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the spheres. He conceived each planet as held in place by being fixed in a celestial crystalline sphere which, in its rotation about the sun as center, carried the planet with it. Having observed that the planets move at different rates, it followed that the various spheres had different rates of rotation, and Pythagoras believed that some law controlled their motions. This he expressed by supposing that each sphere emitted sounds or notes like the strings of a harp, and the harmony was expressed by the belief that the several notes united in a beautiful celestial harmony of most exquisite music. More fantastic than suggestive, yet here in the far-away dawn of scientific history is the foreshadowing of the great thought which two millenniums later was given in Newton's universal law of gravitation.

The fate of Anaxagoras warned Pythagoras against being too overt