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Book III   Proposition 14
Therefore
    the squares on EF, FA are equal to the squares on EG, GC, of which the square on EF is equal to the square on EG, for EF is equal to EG;
therefore
    the square on AF which remains is equal to the square on CG;
therefore
    AF is equal to CG.

And AB is double of AF, and CD double of CG;
therefore
AB is equal to CD.

Being what it was required to prove.
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