1. Eudoxus Of Cnidus --  Encyclopædia Britannica MLA style " eudoxus of cnidus." Encyclopædia Britannica. 2004 APA style eudoxus of cnidus. Encyclopædia Britannica. Retrieved May 2, 2004, from Encyclopædia Britannica Premium http://www.britannica.com/eb/article?eu=33776

2. Eudoxus Of Cnidus next Next About this document. eudoxus of cnidus. Eudoxus (c. 400 BC) is the greatestof the ancient mathematicians, surpassed only by Archimedes but later. 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.

3. Eudoxus Of Cnidus yOOdok'sus, nI'dus Pronunciation Key. eudoxus of cnidus , 408?355 eudoxus of cnidus. eudoxus of cnidus (408355 BC) http://www.infoplease.com/ce5/CE017471.html

HOTWORDS CITE PRINT EMAIL in All Infoplease Almanacs Biographies Dictionary Encyclopedia Home Almanacs Atlas Dictionary ... D-Day Infoplease Tools Periodic Table Conversion Tool Perpetual Calendar Year by Year ... Site Map Also from Infoplease Search Infoplease Info search tips Search Biographies Bio search tips 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. The Columbia Electronic Encyclopedia

4. Eudoxus Of Cnidus. The Columbia Encyclopedia, Sixth Edition. 2001 The Columbia Encyclopedia, Sixth Edition. 2001. eudoxus of cnidus. Heliopolis, Egypt, founded a school in Cyzicus, and spent his later years in Cnidus, where he had an observatory http://www.bartleby.com/65/eu/EudoxusCn.html

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5. 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.

6. Eudoxus Of Cnidus (ca. 400-ca. 347 BC) -- From Eric Weisstein's World Of Scienti Astronomers. Branch of Science. Mathematicians. Branch of Science. Philosophers. Nationality. Greek. eudoxus of cnidus (ca. 400ca. 347 BC) interpreted to indicate that their distances were changing. Eudoxus was the first Greek to make a map of the stars http://www.treasure-troves.com/bios/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.

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 408?355? 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 http://www.slider.com/enc/18000/Eudoxus_of_Cnidus.htm

9. Eudoxus Of Cnidus --  Encyclopædia Britannica continued. eudoxus of cnidus Encyclopædia Britannica Article. To cite thispage MLA style eudoxus of cnidus. Encyclopædia Britannica. 2004. http://www.britannica.com/eb/article?eu=33776&tocid=2180&query=archytas of taren

10. Eudoxus Biography of Eudoxus (408BC355BC) eudoxus of cnidus. Born 408 BC in Cnidus (on Resadiye peninsula), Asia Minor BC in Cnidus, Asia Minor (now Turkey) eudoxus of cnidus was the son of Aischines http://www.math.5u.com/Eudoxus.htm

11. Eudoxus Of Cnidus - Wikipedia, The Free Encyclopedia eudoxus of cnidus. From Wikipedia, the free encyclopedia. Anotherarticle treats of Eudoxus of Cyzicus. eudoxus of cnidus (Greek http://en.wikipedia.org/wiki/Eudoxus_of_Cnidus

Eudoxus of Cnidus From Wikipedia, the free encyclopedia. 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.

12. Eudoxus Of Cnidus yOOdok'sus, nI'dus Pronunciation Key. eudoxus of cnidus , 408?355 eudoxus of cnidus. eudoxus of cnidus (408355 BC) http://www.infoplease.com/ce6/people/A0817824.html

HOTWORDS CITE PRINT EMAIL in All Infoplease Almanacs Biographies Dictionary Encyclopedia Home Almanacs Atlas Dictionary ... D-Day Infoplease Tools Periodic Table Conversion Tool Perpetual Calendar Year by Year ... Site Map Also from Infoplease Search Infoplease Info search tips Search Biographies Bio search tips 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. The Columbia Electronic Encyclopedia

13. Eudoxus Of Cnidus © 1998 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. Eudoxus, born in the city of Cnidus in southern Asia Minor, in the last years of the Vth returned to his native city of Cnidus where he was involved in http://www.dialogues-de-platon.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

14. Eudoxus eudoxus of cnidus (408355 BC). Archimedes, Newton and Gauss are consideredthe most important mathematicians ever. It is difficult http://www.mlahanas.de/Greeks/Eudoxus.htm

EUDOXUS OF CNIDUS (408-355 BC) Archimedes, Newton and Gauss are considered the most important mathematicians ever. It is difficult to say who is the best because it is difficult to compare the knowledge at different times. Should not Pythagoras considered the most important mathematician, since he established mathematics and he is considered the father of mathematics. He may not have discovered the Pythagorean theorem, but he provided a proof and he gave an identity to the number, he declared that everything can be expressed by numbers. I consider that Eudoxus is also to be considered among the greatest. He provided the basis of the exhaustion method, he provided the first geometric model of the cosmos and he wrote Incommensurables, a important book for Greek mathematicians. Archimedes become famous mainly in helping to defend Syracuse and the life of Eudoxus is less spectacular. I consider Eudoxus to be influential and one of the most important mathematicians even if he is almost unknown. Eudoxus, son of Aeschines, Greek mathematician, astronomer, geographer and philosopher, whose genius was apparent from a very young age. He was born in Cnidus (or Cnidos), (Black Sea) He studied first with the famous Pythagorean

15. Ancient Greece : Science And Technology Facts Geometric Numbers. The quadrature of a convex polygon and HippocratesLune. eudoxus of cnidus, one of the the greatest mathematicians. http://www.mlahanas.de/Greeks/Greeks.htm

HELLAS Ancient Greece: Science Technology and other interesting stories Michael Lahanas mlahanas@gmx.net As for the man who believes in beautiful things but not in the existence of Beauty itself, nor is able to follow one who leads him to the knowledge of it, do you think that he lives in a dream or in a waking state? I certainly think that the man who does this is dreaming. Plato The name Greek is no longer a mark of a race, but of an outlook, and is accorded to those who share our culture rather than our blood.. Isocrates Athenian orator, 380 BC. Remarks and questions concerning this site Introduction Who Killed Homer? Ancient Greek Technology technikos First there is practical no original source that describes the technology of ancient Greeks. Archimedes did not consider worth to write about his inventions and the work of Heron is from translations or text written later. We have various indirect sources such as from Vitruvius. A large number of original sources was destroyed by events like the fire of the Alexandria Library, by fanatics, or by natural causes. a) The Antikythera computing device around 80 BC b) A Scientific American paper of De Solla Price Archimedes Devices that use Gears Planetaria used for Education and Research ... b) The first self controlled system; The Clepsydra of Ctesibius and the toilet

16. 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

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19. ASTR 228: Chapter 6 - Aristotelian Science And Cosmology center; The ultimate product of geocentric cosmology was the Ptolemaicsystem. 6.3. eudoxus of cnidus (ca. 400 ca. 347 BC). Associate 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.)

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

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