
On The Heavens
truths of mathematics to totter. The reason is that a principle is
great rather in power than in extent; hence that which was small at
the start turns out a giant at the end. Now the conception of the
infinite possesses this power of principles, and indeed in the
sphere of quantity possesses it in a higher degree than any other
conception; so that it is in no way absurd or unreasonable that the
assumption that an infinite body exists should be of peculiar moment
to our inquiry. The infinite, then, we must now discuss, opening the
whole matter from the beginning.
Every body is necessarily to be classed either as simple or as
composite; the infinite body, therefore, will be either simple or
composite.
But it is clear, further, that if the simple bodies are finite,
the composite must also be finite, since that which is composed of
bodies finite both in number and in magnitude is itself finite in
respect of number and magnitude: its quantity is in fact the same as
that of the bodies which compose it. What remains for us to
consider, then, is whether any of the simple bodies can be infinite in
magnitude, or whether this is impossible. Let us try the primary
body first, and then go on to consider the others.
The body which moves in a circle must necessarily be finite in every
respect, for the following reasons. (1) If the body so moving is
infinite, the radii drawn from the centre will be infinite. But the
space between infinite radii is infinite: and by the space between the
radii I mean the area outside which no magnitude which is in contact
with the two lines can be conceived as falling. This, I say, will be
infinite: first, because in the case of finite radii it is always
finite; and secondly, because in it one can always go on to a width
greater than any given width; thus the reasoning which forces us to
believe in infinite number, because there is no maximum, applies
also to the space between the radii. Now the infinite cannot be
traversed, and if the body is infinite the interval between the
