Ocellus Lucanus on the nature of the universe

by Julius Firmicus Maternus; Proclus; Tauros

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.

THEOREM 7.

Simple bodies are terminated according to species.

Demonstration.—For let the magnitude A be a simple body. Since, therefore, a simple body is moved with a simple motion, A will be moved with a simple motion. And if it is moved in a circle, it will have one nature and one form. But if it is moved according to any one of the motions in a right line, if it is moved from the middle only, it will be fire, but if only to the middle, earth. But, if it is light with respect to one thing, and heavy with respect to another, it will be some one of the middle elements. The species therefore of simple bodies are terminated.

THEOREM 8.

Time is continued and perpetual.

Demonstration.—For, if it is neither continued nor eternal, it will have a certain beginning. Let, therefore, A B be time, and let its beginning be A. But if A is time, it is divisible, and we shall not yet have the beginning of time, but there will be another beginning of the beginning. But, if A is a moment or the now, it will be indivisible, and the boundary of another time: for the now is not only a beginning, but an end. There will therefore be time before A. Again: if B is the boundary of time, if B is time, it may be divided to infinity, and into the many boundaries which it contains. But if B is the now, the same will also be a beginning: for the now is not only a boundary, but a beginning[60].

THEOREM 9.

A motion which is naturally circular is perpetual.