Now, since the numbers BG, GC are equal to one another, and the numbers EH, HF are also equal to one another,
while the multitude of BG, GC is equal to the multitude of EH, HF,
therefore, whatever part or parts BG is of EH, the same part or the same parts is GC of HF also;
so that, in addition, whatever part or parts BG is of EH,
the same part also, or the same parts, is the sum BC of the sum EF. [VII. 5, 6]
But BG is equal to A, and EH to D;
therefore, whatever part or parts A is of D, the same part or the same parts is BC of EF also.
Q. E. D.