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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

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