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On The Heavens   



another more quickly. It is, however, quite possible that a moving

line should in certain cases pass one which is stationary quicker than

it passes one moving in an opposite direction. One has only to imagine

the movement to be slow where both move and much faster where one is

stationary. To suppose one line stationary, then, makes no

difficulty for our argument, since it is quite possible for A to

pass B at a slower rate when both are moving than when only one is.

If, therefore, the time which the finite moving line takes to pass the

other is infinite, then necessarily the time occupied by the motion of

the infinite past the finite is also infinite. For the infinite to

move at all is thus absolutely impossible; since the very smallest

movement conceivable must take an infinity of time. Moreover the

heavens certainly revolve, and they complete their circular orbit in a

finite time; so that they pass round the whole extent of any line

within their orbit, such as the finite line AB. The revolving body,

therefore, cannot be infinite.

(4) Again, as a line which has a limit cannot be infinite, or, if it

is infinite, is so only in length, so a surface cannot be infinite

in that respect in which it has a limit; or, indeed, if it is

completely determinate, in any respect whatever. Whether it be a

square or a circle or a sphere, it cannot be infinite, any more than a

foot-rule can. There is then no such thing as an infinite sphere or

square or circle, and where there is no circle there can be no

circular movement, and similarly where there is no infinite at all

there can be no infinite movement; and from this it follows that, an

infinite circle being itself an impossibility, there can be no

circular motion of an infinite body.

(5) Again, take a centre C, an infinite line, AB, another infinite

line at right angles to it, E, and a moving radius, CD. CD will

never cease contact with E, but the position will always be

something like CE, CD cutting E at F. The infinite line, therefore,

refuses to complete the circle.

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