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Ptolemy about 500 years later. Usually, it is claimed that Eudoxus' theory, described in his treatise On Speeds, was a response to a challenge of Plato. Simplicius tells us that:

Eudoxus of Cnidus was the first of the Greeks to concern himself with hypotheses of this sort, Plato having ... set it as a problem to all earnest students of this subject to find what are the uniform and ordered movements by the assumption of which the phenomena in relation to the movements of the planets can be saved.

In other words, what uniform circular motions could be used to represent the motions of the planets? Quite how much of the impetus for a geometrical theory of the heavens was due to Plato is open to question, however.

The discovery of the spherical nature of the Earth, together with Pythagorean ideas about uniform circular motions, may well have suggested to Eudoxus that the motion of the stars and planets could be modelled by means of a system of concentric spheres with the Earth at their common centre. He supposed that each of the Sun, Moon and planets occupied its own sphere which was attached via its poles to a larger sphere that rotated about other poles. Third and fourth spheres could be added, each rotating at different rates and about different axes, according to mathematical and observational needs. Apart from the sphere of the fixed stars, Eudoxus used three spheres each for the Sun and Moon and four spheres for each of the planets, making twenty-seven in all. In each case, one

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