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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

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