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.