On The Heavens   

Moreover it would be necessary also that their places should be

infinite in extent, so that the movements too of all these bodies

would be infinite. But this is not possible, if we are to hold to

the truth of our original presuppositions and to the view that neither

that which moves downward, nor, by the same reasoning, that which

moves upward, can prolong its movement to infinity. For it is true

in regard to quality, quantity, and place alike that any process of

change is impossible which can have no end. I mean that if it is

impossible for a thing to have come to be white, or a cubit long, or

in Egypt, it is also impossible for it to be in process of coming to

be any of these. It is thus impossible for a thing to be moving to a

place at which in its motion it can never by any possibility arrive.

Again, suppose the body to exist in dispersion, it may be maintained

none the less that the total of all these scattered particles, say, of

fire, is infinite. But body we saw to be that which has extension

every way. How can there be several dissimilar elements, each

infinite? Each would have to be infinitely extended every way.

It is no more conceivable, again, that the infinite should exist

as a whole of similar parts. For, in the first place, there is no

other (straight) movement beyond those mentioned: we must therefore

give it one of them. And if so, we shall have to admit either infinite

weight or infinite lightness. Nor, secondly, could the body whose

movement is circular be infinite, since it is impossible for the

infinite to move in a circle. This, indeed, would be as good as saying

that the heavens are infinite, which we have shown to be impossible.

Moreover, in general, it is impossible that the infinite should move

at all. If it did, it would move either naturally or by constraint:

and if by constraint, it possesses also a natural motion, that is to

say, there is another place, infinite like itself, to which it will

move. But that is impossible.

That in general it is impossible for the infinite to be acted upon

by the finite or to act upon it may be shown as follows.