|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]
the whole triangle ABC is equal to the whole triangle ADC;
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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