The powers of bodies terminated according to magnitude are not infinite.
_Demonstration._—For, if possible, let B be the infinite power of the
finite body A; and let the half of A be taken, which let be C, and let
the power of this be D. But it is necessary that the power D should be
less than the power B: for a part has a power less than that of the
whole. Let the ratio, therefore, of C to A be taken, and D will measure
B. The power B therefore is finite, and it is as C to A, so D to B; and
alternately as C to D, so A to B. But the power D is the power of the
magnitude C, and therefore B will be the power of the magnitude A. The
magnitude A, therefore, has a finite power B; but it was infinite, which
is impossible: for, that a power of the same species should be both
finite and infinite in the same thing, is impossible.