On The Heavens
radii is necessarily infinite: circular motion therefore is an
impossibility. Yet our eyes tell us that the heavens revolve in a
circle, and by argument also we have determined that there is
something to which circular movement belongs.
(2) Again, if from a finite time a finite time be subtracted, what
remains must be finite and have a beginning. And if the time of a
journey has a beginning, there must be a beginning also of the
movement, and consequently also of the distance traversed. This
applies universally. Take a line, ACE, infinite in one direction, E,
and another line, BB, infinite in both directions. Let ACE describe
a circle, revolving upon C as centre. In its movement it will cut BB
continuously for a certain time. This will be a finite time, since the
total time is finite in which the heavens complete their circular
orbit, and consequently the time subtracted from it, during which
the one line in its motion cuts the other, is also finite. Therefore
there will be a point at which ACE began for the first time to cut BB.
This, however, is impossible. The infinite, then, cannot revolve in
a circle; nor could the world, if it were infinite.
(3) That the infinite cannot move may also be shown as follows.
Let A be a finite line moving past the finite line, B. Of necessity
A will pass clear of B and B of A at the same moment; for each
overlaps the other to precisely the same extent. Now if the two were
both moving, and moving in contrary directions, they would pass
clear of one another more rapidly; if one were still and the other
moving past it, less rapidly; provided that the speed of the latter
were the same in both cases. This, however, is clear: that it is
impossible to traverse an infinite line in a finite time. Infinite
time, then, would be required. (This we demonstrated above in the
discussion of movement.) And it makes no difference whether a finite
is passing by an infinite or an infinite by a finite. For when A is
passing B, then B overlaps A and it makes no difference whether B is
moved or unmoved, except that, if both move, they pass clear of one