On The Heavens   

(6) Again, if the heaven is infinite and moves in a circle, we shall

have to admit that in a finite time it has traversed the infinite. For

suppose the fixed heaven infinite, and that which moves within it

equal to it. It results that when the infinite body has completed

its revolution, it has traversed an infinite equal to itself in a

finite time. But that we know to be impossible.

(7) It can also be shown, conversely, that if the time of revolution

is finite, the area traversed must also be finite; but the area

traversed was equal to itself; therefore, it is itself finite.

We have now shown that the body which moves in a circle is not

endless or infinite, but has its limit.



6



Further, neither that which moves towards nor that which moves

away from the centre can be infinite. For the upward and downward

motions are contraries and are therefore motions towards contrary

places. But if one of a pair of contraries is determinate, the other

must be determinate also. Now the centre is determined; for, from

whatever point the body which sinks to the bottom starts its

downward motion, it cannot go farther than the centre. The centre,

therefore, being determinate, the upper place must also be

determinate. But if these two places are determined and finite, the

corresponding bodies must also be finite. Further, if up and down

are determinate, the intermediate place is also necessarily

determinate. For, if it is indeterminate, the movement within it

will be infinite; and that we have already shown to be an

impossibility. The middle region then is determinate, and consequently

any body which either is in it, or might be in it, is determinate. But

the bodies which move up and down may be in it, since the one moves

naturally away from the centre and the other towards it.

From this alone it is clear that an infinite body is an