Museo Galileo
Virtual Museum
Eudoxus of Cnidos
First half 4th C. B.C.E.

Despite his stature as one of the greatest mathematicians of antiquity, there is little biographical data on Eudoxus. Born in Cnidos (Asia Minor), he studied geometry with Archytas of Taranto, medicine with Philiston, and philosophy with Plato in Athens. In c. 378 B.C.E., at the request of Agesilaus II, King of Sparta, he went on a diplomatic journey to Egypt, then ruled by Nectanebos I. He stayed there for about a year and learned the rudiments of planetary motions from the priests of Heliopolis. It is said that the bull Apis licked his clothes, leading the priests to predict a brief but illustrious life for him. Having settled at Cyzicus, in the Propontis, Eudoxus founded a school that became famous and that corresponded with Plato's Academy. Of the many works by Eudoxus on geometry, geography, and philosophy, only scattered fragments remain. He is the author of the exhaustion method to determine surfaces and volumes of solids, the theory of proportions enunciated in Book V of Euclid's Elements, the formula for finding the volume of a pyramid, and other mathematical demonstrations. In astronomy, he proposed the four-year cycle - three years of 365 days and one of 366 - later adopted in the calendar reform by Julius Caesar. Eudoxus wrote a work on stellar Phenomena and another On the velocities of the homocentric spheres that he had devised to provide a geometrical explanation of the geocentric motions of the Sun, Moon, and planets along the zodiac. About a hundred surviving fragments of a work of his on geography show that Eudoxus also tackled the general description of the inhabited world.