For, if F is the same with one of the numbers A, B, C, and measures D according to E,
therefore one of the numbers A, B, C also measures D according to E.
But one of the numbers A, B, C measures D according to some one of the numbers A, B, C; IX. 11]
therefore E is also the same with one of the numbers A, B, C: which is contrary to the hypothesis.
Therefore F is not the same as any one of the numbers A, B, C.
Similarly we can prove that F is measured by A, by proving again that F is not prime.
For, if it is, and measures D, it will also measure A [IX. 12], which is prime, though it is not the same with it: which is impossible;
therefore F is not prime.
Therefore it is composite.
But any composite number is measured by some prime number; [VII. 31]
therefore F is measured by some prime number.
I say next that it will not be measured by any other prime except A.