Ocellus Lucanus on the nature of the universe

by Julius Firmicus Maternus; Proclus; Tauros

THEOREM 6.

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.