Eudoxus of Cnidus (410 or 408 BC ­ 355 or 347 BC) was a Greek astronomer, mathematician, physician, scholar and student 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. Theodosius of Bithynia's Sphaerics may be based on a work of Eudoxus.

Eudoxus was the son of Aeschines of Cnidus, located in Asia Minor. Eudoxus first travelled to Tarentum to study with Archytas, from whom he learned mathematics. While in Italy, Eudoxus visited Sicily, where he studied medicine with Philiston.

Around 387 BC, at the age of 23, he traveled with the physician Theomedon to Athens to study with the followers of Socrates. He eventually became the pupil of Plato, with whom he studied for several months, but due to a disagreement they had a falling out. Eudoxus was quite poor and could only afford an apartment at the Piraeus. To attend Plato's lectures, he walked the seven miles each direction, each day. Due to his poverty, his friends raised funds sufficient to send him to Heliopolis, Egypt to pursue his study of astronomy and mathematics. He lived there 16 months. From Egypt, he then traveled north to Cyzicus, located on the south shore of the Sea of Marmara, and the Propontis. He traveled south to the court of Maussolus. During his travels he gathered many students of his own.

Around 368 BC, he returned to Athens with his students. Eudoxus eventually returned to his native Cnidus, where he served in the city assembly. While in Cnidus, he built an observatory and continued writing and lecturing on theology, astronomy and meteorology. He had one son, Aristagoras, and three daughters, Actis, Philtis and Delphis.

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 1500s, it became the basis for quantitative work in science for a century, until it was replaced by the algebraic methods of Descartes.

Eudoxus rigorously developed Antiphon's 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.

Mathematics

Astronomy

In ancient Greece, astronomy was a branch of mathematics; astronomers sought to create geometrical models that could imitate the appearances of celestial motions. Identifying the astronomical work of Eudoxus as a separate category is therefore a modern convenience. Some of Eudoxus' astronomical texts whose names have survived include:

  • Disappearances of the Sun, possibly on eclipses
  • Oktaeteris, on an eight-year lunisolar cycle of the calendar
  • Phaenomena and Entropon, on spherical astronomy, probably based on observations made by Eudoxus in Egypt and Cnidus
  • On Speeds, on planetary motions

We are fairly well informed about the contents of Phaenomena, for Eudoxus' prose text was the basis for a poem of the same name by Aratus. Hipparchus quoted from the text of Eudoxus in his commentary on Aratus.

Wikipedia

http://www.crystalinks.com/eudoxus.html

 

 

 

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.

Further information about Eudoxus can be found in his mathematical biography.

Eudoxus (Eudoxos) is Greek for "of good repute".

Cnidus, latitude 36º40'N, longitude 27º20'E, was a city on the Western tip of the Resadiye peninsula in what is now Turkey. It is close to the Greek islands of Cos and Rhodes and the city of Halicarnassus, where King Mausolus's tomb, the Mausoleum, was one of the seven wonders of the ancient world.

http://www.eudoxus.com/eudoxus.html

 

see also  

- Maths
-Constellations
  -Planets