1. Hippocrates hippocrates of chios taught in Athens and worked on the classical problems of hippocrates of chios, the discoverer of the quadrature of the lune, http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Hippocrates.html

Hippocrates of Chios Born: about 470 BC in Chios (now Khios), Greece Died: about 410 BC Click the picture above to see a larger version Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Version for printing Hippocrates of Chios taught in Athens and worked on the classical problems of squaring the circle and duplicating the cube Iamblichus [4] writes:- One of the Pythagoreans Hippocrates lost his property, and when this misfortune befell him he was allowed to make money by teaching geometry. Heath [6] recounts two versions of this story:- One version of the story is that Hippocrates was a merchant, but lost all his property through being captured by a pirate vessel. He then came to Athens to persecute the offenders and, during a long stay, attended lectures, finally attaining such proficiency in geometry that he tried to square the circle. Heath also recounts a different version of the story as told by Aristotle ... he allowed himself to be defrauded of a large sum by custom-house officers at Byzantium, thereby proving, in Aristotle 's opinion, that, though a good geometer, he was stupid and incompetent in the business of ordinary life.

2. Hippocrates Of Chios Hippocrates, born in the island of Chios, in Ionia, started, according to a tradition recorded in Philoponus' Commentary on Aristotle's http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

3. Hippocrates Of Chios Biography of hippocrates of chios http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

4. Hippocrates Of Chios hippocrates of chios. mid fifth century BCE. hippocrates of chios. One of thegreatest geometers of antiquity, Hippocrates, started out as a merchant. http://www.math.sfu.ca/histmath/Europe/Euclid300BC/HIPPOCRATES.HTML

Hippocrates of Chios mid fifth century B.C.E. One of the greatest geometers of antiquity, Hippocrates, started out as a merchant. Aside from being a brilliant mathematician, Aristotle said he was not a very clever merchant, since he was cheated of his money by crooked tax officials in Byzantium (some say he was robbed by pirates.) After moving to Athens around 430 B.C.E. to prosecute the offenders, he attended lectures in his leisure time and eventually became a teacher of geometry. One of Hippocrates achievements was that of the quadrature or squaring of the circle. Hippocrates also worked on the duplication of the cube and was the first to reduce the problem of doubling the cube of side a to the problem of discovering two mean proportionals b, c between a and 2a. For if a:b = b:c = c:2a then a :b = (a:b) = (a:b)(b:c)(c:2a)=a:2a and b . Hippocrates was unable to solve this proportion of finding two mean proportionals between one straight line and another line twice as long. The approach Hippocrates took to the problem simplified it from one of solid geometry to one of plane geometry. Hippocrates is said to be the first to have written an Elements of Geometry

5. Hippocrates hippocrates of chios http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

6. History Of Math Notes - Simon Fraser University hippocrates of chios. 1st to attack cube and circle problems. The theorems heused he organized into the 1st recorded book on the elements of geometry. http://www.math.sfu.ca/histmath/math380notes/math380.html

History of Math Notes These are my notes from Math-380 lectures in Spring 1998. Also available in Microsoft Word 97 format: math380.zip Babylon Oldest civilization: Mesopotamia (Babylonia) The superiority of Babylonian mathematics is based on the place-value notation of its number system. 3500 BC Clay tablets with numbers 1800 BC King Hamorabi wrote laws on clay tablets Flourishing period of Babylonian math. 700’s BC King Nabonasssar Eclipse records 530 BC Triangular inscriptions of Bisistun (Iran) Cuneiform (script language of Babylon) deciphered by Rawlonson in 1800s Number System Base 60 Positional Had a special symbol for empty places (zero) Algebra Uses algorithms , but doesn’t explain them No symbols Only one solution in quadratic equation , not the usual two. No negative numbers No apparent practical value (always produced nice round numbers) Study of solutions of Pythagorean triangles Babylonians were the only ancient people to solve quadratic equations as we do today. Right Triangles st to state Pythagorean theorem They knew how to solve a + b = c Plimpton 322 Root Extraction Approximated roots by method of "completing the square"

7. Hippocrates Chicago Marquis Hippocrates. Encyclopedia Britannica (Online) http//www.eb.com/Hippocrates (November 12, 1997) http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

8. Hippocrates Of Chios Hippocrates, born in the island of Chios, in Ionia, started, according to atradition recorded in Philoponus Commentary on Aristotle s Physics, http://plato-dialogues.org/tools/char/hipchios.htm

Bernard SUZANNE Last updated December 5, 1998 Plato and his dialogues : Home Biography Works History of interpretation ... New hypotheses - Map of dialogues : table version or non tabular version . Tools : Index of persons and locations Detailed and synoptic chronologies - Maps of Ancient Greek World . Site information : About the author This page is part of the "tools" section of a site, Plato and his dialogues , dedicated to developing a new interpretation of Plato's dialogues. The "tools" section provides historical and geographical context (chronology, maps, entries on characters and locations) for Socrates, Plato and their time. For more information on the structure of entries and links available from them, read the notice at the beginning of the index of persons and locations Hippocrates, born in the island of Chios , in Ionia, started, according to a tradition recorded in Philoponus' Commentary on Aristotle's Physics , as a merchant and came to Athens to prosecute pirates who had robbed him of all his goods. Required to stay there for a while to settle his case, he consorted with philosophers and became interested in mathematics, so that in the end, he stayed in Athens from about 450 to 430 B. C. He was, according to Proclus ( Commentary on Euclid , I), the first to write Elements (possibly around B. C.), more than one century before those of Euclid (usually dated from around 300 B. C.), but his works are no longer extant and are known only from references by later commentators. In trying to square the circle, Hippocrates adressed the problem of the surface of lunes, figures included between two intersecting arcs of circles.

9. Hippocrates Biography Of Hippocrates Biography of Hippocrates. Hippocrates, (460377? BC), an extraordinary medical writer of Greece. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

10. Chios Chios was he birthplace of the great mathematician hippocrates of chios (not tobe confused with the famous physician of the same name, Hippocrates of Cos), http://plato-dialogues.org/tools/loc/chios.htm

Bernard SUZANNE Last updated November 15, 1998 Plato and his dialogues : Home Biography Works History of interpretation ... New hypotheses - Map of dialogues : table version or non tabular version . Tools : Index of persons and locations Detailed and synoptic chronologies - Maps of Ancient Greek World . Site information : About the author This page is part of the "tools" section of a site, Plato and his dialogues , dedicated to developing a new interpretation of Plato's dialogues. The "tools" section provides historical and geographical context (chronology, maps, entries on characters and locations) for Socrates, Plato and their time. By clicking on the minimap at the beginning of the entry, you can go to a full size map in which the city or location appears. For more information on the structure of entries and links available from them, read the notice at the beginning of the index of persons and locations Large island off the coast of Asia Minor, south of Lesbos , and main city on that island (area 7) Chios was a member city of the Ionian Confederacy, the

11. Hippocrates Of Chios hippocrates of chios mid fifth century B.C.E. One of the greatest geometers of antiquity, Hippocrates, started out as a merchant. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

12. Hippocrates Of Chios (ca. 450 BC) -- From Eric Weisstein's World Of Scientific B hippocrates of chios (ca. 450 BC) Dunham, W. Hippocrates Quadrature of theLune. Ch. 1 in Journey Through Genius The Great Theorems of Mathematics. http://scienceworld.wolfram.com/biography/HippocratesofChios.html

Branch of Science Mathematicians Nationality Greek Hippocrates of Chios (ca. 450 BC) Greek mathematician who squared lunes in the 5th century B. C. Additional biographies: Greek and Roman Science and Technology References Dunham, W. "Hippocrates' Quadrature of the Lune." Ch. 1 in Journey Through Genius: The Great Theorems of Mathematics. New York: Wiley, pp. 1-20, 1990. Heath, T. L. A History of Greek Mathematics, Vol. 1: From Thales to Euclid. New York: Dover, p. 185, 1981.

13. Hippocrates Of Chios Example Essays.com - Over 101 000 Essays hippocrates of chios by Rob Fisch It can be argued that if Euclid is the father of Geometry that hippocrates of chios could be considered the http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

14. Hippocrates Of Chios --  Encyclopædia Britannica hippocrates of chios Greek geometer who compiled the first known work on theelements of geometry nearly a century before Euclid. http://www.britannica.com/eb/article?tocId=9040541

15. Hippocrates Links Hippocrates Image Source http//scienceworld.wolfram.com/biograp. .. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

16. Ion Of Chios --  Britannica Student Encyclopedia hippocrates of chios Greek geometer who compiled the first known work on theelements of hippocrates of chios University of St. Andrews, Scotland http://www.britannica.com/ebi/article?tocId=9327216

17. Hippocrates hippocrates of chios Ca. 470 BCE to 410 BCE. A Pythagorean, hippocrates of chios spent many years in Athens studying and teaching mathematics. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

18. Quadrature Of A Convex Polygon And The Lune Of Hippocrates hippocrates of chios was able to show that the area of the “Lune” (a lune is hippocrates of chios ( (not Kos! )) spent his life studying geometry after http://www.mlahanas.de/Greeks/PolygonQuadrature.htm

Quadrature of a Convex Polygon and the Lune of Hippocrates Michael Lahanas Griechische Mathematik: Hippokrates Quadratur Some report also, that Thales and Hippocrates the mathematician traded; and that Plato defrayed the charges of his travels by selling oil in Egypt. Solon By Plutarch It is believed that Greeks knew a method for reducing a convex polygon of any number of sides to a triangle of equal area. In the figure below we consider a polygon ABCFGHJ. We take a side CF extended to meet a line GK from an adjacent vertex, running parallel to the diagonal FH in the polygon. We cut a corner by connecting H with K, while maintaining the same area. So we see a complex figure equated to a simpler one. The polygon with 7 vectices ABCFGHJ has the same area as the polygon with 6 vertices ABCKHJ. To see this we construct a parallel to FH at G. Extend CF that meets this parallel at K. FHK and FGH have the same height and base FH. A similar process can be continued with the polygon ABCKHJ again until we obtain a triangle. First Step: Construct a rectangle with an area equal to the triangle assumed to be ABC. For this bisect the height AD at E. Now the rectangle HJIG with width IJ = BC and height JH = ED has the same area as the triangle ABC.

19. Hippocrates Of Chios hippocrates of chios by Rob Fisch It can be argued that if Euclid is the father of Geometry that hippocrates of chios could be considered the http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

20. Timeline Related To Greek Science And Technology 1/2 hippocrates of chios squared the lune, a major step toward squaring the circle,probably using the theorem that circles are to one another as the squares of http://www.mlahanas.de/Greeks/HistoricEvents.htm

How Science was Born in 300 BC and Why It Had to Be Reborn Timeline related to Greek Science and Technology Part 1 Griechische Wissenschaft Zeitlinie 1184 BC Aeschylus writes in Agamemnon that smoke signals were used to send the message from Troy to the city Argos of the victory by the Greeks 1100-800 BC Dark Ages in Greece, Mycenian civilization decline, Invasion of Dorians and Ionians 800 BC Vowels were by the Greeks to consonants of Phoenician origin. 800-701 BC Homer refers to highly developed battlefield surgery. 776 BC Olympic Games About 700 BC Gold coins were introduced in Lydia western Anatolia, as a standard of exchange. Development of Biremes Ships. 700-601 BC Caleus (Kaleus) from Samos is the first to sail through Straits of Gibraltar (Pillars of Hercules). Glaucus of Chios invents soldering of iron. 688 BC Boxing added to Olympic discipline 650 BC Development of Triremes Ships. Although the invention could be around 700 BC. Ameinocles the Corinthian, to whom this invention is ascribed, made the Samians acquainted with it (Thucyd. i.13; Plin.H.N.vii.57) but triremes were used only later. 624 BC Horse Racing added to Olympic discipline Around 600 BC the Cretan poet Epimenides is attributed to have invented the linguistic paradox with his phrase "Cretans are ever liars" - the Liar's Paradox. 2500 years later, the mathematician Kurt Gödel invents an adaptation of the Liar's Paradox that reveals serious axiomatic problems at the heart of modern mathematics.

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