For since, as A is to B, so is C to D,
therefore, whatever part or parts A is of B, the same part or the same parts is C of D also. [VII. Def. 20]
Therefore, alternately, whatever part or parts A is of C, the same part or the same parts is B of D also. [VII. 10]
Therefore, as A is to C, so is B to D. [VII. Def. 20]
Q. E. D.