If a cube number do not measure a cube number, neither will the side measure the side; and, if the side do not measure the side, neither will the cube measure the cube.

For let the cube number A not measure the cube number B, and let C be the side of A, and D of B; I say that C will not measure D.

For if C measures D, A will also measure B. [VIII. 15]

But A does not measure B; therefore neither does C measure D.

Again, let C not measure D; I say that neither will A measure B.

For, if A measures B, C will also measure D. [VIII. 15]

But C does not measure D; therefore neither will A measure B. Q. E. D.