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On The Heavens   

and the circle has completed its own movement, i.e. traversed its

own circumference, at one and the same moment. But it is difficult

to conceive that the pace of each star should be exactly

proportioned to the size of its circle. That the pace of each circle

should be proportionate to its size is not absurd but inevitable:

but that the same should be true of the movement of the stars

contained in the circles is quite incredible. For if, on the one

and, we suppose that the star which moves on the greater circle is

necessarily swifter, clearly we also admit that if stars shifted their

position so as to exchange circles, the slower would become swifter

and the swifter slower. But this would show that their movement was

not their own, but due to the circles. If, on the other hand, the

arrangement was a chance combination, the coincidence in every case of

a greater circle with a swifter movement of the star contained in it

is too much to believe. In one or two cases it might not inconceivably

fall out so, but to imagine it in every case alike is a mere

fiction. Besides, chance has no place in that which is natural, and

what happens everywhere and in every case is no matter of chance.

(3) The same absurdity is equally plain if it is supposed that the

circles stand still and that it is the stars themselves which move.

For it will follow that the outer stars are the swifter, and that

the pace of the stars corresponds to the size of their circles.

Since, then, we cannot reasonably suppose either that both are in

motion or that the star alone moves, the remaining alternative is that

the circles should move, while the stars are at rest and move with the

circles to which they are attached. Only on this supposition are we

involved in no absurd consequence. For, in the first place, the

quicker movement of the larger circle is natural when all the

circles are attached to the same centre. Whenever bodies are moving

with their proper motion, the larger moves quicker. It is the same

here with the revolving bodies: for the are intercepted by two radii

will be larger in the larger circle, and hence it is not surprising

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