For, since, as A is to B, so is D to E,
therefore, alternately, as A is to D, so is B to E. [VII. 13]
Again, since, as B is to C, so is E to F,
therefore, alternately, as B is to E, so is C to F. [VII. 13]
But, as B is to E, so is A to D;
therefore also, as A is to D, so is C to F.
Therefore, alternately, as A is to C, so is D to F. [id.]