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.
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