1. History Of Math - Eudoxus Of Cnidus Profile of the 5thcentury Greek mathematician who introduced the theory of proportion, the concept of magnitude, and the method of exhaustion. eudoxus of cnidus. Eudoxus (c. 400 B.C.) is the greatest of the ancient mathematicians, surpassed only by Archimedes http://www.math.tamu.edu/~don.allen/history/eudoxus/eudoxus.html

Next: About this document Eudoxus of Cnidus Eudoxus (c. 400 B.C.) is the greatest of the ancient mathematicians, surpassed only by Archimedes but later. Biographical highlights: Eudoxus was born in Cnidos, on the Black Sea. He studied mathematics with Archytus in Tarentum. He studied medicine with Philistium on Sicily. At 23 years he went to Plato's academy in Athens to study philosophy and rhetoric. Some time later he went to Egypt to learn astronomy at Helopolis. He established a school at Cyzicus on the sea of Marmora and had many pupils. In 365 B. C. he returned to Athens with his pupils. He became a colleague of Plato. At the age of 53 he died in Cnidos, highly honored as a lawgiver. He was the leading mathematician and astronomer of his day. Eudoxus was the most reknown astronomer and mathematician of his day. In astronomy devised an ingenious planetary system based on spheres. The spherical earth is at rest at the center. Around this center, 27 concentric spheres rotate. The exterior one caries the fixed stars, The others account for the sun, moon, and five planets.

2. Encyclopædia Britannica Encyclopædia Britannica. eudoxus of cnidus. Encyclopædia Britannica Article http://www.britannica.com/eb/article?eu=33776

3. ASTR 228: Chapter 6 - Aristotelian Science And Cosmology 6.3. eudoxus of cnidus (ca. 400 ca. http://www.physics.gmu.edu/classinfo/astr228/CourseNotes/ln_ch06.htm

Chapter 6. Aristotelian Science and Cosmology Latest Modification: March 19, 1996 6.1. Socrates of Athens (470 - 399 b.c.) Ex stone cutter turned philosopher Represents a watershed in Greek philosophy; turned philosophical discussion from cosmological questions of the 5th and 6th century to questions of political and ethical concerns Plato of Athens (428 - 348 B.C.) Two-sphere concept, Earth as one sphere, surrounded by second set of spheres - the celestial realm Set task, according to Simplicius, of finding out "the uniform and ordered motions by the assumption of which the apparent movements of the planets can be accounted for" Aesthetic argument based on symmetry; apparently reasoned that celestial realm was arrayed on perfect geometric figure, the sphere, with planets moving in perfectly symmetric plane figure, the circle Generations of astronomers thought that planetary movements must be accounted for by combinations of uniform circular motions with Earth at center The ultimate product of geocentric cosmology was the Ptolemaic system. 6.3. Eudoxus of Cnidus (ca. 400 - ca. 347 B.C.)

4. Eudoxus eudoxus of cnidus. Born 408 BC in Cnidus (on Resadiye eudoxus of cniduswas the son of Aischines. As to his teachers, we know that http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Eudoxus.html

Eudoxus of Cnidus Born: 408 BC in Cnidus (on Resadiye peninsula), Asia Minor (now Turkey) Died: 355 BC in Cnidus, Asia Minor (now Turkey) Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Eudoxus of Cnidus was the son of Aischines. As to his teachers, we know that he travelled to Tarentum, now in Italy, where he studied with Archytas who was a follower of Pythagoras . The problem of duplicating the cube was one which interested Archytas and it would be reasonable to suppose that Eudoxus's interest in that problem was stimulated by his teacher. Other topics that it is probable that he learnt about from Archytas include number theory and the theory of music. Eudoxus also visited Sicily, where he studied medicine with Philiston, before making his first visit to Athens in the company of the physician Theomedon. Eudoxus spent two months in Athens on this visit and he certainly attended lectures on philosophy by Plato and other philosophers at the Academy which had only been established a short time before. Heath [3] writes of Eudoxus as a student in Athens:- ... so poor was he that he took up his abode at the Piraeus and trudged to Athens and back on foot each day. After leaving Athens, he spent over a year in Egypt where he studied astronomy with the priests at Heliopolis. At this time Eudoxus made astronomical observations from an observatory which was situated between Heliopolis and Cercesura. From Egypt Eudoxus travelled to Cyzicus in northwestern Asia Minor on the south shore of the sea of Marmara. There he established a School which proved very popular and he had many followers.

5. Eudoxus Biography of Eudoxus (408BC355BC) eudoxus of cnidus. Born 408 BC in Cnidus (on Resadiye peninsula), Asia Minor (now Turkey) http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Eudoxus.html

Eudoxus of Cnidus Born: 408 BC in Cnidus (on Resadiye peninsula), Asia Minor (now Turkey) Died: 355 BC in Cnidus, Asia Minor (now Turkey) Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Eudoxus of Cnidus was the son of Aischines. As to his teachers, we know that he travelled to Tarentum, now in Italy, where he studied with Archytas who was a follower of Pythagoras . The problem of duplicating the cube was one which interested Archytas and it would be reasonable to suppose that Eudoxus's interest in that problem was stimulated by his teacher. Other topics that it is probable that he learnt about from Archytas include number theory and the theory of music. Eudoxus also visited Sicily, where he studied medicine with Philiston, before making his first visit to Athens in the company of the physician Theomedon. Eudoxus spent two months in Athens on this visit and he certainly attended lectures on philosophy by Plato and other philosophers at the Academy which had only been established a short time before. Heath [3] writes of Eudoxus as a student in Athens:- ... so poor was he that he took up his abode at the Piraeus and trudged to Athens and back on foot each day. After leaving Athens, he spent over a year in Egypt where he studied astronomy with the priests at Heliopolis. At this time Eudoxus made astronomical observations from an observatory which was situated between Heliopolis and Cercesura. From Egypt Eudoxus travelled to Cyzicus in northwestern Asia Minor on the south shore of the sea of Marmara. There he established a School which proved very popular and he had many followers.

6. Infinity crucial role in the Elements. There Euclid explains the method ofexhaustion due to eudoxus of cnidus. Often now this method is http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Infinity.html

Infinity Number theory index History Topics Index An article on infinity in a History of Mathematics Archive presents special problems. Does one concentrate purely on the mathematical aspects of the topic or does one consider the philosophical and even religious aspects? In this article we take the view that historically one cannot separate the philosophical and religious aspects from mathematical ones since they play an important role in how ideas developed. This is particularly true in ancient Greek times, as Knorr writes in [26]:- The interaction of philosophy and mathematics is seldom revealed so clearly as in the study of the infinite among the ancient Greeks. The dialectical puzzles of the fifth-century Eleatics, sharpened by Plato and Aristotle in the fourth century, are complemented by the invention of precise methods of limits, as applied by Eudoxus in the fourth century and Euclid and Archimedes in the third. Of course from the time people began to think about the world they lived in, questions about infinity arose. There were questions about time. Did the world come into existence at a particular instant or had it always existed? Would the world go on for ever or was there a finite end? Then there were questions about space. What happened if one kept travelling in a particular direction? Would one reach the end of the world or could one travel for ever? Again above the earth one could see stars, planets, the sun and moon, but was this space finite or do it go on for ever?

7. Eudoxus Of Cnidus (ca. 400-ca. 347 BC) -- From Eric Weisstein's World Of Scienti eudoxus of cnidus (ca. 400ca. 347 BC), Greek philosopher, astronomer,and mathematician who accepted Plato's notion of the rotation http://scienceworld.wolfram.com/biography/Eudoxus.html

Branch of Science Astronomers Branch of Science Mathematicians ... Greek Eudoxus of Cnidus (ca. 400-ca. 347 BC) Greek philosopher, astronomer, and mathematician who accepted Plato's notion of the rotation of the planets around the Earth on crystalline spheres, but noticed discrepancies with observations. He tried to adjust Plato's model by postulating that each crystalline sphere had its poles set to the next sphere. His model contained no mechanical explanation; it was simply a mathematical description. There were problems, however, with his model. First of all, each "hippopede" produced by the superposition of the motions of two spheres produced the same curve, yet the retrogressions of planets were observed to exhibit differing shapes. Secondly, although his models predicted tolerable retrogressions for Jupiter and Saturn and not for Mars or Venus Thirdly, his model in no way accounted for the observed differences in the lengths of the seasons Finally, the model failed to account for variations in the observed diameter of the Moon or changes in the brightness of planets, which were correctly interpreted to indicate that their distances were changing. Eudoxus was the first Greek to make a map of the stars.

8. 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.infoplease.com/ce5/CE017471.html

The # 1 wireless color security cam! Ultimate home movie ! Genuine Indian and Asian astrology reports and consultations by reputed Vedic Astrologers. Step-by-step guide to finding money for a growing business All Infoplease All Almanacs General Entertainment Sports Biographies Dictionary Encyclopedia Infoplease Home Almanacs Atlas Dictionary ... Fact Monster Kids' reference Info:Daily Fun facts Homework Center Newsletter You've got info! Help Site Map Visit related sites from: Family Education Network Encyclopedia Eudoxus of Cnidus [y OO u s, n I 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. Eudoxia Eudoxus of Cyzicus Search Infoplease Info search tips Search Biographies Bio search tips About Us Contact Us Link to Infoplease ... Privacy

9. Eudoxus Of Cnidus - Wikipedia eudoxus of cnidus (ca.408 BC ca.347 BC) was a Greek astronomer, mathematician, physician, scholar and friend of Plato. http://www.wikipedia.com/wiki/Eudoxus_of_Cnidus

Main Page Recent changes Edit this page Older versions Special pages Set my user preferences My watchlist Recently updated pages Upload image files Image list Registered users Site statistics Random article Orphaned articles Orphaned images Popular articles Most wanted articles Short articles Long articles Newly created articles Interlanguage links All pages by title Blocked IP addresses Maintenance page External book sources Printable version Talk Log in Help Eudoxus of Cnidus From Wikipedia, the free encyclopedia. Eudoxus of Cnidus (ca. 408 BC - ca. 347 BC ) was a Greek astronomer mathematician physician , scholar and friend of Plato . (His name is sometimes spelled Eudoxos ; the use of the letter "u" is a Latinization.) Since all his own works are lost, our knowledge of him is obtained from secondary sources, such as Agratus 's poem on astronomy. 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. He invented the method of exhaustion , which was used masterfully by Archimedes . The work of Eudoxus and Archimedes as precursors of calculus was only exceeded in mathematical sophistication and rigour by Newton himself.

10. TMTh:: EUDOXUS OF CNIDUS MATHEMATICIAN eudoxus of cnidus (fl. 408355 BC) Life Celebrated Greekmathematician, astronomer, geographer and philosopher, whose http://www.tmth.edu.gr/en/aet/1/46.html

Home Ancient Greek Scientists AGRICULTURALISTS ARCHITECTS ... PHYSICISTS MATHEMATICIAN EUDOXUS OF CNIDUS (fl. 408-355 BC) Life Celebrated Greek mathematician, astronomer, geographer and philosopher, whose genius was apparent from a very young age. He studied first with the famous Pythagorean Archytas of Tarentum; later a wealthy patron, impressed by the ability of this poor student, paid his way to Athens so that he could study at Plato's Academy. Here he was trained in the Platonic method, but continued to work out his own philosophy, which in physics was quite similar to that of Aristippus. He later spent some time in Egypt studying astronomy. The learned men of Egypt so admired his genius that they built him an observatory! When he returned to Greece he founded a school at Cyzicus in the Propontis, which attracted students from all over Greece. Work His most important works were: MATHEMATICS "Axiom of continuity" (Eudoxus-Archimedes): Discussed by Archimedes and one of the foundations of modern mathematics. The basis of both integral and differential calculus, it was first applied by Eudoxus and later expanded by Archimedes. Centuries later, Newton and Leibnitz based their work on this theorem. "Method of exhaustion": For the calculation of the volume of the pyramid and cone. Archimedes notes that Eudoxus was the first to prove that the cone and the pyramid are one-third respectively of the cylinder and prism with the same base and height.

11. Eudoxus Of Cnidus. The Columbia Encyclopedia, Sixth Edition. 2001 eudoxus of cnidus. (y d k´s s, n ´d s) (KEY) , 408?355? http://www.bartelby.com/65/eu/EudoxusCn.html

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12. TMTh:: Ancient Greek Technologists OF ASSOS CTESIBIUS OF ALEXANDRIA DAMO OF CROTON DEMOCRITUS DIOCLES OF ALEXANDRIADIOPHANTUS OF ALEXANDRIA EUCLID EUDEMUS OF RHODES eudoxus of cnidus GEMINUS OF http://www.tmth.edu.gr/en/aet/1.html

Home Ancient Greek Scientists AGRICULTURALISTS ARCHITECTS ARTISTS ASTRONOMERS ... ZENO OF ELEA Read about the life and Work of Ancient Greek Scientists. Choose the desired category from the list on the left and the desired scientist from the list on the right Based on the Greek book: K. Georgakopoulos, "Ancient Greek Scientists", Athens, 1995 Contact the Technology Museum

13. Eudoxus Of Cnidus eudoxus of cnidus . http://episte.math.ntu.edu.tw/people/p_eudoxus/

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14. Eudoxus Of Cnidus. The Columbia Encyclopedia, Sixth Edition. 2001 The Columbia Encyclopedia, Sixth Edition. 2001. eudoxus of cnidus. (y d k´s s, n´d s) (KEY) , 408?–355? BC, Greek astronomer, mathematician, and physician. http://www.bartleby.com/65/eu/EudoxusCn.html

Select Search All Bartleby.com All Reference Columbia Encyclopedia World History Encyclopedia World Factbook Columbia Gazetteer American Heritage Coll. Dictionary Roget's Thesauri Roget's II: Thesaurus Roget's Int'l Thesaurus Quotations Bartlett's Quotations Columbia Quotations Simpson's Quotations English Usage Modern Usage American English Fowler's King's English Strunk's Style Mencken's Language Cambridge History The King James Bible Oxford Shakespeare Gray's Anatomy Farmer's Cookbook Post's Etiquette Bulfinch's Mythology Frazer's Golden Bough All Verse Anthologies Dickinson, E. Eliot, T.S. Frost, R. Hopkins, G.M. Keats, J. Lawrence, D.H. Masters, E.L. Sandburg, C. Sassoon, S. Whitman, W. Wordsworth, W. Yeats, W.B. All Nonfiction Harvard Classics American Essays Einstein's Relativity Grant, U.S. Roosevelt, T. Wells's History Presidential Inaugurals All Fiction Shelf of Fiction Ghost Stories Short Stories Shaw, G.B. Stein, G. Stevenson, R.L. Wells, H.G. Reference Columbia Encyclopedia PREVIOUS NEXT ... BIBLIOGRAPHIC RECORD The Columbia Encyclopedia, Sixth Edition. Eudoxus of Cnidus (y d s, n

15. Eudoxus Of Cnidus Eudoxus, born in the city of Cnidus in southern Asia Minor, in the last yearsof the Vth century BC, is one of the great mathematicians of all times, and 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

16. Eudoxus Of Cnidus - Wikipedia eudoxus of cnidus. eudoxus of cnidus (ca.408 BC ca.347 BC) was a Greekastronomer, mathematician, physician, scholar and friend of Plato. http://www.wikipedia.org/wiki/Eudoxus_of_Cnidus

Main Page Recent changes Edit this page Older versions Special pages Set my user preferences My watchlist Recently updated pages Upload image files Image list Registered users Site statistics Random article Orphaned articles Orphaned images Popular articles Most wanted articles Short articles Long articles Newly created articles Interlanguage links All pages by title Blocked IP addresses Maintenance page External book sources Printable version Talk Log in Help Eudoxus of Cnidus From Wikipedia, the free encyclopedia. Eudoxus of Cnidus (ca. 408 BC - ca. 347 BC ) was a Greek astronomer mathematician physician , scholar and friend of Plato . (His name is sometimes spelled Eudoxos ; the use of the letter "u" is a Latinization.) Since all his own works are lost, our knowledge of him is obtained from secondary sources, such as Agratus 's poem on astronomy. 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. He invented the method of exhaustion , which was used masterfully by Archimedes . The work of Eudoxus and Archimedes as precursors of calculus was only exceeded in mathematical sophistication and rigour by Newton himself.

17. List Of Astronomical Topics - Wikipedia Eratosthenes Eridanus Eros Escape velocity Eta Carinae Euclidean geometry Euctemon Eudoxus eudoxus of cnidus Euler Euler's angle http://www.wikipedia.org/wiki/List_of_astronomical_topics

18. Bigchalk: HomeworkCentral: Eudoxus Of Cnidus (Ancient) Looking for the best facts and sites on eudoxus of cnidus? This HomeworkCentralsection eudoxus of cnidus. Brief Biography; eudoxus of cnidus. http://www.bigchalk.com/cgi-bin/WebObjects/WOPortal.woa/Homework/High_School/Sci

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19. Eudoxus Of Cnidus eudoxus of cnidus 408?355? bc , Greek astronomer, mathematician,and physician. From the eudoxus of cnidus. 408?-355? bc , Greek http://www.slider.com/enc/18000/Eudoxus_of_Cnidus.htm

Home Encyclopeadia E Erp - Eth ... Rope Ladders Slider Search: The Web Encyclopaedia Shopping Index Help Encyclopaedia 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. Add URL Advertise Contact Us

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