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Book I   Proposition 43
Now, since the triangle AEK is equal to the triangle AHK, and KGC to KFC,
    the triangle AEK together with KGC is equal to the triangle AHK together with KFC. [C.N.2]

And
    the whole triangle ABC is equal to the whole triangle ADC;
therefore
    the complement BK which remains is equal to the complement KD which remains. [C.N.3]

Being what it was required to prove.
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