21. 4th Century BC: Information From Answers.com In the year 380 bce Astronomy eudoxus of cnidus b. Cnidus (Turkey) c. 408 bce , d.Cnidus, c. 355 bce develops the first version of a theoretical. http://www.answers.com/topic/4th-century-bc

showHide_TellMeAbout2('false'); Business Entertainment Games Health ... More... On this page: Wikipedia Mentioned In Or search: - The Web - Images - News - Blogs - Shopping 4th century BC In the year bce Astronomy Eudoxus of Cnidus [b. Cnidus (Turkey) c. 408 bce , d. Cnidus, c. 355 bce ] develops the first version of a theoretical explanation of the motions of the planets, probably in response to a problem posed by Plato. He assigns each planet three or four spheres, each of which is centered on Earth. As the planet moves on the innermost sphere, that sphere is also carried by the next sphere out, which in turn is carried by the third sphere (and that by a fourth for each planet, with three needed only for the Sun and Moon). Each sphere moves uniformly on its own axis of rotation. By carefully choosing the axes and speeds for each of 27 spheres, the system describes the motions of all the heavenly bodies up to the limits of observations at that time. See also bce Astronomy bce Astronomy Communication Eudoxus improves on the primitive map of the Earth of Hecataeus.

22. Eudoxus Of Cnidus Eudoxus, born in the city of Cnidus in southern Asia Minor, in the last years ofthe Vth century BC, is one of the great mathematicians of all times, http://plato-dialogues.org/tools/char/eudoxus.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 Eudoxus, born in the city of Cnidus in southern Asia Minor, in the last years of the Vth century B. C., is one of the great mathematicians of all times, and probably the greatest of ancient Greece's mathematicians. He may have belonged to a family of physicians, because, at the time, Cnidus was famous for its school of medicine, and started his carrier travelling with fellow-physicians. When he was 23, he stayed for two months in , going each day to Athens to listen to Plato and other Socratics. Later he went to Egypt, where he learned astronomy from priests of Heliopolis. Back from Egypt, he went to

23. Synoptic Chronology Of Greek Thinkers And Writers Archytas of Tarentum, Aristippus of Cyrene, Aristophanes, Aristotle, Democritus,Empedocles, Epicurus, Euclid of Megara, eudoxus of cnidus, Euripides, http://plato-dialogues.org/tools/synopsis.htm

Bernard SUZANNE Last updated January 3, 1999 Plato and his dialogues : Home Biography Works and links to them 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 Synoptic chronology of Greek Thinkers and Writers This synopsis presents a visual chronology of some of the Greek writers and thinkers that preceeded, were contemporaries of, and followed Socrates and Plato, allowing to quickly see in what order they lived and who was contemporary of whom. It also includes for context some of the most prominent political leaders of the time. The dates are associated with the Olympiad numbers that were used as reference by the Greek themselves. The reader must be warned that many of the dates of birth and death here provided are only tentative, and may differ in different sources, sometimes (such as with Parmenides, for instance) by several years. The purpose of this synopsis is not to pretend to utmost accuracy, or to suggest new datings, but to provide a feel for who might have been contemporary of whom. Accordingly, the dates used were those available from widely available history books or encyclopediae, and I didn't try to ascertain these before using them. To get a more "concrete" feel for this chronology, a

24. Eudoxus Of Cnidus. The Columbia Encyclopedia, Sixth Edition. 2001-05 eudoxus of cnidus. The Columbia Encyclopedia, Sixth Edition. 200105. http://www.bartleby.com/65/eu/EudoxusCn.html

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25. Eudoxus Of Cnidus eudoxus of cnidus, yOOdok sus, ni dus Pronunciation Key. eudoxus of cnidus ,408?–355? BC, Greek astronomer, mathematician, and physician. http://www.factmonster.com/ce6/people/A0817824.html

Home U.S. People Word Wise ... Homework Center Fact Monster Favorites 2006 TFK Almanac Quiz: Charlie and the Chocolate Factory SpongeBob Lemony Snicket ... Fantasy Books Reference Desk Atlas Almanacs Dictionary Encyclopedia ... Encyclopedia Eudoxus of Cnidus [y OO u u s] Pronunciation Key Eudoxus of Cnidus B.C. , Greek astronomer, mathematician, and physician. From the accounts of various ancient writers, he appears to have studied with Plato in Athens, spent some time in Heliopolis, Egypt, founded a school in Cyzicus, and spent his later years in Cnidus, where he had an observatory. It is claimed that he calculated the length of the solar year, indicating a calendar reform like that made later by Julius Caesar, and that he was the discoverer of some parts of geometry included in the work of Euclid. He was the first Greek astronomer to explain the movements of the planets in a scientific manner. His system involved a number of concentric spheres supporting the planets in their paths. Some scientists still held this belief at the time of Copernicus. The Columbia Electronic Encyclopedia

26. Cyzicus eudoxus of cnidus eudoxus of cnidus , 408?–355? BC, Greek astronomer, mathematician,and physician. From the See more Encyclopedia articles on http://www.factmonster.com/ce6/history/A0814440.html

Home U.S. People Word Wise ... Homework Center Fact Monster Favorites 2006 TFK Almanac Quiz: Charlie and the Chocolate Factory SpongeBob Lemony Snicket ... Fantasy Books Reference Desk Atlas Almanacs Dictionary Encyclopedia ... Encyclopedia Cyzicus u s] Pronunciation Key Cyzicus , ancient city, NW Turkey, at the neck of the Cyzicus Peninsula. Strategically located, it rivaled Byzantium in commercial importance. Founded (756 B.C. ) by Greek colonists from Miletus, it was a member of the Delian League. In 410 B.C. , Alcibiades defeated a Spartan fleet off Cyzicus, and in 74 B.C. the city withstood a siege by Mithradates VI of Pontus. As a reward for its loyalty, it became a free city under Roman rule. In A.D. 675 the town was pillaged by the Arabs and then used as a base for a siege of Constantinople. There are ruins of a large temple built by Roman Emperor Hadrian and of other public buildings. The Columbia Electronic Encyclopedia, Page Tools: Cite Print See more Encyclopedia articles on: Ancient History, Middle East AD AD AD ADS Business Cards Link to Fact Monster Add Fact Monster search ... Privacy Brought to you by: Information Please

27. Eudoxus Of Cnidus Biography / Biography Of Eudoxus Of Cnidus Biographies eudoxus of cnidus Biography profile biographies life history. http://www.bookrags.com/biography/eudoxus-of-cnidus/

Eudoxus of Cnidus Biography Literature Summaries Study Guides Essays Search BookRags.com English History Other Subjects Essays Biographies Research Topics eBooks Register Login Help Literature Study Guides ... Games Welcome, Guest Why not Login or Register Biography Navigation Eudoxus of Cnidus Index Main Biography World of Mathematics Biography 2000 B.C. To A.D. 699: Mathematics Biography 2000 B.C. To A.D. 699: Mathematics Biography How to Cite Order the PDF Home Biography Eudoxus of Cnidus Biographies Complete Biographical Resource See related items by keyword: theory earth center asia ... astronomical work Name: Eudoxus of Cnidus Birth Date: c. 408 B.C. Death Date: c. 355 B.C. Place of Birth: Cnidus, Greece Nationality: Greek Gender: Male Occupations: astronomer, mathematician, physician Eudoxus of Cnidus Biographies The following biographies focus on different aspects of Eudoxus of Cnidus's life and work. All biographies listed are included in the Eudoxus of Cnidus Biography Pass. Main Biography (3.1 pages) World of Mathematics Biography (1.2 pages) 2000 B.C. To A.D. 699: Mathematics Biography (1.9 pages) 2000 B.C. To A.D. 699: Mathematics Biography (0.2 pages) Eudoxus of Cnidus Biography Each biography is written by a biographical expert, professional educator, or scholar of the individual.

28. Eudoxus Of Cnidus eudoxus of cnidus (The Columbia Encyclopedia, Sixth Edition). Eudoxus ofCnidus (408355 BC) (The Hutchinson Dictionary of Scientific Biography) http://www.infoplease.com/ce6/people/A0817824.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 School Shootings ... 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 Eudoxus of Cnidus [y OO u u s] Pronunciation Key Eudoxus of Cnidus B.C.

29. Cnidus eudoxus of cnidus (The Columbia Encyclopedia, Sixth Edition) Eudoxus ofCnidus (408355 BC) (The Hutchinson Dictionary of Scientific Biography) http://www.infoplease.com/ce6/history/A0812661.html

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30. Eudoxus Of Cnidus eudoxus of cnidus Born c. 390 BC Birthplace Cnidus, Asia Minor Eudoxus, ofCnidus, Greek savant, flourished about the middle of the 4th century BC. http://www.nndb.com/people/658/000096370/

This is a beta version of NNDB Search: All Names Living people Dead people Band Names Book Titles Movie Titles Full Text for Eudoxus of Cnidus Born: c. 390 BC Birthplace: Cnidus, Asia Minor Died: c. 340 BC Location of death: Cnidus, Asia Minor Cause of death: unspecified Gender: Male Ethnicity: White Occupation: Mathematician Astronomer Level of fame: Niche Executive summary: Influential Greek mathematician Plato , but, being dismissed, passed over into Egypt, where he remained for sixteen months with the priests of Heliopolis. He then taught physics in Cyzicus and the Propontis, and subsequently, accompanied by a number of pupils, went to Athens. Towards the end of his life he returned to his native place, where he died. Strabo states that he discovered that the solar year is longer than 365 days by 6 hours; Vitruvius that he invented a sundial. The Phaenomena of Aratus is a poetical account of the astronomical observations of Eudoxus. In astronomy he described constellations, and attempted a model of the solar system. Several works have been attributed to him, but they are all lost; some fragments are preserved in the extant work of the astronomer Hipparchus. According to Aristotle 's Ethics , Eudoxus held that pleasure was the chief good, because (1) all beings sought it and endeavored to escape its contrary, pain; (2) it is an end in itself, not a relative good. Aristotle, who speaks highly of the sincerity of Eudoxus's convictions, while giving a qualified approval to his arguments, considers him wrong in not distinguishing the different kinds of pleasure and in making pleasure the

31. Eudoxus Of Cnidus (c. 400-c. 347 B.C.) eudoxus of cnidus (c. 400c. 347 BC). A Greek mathematician and astronomer whodevised a scheme of the heavens in which the Sun, Moon, and planets traveled http://www.daviddarling.info/encyclopedia/E/Eudoxus.html

Return to The Worlds of David Darling INDEX LATEST NEWS ARCHIVE ... Z entire Web this site Eudoxus of Cnidus (c. 400-c. 347 B.C.) A Greek mathematician and astronomer who devised a scheme of the heavens in which the Sun, Moon, and planets traveled around Earth on 27 geocentric spheres, rotating at different speeds and inclinations. This concept of planetary motion, refined by Callipus and ultimately by Ptolemy , provided the standard model of the cosmos for 2,000 years. GREEK ASTRONOMY BACK TO TOP var site="s13space1234"

32. AllRefer.com - Eudoxus Of Cnidus (Astronomy, Biography) - Encyclopedia AllRefer.com reference and encyclopedia resource provides complete informationon eudoxus of cnidus, Astronomy, Biographies. http://reference.allrefer.com/encyclopedia/E/EudoxusCn.html

AllRefer Channels :: Health Yellow Pages Reference Weather September 01, 2005 Medicine People Places History ... Maps Web AllRefer.com You are here : AllRefer.com Reference Encyclopedia Astronomy, Biographies ... Eudoxus of Cnidus By Alphabet : Encyclopedia A-Z E Eudoxus of Cnidus, Astronomy, Biographies Related Category: Astronomy, Biographies Eudoxus of Cnidus [y OO u s, n I u s] Pronunciation Key B.C. , Greek astronomer, mathematician, and physician. From the accounts of various ancient writers, he appears to have studied with Plato in Athens, spent some time in Heliopolis, Egypt, founded a school in Cyzicus, and spent his later years in Cnidus, where he had an observatory. It is claimed that he calculated the length of the solar year, indicating a calendar reform like that made later by Julius Caesar, and that he was the discoverer of some parts of geometry included in the work of Euclid. He was the first Greek astronomer to explain the movements of the planets in a scientific manner. His system involved a number of concentric spheres supporting the planets in their paths. Some scientists still held this belief at the time of Copernicus. Topics that might be of interest to you: mathematics Related Categories: People Science and Technology Science and Technology Astronomy and Space Exploration ... Biographies More articles from AllRefer Reference on Eudoxus of Cnidus SITE MAPS Encyclopedia US Gazetteer: US States A-C US States D-H US States I-L US States M ... Countries A-Z Content on this web site is provided for informational purposes only. We accept no responsibility for any loss, injury or inconvenience sustained by any person resulting from information published on this site. We encourage you to verify any critical information with the relevant authorities.

33. Eudoxus We re here with the ghost of the famous mathematician, eudoxus of cnidus. “eudoxus of cnidus Encylcopedia Britanica. 1999 ed. http://www.3villagecsd.k12.ny.us/wmhs/Departments/Math/OBrien/eudoxus.html

Eudoxus We're here with the ghost of the famous mathematician, Eudoxus of Cnidus. Responsible for many mathematical feats, he was also a famous astronomer and legislator. Q. When were you born? A. About 400 BC. My father was Aischimes. Q. Where were you born? A. Cnidus, on the Black Sea. It is located in Asia Minor, or current day Turkey. Q. Did you receive any education? A. First I studied under Archytas, a follower of Pythagoras, who influenced my math career. I later studied medicine with Philistium on Sicily. Then when I was twenty-three years old, I went to Plato's academy in Athens where I studied philosophy and rhetoric. I also studied astronomy in Egypt at Helopolis. Q. After receiving your education, what did you do? A. I established a school at Cyzicus, located in northwestern Asia Minor, on the shore of the Marmora Sea. I returned with my pupils to Athens in 365 BC. There, I became a colleague of Plato and a respected legislator. Q. Were you close friends with Plato? A. Actually, he was jealous of how popular my school was. So, as you can imagine, we weren't exactly great friends. Q. When did you die?

34. Encyclopedia Of Astronomy And Astrophysics » Eudoxus Of Cnidus (c. 400–c. eudoxus of cnidus (c. 400–c. 347 BC). DOI 10.1888/0333750888/3609; PublishedNovember 2000. Icon Full text (PDF, 21K) http://eaa.iop.org/index.cfm?action=summary&doc=eaa/3609@eaa-xml

35. Encyclopedia Of Astronomy And Astrophysics » Planetary Theory From Eudoxus To C Planetary Theory from Eudoxus to Copernicus. Author. NM Swerdlow. DOI10.1888/0333750888/1923; Published November 2000 eudoxus of cnidus http://eaa.iop.org/index.cfm?action=summary&doc=eaa/1923@eaa-xml

36. Article About "Eudoxus Of Cnidus" In The English Wikipedia On 24-Jul-2004 The eudoxus of cnidus reference article from the English Wikipedia on 24Jul-2004 eudoxus of cnidus. Another article treats of Eudoxus of Cyzicus. http://july.fixedreference.org/en/20040724/wikipedia/Eudoxus_of_Cnidus

The Eudoxus of Cnidus reference article from the English Wikipedia on 24-Jul-2004 (provided by Fixed Reference : snapshots of Wikipedia from wikipedia.org) Eudoxus of Cnidus Another article treats of Eudoxus of Cyzicus Eudoxus of Cnidus Greek 408 BC - circa 347 BC ) was a Greek astronomer mathematician physician , scholar and friend of Plato . Since all his own works are lost, our knowledge of him is obtained from secondary sources, such as Aratus 's poem on astronomy He was a pupil in mathematics of Archytas in Athens . In mathematical astronomy his fame is due to the introduction of the astronomical globe , and his early contributions to understanding the movement of the planets His work on proportions shows tremendous insight into numbers ; it allows rigorous treatment of continuous quantities and not just whole numbers or even rational numbers . When it was revived by Tartaglia and others in the , it became the basis for quantitative work in science for a century, until it was replaced by the algebraic methods of Descartes Eudoxus invented the method of exhaustion, which was used in a masterly way by Archimedes . The work of Eudoxus and Archimedes as precursors of calculus was only exceeded in mathematical sophistication and rigour by Newton himself.

37. Eudoxus Systems - Biography Of Eudoxus biography of eudoxus of cnidus, ancient greek mathematician and astronomer. eudoxus of cnidus (c.408 c.355 BC) was one of the greatest Greek http://www.eudoxus.com/eudoxus.html

Home Search About us Eudoxus Tools We Use What is Optimization? MP in Action Lecture Notes ... Site Map Eudoxus of Cnidus Eudoxus of Cnidus (c.408 - c.355 BC) was one of the greatest Greek mathematicians. He was also an astronomer, philosopher and legislator. His main contributions to mathematics were: the theory of proportion, which resolved the crisis in Greek mathematics caused by the discovery of irrational numbers; the method of exhaustion, which was a precursor (by 2000 years) of the integral calculus. He may also have been responsible for the development of the axiomatic method, the foundation of modern mathematics. His work in astronomy has stood the test of time less well. He developed a model of the universe which sought to explain the motions of the sun, the moon and the planets by fixing them to a system of 27 (or according to some authorities, 55) concentric spheres. These rotated on assorted axes at various speeds with the earth at the centre. Even with all this ingenuity he was unable to explain the motions of Venus and Mars nor the variation in brightness of the moon. His scheme was a magnificent attempt to explain observed phenomena, but wrong. More long lasting in its influence was 'the sphere of Eudoxus'. This was an engraved celestial globe which showed the constellations together with their names. Eudoxus did not invent these, but carried them over from an earlier civilisation, most probably the Babylonians of c. 2500 BC. These names have remained in use to this day and are also the names we use as the signs of the Zodiac.

38. Eudoxus Systems - Optimization Solutions For Industry Eudoxus Systems specialises in mathematical modelling using linear We calledour company Eudoxus after the Greek mathematician eudoxus of cnidus. http://www.eudoxus.com/us.html

Home Search About us Eudoxus Tools We Use What is Optimization? MP in Action ... Site Map About us Eudoxus Systems Ltd is a group of mathematicians who enjoy helping businesses to make better decisions and run their operations more efficiently. We do this by analysing business problems and building mathematical models of them. We then apply mathematical techniques such as optimization to the models and translate the resulting solutions back into the real world. Often we embed our models within operational systems so that they can provide day-to-day assistance to those businesses. Our main technical strength lies in models involving linear programming and its more complex relative, integer programming . These are techniques which we have been using for the past 20 years to tackle planning and scheduling problems around the world. We also believe in promoting their wider use, hence this web site with its examples of applications and its lecture notes to help you learn how to apply the techniques yourself. The main business areas in which we work are the oil industry and paper and packaging. The oil industry reflects our background: at one time or another all our staff have been employed by BP or its software subsidiary, Scicon. Paper and packaging is a more recent interest and reflects the complexity of the problems facing the industry, where planning and scheduling problems are made harder by the complexities of deckling and trim loss optimization.

39. Read About Eudoxus Of Cnidus At WorldVillage Encyclopedia. Research Eudoxus Of C eudoxus of cnidus. Everything you wanted to know about eudoxus of cnidus but hadno clue how to find it.. Learn about eudoxus of cnidus here! http://encyclopedia.worldvillage.com/s/b/Eudoxus_of_Cnidus

Culture Geography History Life ... WorldVillage Eudoxus of Cnidus From Wikipedia, the free encyclopedia. Another article treats of Eudoxus of Cyzicus Eudoxus of Cnidus Greek or 408 BC or 347 BC ) was a Greek astronomer mathematician physician , scholar and friend of Plato . Since all his own works are lost, our knowledge of him is obtained from secondary sources, such as Aratus 's poem on astronomy He was a pupil in mathematics of Archytas in Athens . In mathematical astronomy his fame is due to the introduction of the astronomical globe , and his early contributions to understanding the movement of the planets His work on proportions shows tremendous insight into numbers ; it allows rigorous treatment of continuous quantities and not just whole numbers or even rational numbers . When it was revived by Tartaglia and others in the , it became the basis for quantitative work in science for a century, until it was replaced by the algebraic methods of Descartes Eudoxus invented the method of exhaustion , which was used in a masterly way by Archimedes . The work of Eudoxus and Archimedes as precursors of calculus was only exceeded in mathematical sophistication and rigour by Indian Mathematician Bhaskara and later by Newton An algebraic curve (the Kampyle of Eudoxus) is named after him a x = b (x + y Also

40. Eudoxus Of Cnidus eudoxus of cnidus ca. 408 ~ 355 BCE. Eudoxus Mathematics. Choose One of theFollowing, Eudoxus Theory of Propostions. For more about Eudoxus and links http://math.furman.edu/~jpoole/mth15hp/eudoxus/eudoxus.htm

Eudoxus of Cnidus ca. 408 ~ 355 BCE Eudoxus' Mathematics: Choose One of the Following: Eudoxus' Theory of Propostions For more about Eudoxus and links to other sites visit: St. Andrews University's Eudoxus of Cnidus Back to Mth.15 Home Page

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