EUDOXUS of Cnidus, Greek savant, probably lived from 408 to 355 B.C. It is chiefly as a mathematician and astronomer that his name has come down to us (see ASTRONOMY, History). From a life by Diogenes Laertius, we learn that he studied at Athens under Plato, but, being dismissed went to Egypt, where he re mained for 16 months with the priests of Heliopolis; here he probably began his astronomical observations. He then founded a school in Cyzicus and the Propontis, and subsequently, accom panied by a number of pupils, went to Athens, where he took a part in public affairs, and 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 sun-dial. The Phaenomena of Aratus is a poetical account of the astronomical observations of Eudoxus. Several works have been attributed to him, but they are all lost ; some fragments are preserved in the extant T(.v 'Aparov Kai EvhoEov f acvo,u vwv (343Xia Tpia of the astronomer Hipparchus (ed. C. Manitius 1894).
Eudoxus was a mathematician of some importance. He dis covered that part of geometry which is now included in the fifth book of Euclid; the proofs he used were very much like those now used. He also originated several theorems of the "golden section" of a line. Eudoxus used the "method of exhaustion," which he had established to show that the volume of a pyramid or cone was one-third of the volume of a prism or cylinder on the same base. The "method of exhaustion" was of great use to geometers, for, although it was very laborious, it was rigid and avoided the use of infinitesimals. It is probable that the proof that the volumes of spheres are to one another as the cubes of their radii is due to him. Eudoxus was the first astronomer to give a scientific explanation of the paths of planets. He assumed that each planet was fixed to a transparent spherical shell capable of rotating about an axis inside another spherical shell and so on. Four shells, each rotating in a different direction and performing a different function, were necessary for each planet. Altogether 26 spherical shells were necessary for the solar system, but later astronomers were forced to increase this number as new dis coveries were made, and eventually the idea was superseded.
See J. A. Letronne, Sur les ecrites et les travaux d'Eudoxe de Cnide; d'apres L. Ideler (1841) ; G. V. Schiaparelli, Le Sfere omocentriche di Eudosso (Milan, 1876) ; T. H. Martin in Academie des inscriptions, Oct. 3, 1879; article in Ersch and Gruber's Allgemeine Encykloplidie.