For, since A by multiplying B has made D,
therefore B measures D according to the units in A.
But the unit F also measures the number A according to the units in it;
therefore the unit F measures the number A the same number of times that B measures D.
Therefore, as the unit F is to the number A, so is B to D. [VII. Def. 20]
For the same reason, as the unit F is to the number A, so also is C to E;
therefore also, as B is to D, so is C to E.
Therefore, alternately, as B is to C, so is D to E. [VII. 13]
Q. E. D.