, pupil of Thales. Introduced the apeiron (infinity). Formulated a theory of origin and evolution of life, according to which life originated in the sea from the moist element which evaporated from the sun ( On Nature ). Was the first to model the Earth according to scientific principles. According to him, the Earth was a cylinder with a north-south curvature, suspended freely in space, and the stars where attached to a sphere that rotated around Earth. Links: Anaximander, Internet Encyclopedia of Philosophy

53. Index Of Ancient Greek Philosophers - Scientists hippocrates of chios. Wrote his Elements almost one century before Euclid s.Hippocrates of Cos (460377 BC). Considered as the father of Medicine. http://www.ics.forth.gr/~vsiris/ancient_greeks/presocratics.html

PreSocratics (7th - 5th century B.C.) Period marking the begining of science, as well as the development of literature, arts, politics, and philosophy. During these years, the city-states (polis in Greek) flourish. These include the Sparta and Athens. Within this period the Ionian school of natural philosophy was founded by Thales of Miletus . This is considered the first school for speculating about nature in a scientific way, hence signifies the birth of science. The Pythagorean brotherhood is formed by Pythagoras of Samos . This society performed a great deal of progress in mathematics, but also had mystical beliefs. In addition to the Ionian and Pythagorian, other schools of this period include the Eleatic , the Atomists, and the Sophists All philosophers - scientists up to Democritus are considered to be PreSocratics. Philosophers-Scientists Thales of Miletus (624-560 B.C.). Astronomer, mathematician and philosopher. Learned astronomy from the Babylonians. Founder of the Ionian school of natural philosophy. Predicted the solar eclipse on May 28, 585. Proved general geometric propositions on angles and triangles. Considered water to be the basis of all matter. He believed that the Earth floated in water. Used the laws of prospectives to calculate the height of the pyramids. Links: Thales of Miletus, Encyclopedia Britannica

54. Harvard University Press/Ancilla To Pre-Socratic Philosophers/Contents hippocrates of chios 43. Theodorus 44. Philolaus 45. Eurytus 46. Archippus. Lysis.Opsimus 47. Archytas 48. Occelus (Ocellus) 49. Timaeus 50. Hicetas http://www.hup.harvard.edu/contents/FREANX_toc.html

Ancilla to Pre-Socratic Philosophers A Complete Translation of the Fragments in Diels, Fragmente der Vorsokratiker Kathleen Freeman Foreword 1. Orpheus 2. Musaeus 3. Epimenides 4. Hesiod 5. Phocus 6. Cleostratus 7. Pherecydes 8. Theagenes 9. Acusilaus 10. The Seven Sages 11. Thales 12. Anaximander 13. Anaximenes 14. Pythagoras 15. Cercops 16. Petron 17. Bro(n)tinus 18. Hippasos 19. Calliphon and Democedes 20. Parm(en)iscus 21. Xenophanes 22. Heracleitus 23. Epicharmus 24. Alcmaeon 25. Iccus 26. Paron 27. Ameinias 28. Parmenides 29. Zeno 30. Melissus 31. Empedocles 32. Menestor 33. Xuthus 34. Boidas 35. Thrasyalces 36. Ion of Chios 37. Damon 38. Hippon of Samos 39. Phaleas and Hippodamus 40. Polycleitus 41. Oenopides 42. Hippocrates of Chios 43. Theodorus 44. Philolaus 45. Eurytus 46. Archippus. Lysis. Opsimus 47. Archytas 48. Occelus (Ocellus) 49. Timaeus 50. Hicetas 51. Ecphantus 52. Xenophilus 53. Diocles, Echecrates, Polymnastus, Phanton: Arion

55. Harvard University Press/Translated By Ivor Thomas, Greek Mathematical Works, II Proclus; Thales; Pythagorean geometry; Democritus; hippocrates of chios;duplicating the cube and squaring the circle; trisecting angles; Theaetetus; http://www.hup.harvard.edu/catalog/L362.html

FROM THE LOEB CLASSICAL LIBRARY TRANSLATED BY IVOR THOMAS Greek Mathematical Works, II, From Aristarchus to Pappus The wonderful achievement of Greek mathematics is here illustrated in two volumes of selected mathematical works. Volume I ( Loeb Classical Library no. 335 ) contains: The divisions of mathematics; mathematics in Greek education; calculation; arithmetical notation and operations, including square root and cube root; Pythagorean arithmetic, including properties of numbers; square root of 2; proportion and means; algebraic equations; Proclus; Thales; Pythagorean geometry; Democritus; Hippocrates of Chios; duplicating the cube and squaring the circle; trisecting angles; Theaetetus; Plato; Eudoxus of Cnidus (pyramid, cone); Aristotle (the infinite, the lever); Euclid. Volume II contains: Aristarchus (distances of sun and moon); Archimedes (cylinder, sphere, cubic equations; conoids; spheroids; spiral; expression of large numbers; mechanics; hydrostatics); Eratosthenes (measurement of the earth); Apollonius (conic sections and other works); later development of geometry; trigonometry (including Ptolemy's table of sines); mensuration: Heron of Alexandria; algebra: Diophantus (determinate and indeterminate equations); the revival of geometry: Pappus. Indexes 704 pages Hardcover edition January 1941 ISBN 0-674-99399-3

56. Adventures In CyberSound: Euclid Among these are hippocrates of chios (5th century BC), not to be confused withthe physician Hippocrates of Cos (flourished 400 BC). http://www.acmi.net.au/AIC/EUCLID_BIO.html

A D V E N T U R E S in C Y B E R S O U N D Euclid (alt: Euklid, Eucleides) : 365 - 300 BC Euclid's The Optics is the earliest surviving work on geometrical optics, and is generally found in Greek manuscripts along with elementary works on spherical astronomy. There were a number of medieval Latin translations, which became of new importance in the fifteenth century for the theory of linear perspective. This technique is beautifully illustrated in the miniature of a street scene in this elegant manuscript from the library of the Duke of Urbino. It may once have been in the possession of Piero della Francesca, who wrote one of the principal treatises on perspective in painting. Source: The Vatican Library Euclid , Greek Eucleides (fl. c. 300 BC, Alexandria), the most prominent mathematician of Greco-Roman antiquity, best known for his treatise on geometry, the Elements Life and work Of Euclid's life it is known only that he taught at and founded a school at Alexandria in the time of Ptolemy I Soter , who reigned from 323 to 285/283 BC. Medieval translators and editors often confused him with the philosopher

57. Mathematics: Development Of Mathematics BC), hippocrates of chios made the beginnings of an axiomatic approach to geometryand Zeno of Elea proposed his famous paradoxes concerning the infinite http://www.infoplease.com/ce6/sci/A0859534.html

in All Infoplease Almanacs Biographies Dictionary Encyclopedia Daily Almanac for Sep 1, 2005 Skip Navigation Home Almanacs ... Word of the Day Editor's Favorites Back to School Hurricanes Daylight Saving Time Energy Consumption ... Mississippi Infoplease Tools Periodic Table Conversion Tool Perpetual Calendar Year by Year ... Site Map College Center Scholarship Search College Resources Career Center Job Search Post Your Resume Continuing Ed. more . . . Search: Infoplease Info search tips Search: Biographies Bio search tips google_ad_client = 'pub-1894504138907931'; google_ad_width = 120; google_ad_height = 240; google_ad_format = '120x240_as'; google_ad_type = 'text'; google_ad_channel =''; google_color_border = ['336699','B4D0DC','DFF2FD','B0E0E6']; google_color_bg = ['FFFFFF','ECF8FF','DFF2FD','FFFFFF']; google_color_link = ['0000FF','0000CC','0000CC','000000']; google_color_url = ['008000','008000','008000','336699']; google_color_text = ['000000','6F6F6F','000000','333333']; Encyclopedia mathematics Development of Mathematics The earliest records of mathematics show it arising in response to practical needs in agriculture, business, and industry. In Egypt and Mesopotamia, where evidence dates from the 2d and 3d millennia B.C.

58. Math Forum - Geometry Problem Of The Week as is the part of the outer semicircle that s not part of the original semicircle.What did hippocrates of chios prove about these two regions? http://mathforum.org/geopow/archive/011797.geopow.html

A Math Forum Project Hippocrates' Lunes - January 13-17, 1997 Problems from Spring 1997 All Problems Search POWs not part of the original semicircle. Rumor has it that Hippocrates of Chios proved something about the two shaded regions, but the next page of my book is missing. What's the story? Solutions Annie says: We had a good batting average this week - 34 right and only 3 wrong. One of the "wrong" ones was essentially right but I could not for the life of me understand the explanation. Another person did all the work but never stated what the answer was. And the other person didn't understand what I was looking for. All in all, a pretty decent week. Here are some comments from Dale Pearson, who teaches at Highland Park Senior High School: It was surprising to most of my students that the two yellow figures must be equal in area. Only one student suspected that this might be the case before any calculations were made. Most students thought that the triangle was larger. A couple of students thought that the moon-shaped figure was larger. This was not the end of the surprises, however. Many students has difficulty finding any relationships whatsoever among the elements of the figure until they found a orderly way to keep track of their results.

59. Euclid - Books I-IX in his account of the quadrature of certain lunes by hippocrates of chios, “As regards hippocrates of chios we must pay more attention to Eudemus, http://www.headmap.org/unlearn/euclid/before/proclus.htm

@import url(../../../ul-css/3-col-nn4-new-main.css); the teS Euclids elements BOOKS I-IX translated by T.L. Heath BACKGROUND euclid and the traditions about him. euclid's other works. greek commentators on the elements ... modern algebraic interpretations [see also: equations - Diophantus; conics - Appolonius] HEADMAP home unlearning EUCLID BOOK I BOOK II BOOK III BOOK IV ... BOOK IX OVERVIEW book 1, triangles book 2, quadratics books 3 and 4, circles book 5, theory of proportion book 6, geometry and the theory of proportion books 7, 8 and 9 ,number theory GEOMETRICAL ALGEBRA book II identities gemetrical solution of quadratics application of areas transformation of areas ... Book V notes Book VII notes Book VIII notes Book IX notes [p. 29] CHAPTER IV. PROCLUS AND HIS SOURCES It is well known that the commentary of Proclus on Eucl. Book I. is one of the two main sources of information as to the history of Greek geometry which we possess, the other being the Collection of Pappus. They are the more precious because the original works of the forerunners of Euclid, Archimedes and Apollonius are lost, having probably been discarded and forgotten almost immediately after the appearance of the masterpieces of that great trio. Proclus himself lived 410-485 A.D., so that there had already passed a sufficient amount of time for the tradition relating to the pre-Euclidean geometers to become obscure and defective. In this connexion a passage is quoted from Simplicius

60. Math-History Timeline Elements of hippocrates of chioshippocrates of chios (470 – 410 BCE) Hippocratesof Chios was an excellent geometer who taught in Athens. http://www.math.wichita.edu/~richardson/timeline.html

A Time-line for the History of Mathematics (Many of the early dates are approximates) This work is under constant revision, so come back later. Please report any errors to me at richardson@math.wichita.edu. It should be noted that the brief descriptions given are just that "brief." Their purpose is to hopefully instill a little curiosity and encourage the reader to seek out further knowledge on these people and topics. 50,000 B.C.E. Evidence of counting 50,000 B.C.E. Neanderthal man 25,000 B.C.E. Primitive geometrical designs 25,000 B.C.E. Paleolithic art: Cro-Magnon man 4000 B.C.E. Use of metals 3500 B.C.E. Writing 3000 B.C.E. Hieroglyphic numerals in Egypt 3000 B.C.E. Use of wheeled vehicles Wheeled vehicles first appeared in Mesopotamia (the region between the Tigris and the Euphrates Rivers ) around 3000 B.C.E. They were originally four-wheel vehicles drawn by slow-moving animals. The wheels on the earliest vehicles were fixed to the axles rather than rotating around a hub. The axles themselves were held in place with wooden pegs on each side of the axle. The axle rotated against the bed of the vehicle and this probably helped round the axles. 2773 B.C.E. Likely introduction of the Egyptian calendar (Some hypothesize 4241 B.C.E. as the origin.)

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