Every body must necessarily be either finite or infinite, and if infinite, either of similar or of dissimilar parts.If its parts are dissimilar, they must represent either a finite or an infinite number of kinds.That the kinds cannot be infinite is evident, if our original presuppositions remain unchallenged.For the primary movements being finite in number, the kinds of simple body are necessarily also finite, since the movement of a simple body is simple, and the simple movements are finite, and every natural body must always have its proper motion.Now if the infinite body is to be composed of a finite number of kinds, then each of its parts must necessarily be infinite in quantity, that is to say, the water, fire, &c., which compose it.But this is impossible, because, as we have already shown, infinite weight and lightness do not exist.
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.
(1.The infinite cannot be acted upon by the finite.) Let A be an infinite, B a finite, C the time of a given movement produced by one in the other.Suppose, then, that A was heated, or impelled, or modified in any way, or caused to undergo any sort of movement whatever, by in the time C.Let D be less than B; and, assuming that a lesser agent moves a lesser patient in an equal time, call the quantity thus modified by D, E.Then, as D is to B, so is E to some finite quantum.We assume that the alteration of equal by equal takes equal time, and the alteration of less by less or of greater by greater takes the same time, if the quantity of the patient is such as to keep the proportion which obtains between the agents, greater and less.If so, no movement can be caused in the infinite by any finite agent in any time whatever.For a less agent will produce that movement in a less patient in an equal time, and the proportionate equivalent of that patient will be a finite quantity, since no proportion holds between finite and infinite.
(2.The infinite cannot act upon the finite.) Nor, again, can the infinite produce a movement in the finite in any time whatever.
Let A be an infinite, B a finite, C the time of action.In the time C, D will produce that motion in a patient less than B, say F.Then take E, bearing the same proportion to D as the whole BF bears to F.E
