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.

Eudoxus also excelled as a mathematician. His work on ratios formed the basis for Book V of Euclid's Elements, and anticipated in a number of ways the notion of algebra, which is otherwise absent from ancient Greek mathematics. Eudoxus also constructed many geometric proofs and developed the method of exhaustion later extended by Archimedes.

Archimedes, Plato

Additional biographies: MacTutor (St. Andrews), Bonn, Greek and Roman Science and Technology