For, if C, B are not prime to one another, some number will measure C, B.
Let a number measure them, and let it be D.
Since D measures C, and C measures A, therefore D also measures A.
But it also measures B;
therefore D measures A, B which are prime to one another: which is impossible. [VII. Def. 12]
Therefore no number will measure the numbers C, B.
Therefore C, B are prime to one another.
Q. E. D.