Since, as AB is to CD, so is AE to CF,
whatever part or parts AB is of CD,
the same part or the same parts is AE of CF also; [VII. Def. 20]
Therefore also the remainder EB is the same part or parts of FD that AB is of CD. [VII. 7, 8]
Therefore, as EB is to FD, so is AB to CD. [VII. Def. 20]
Q. E. D.