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Book III   Proposition 31
Therefore
    the whole angle BAC is equal to the two angles ABC, ACB.
But
    the angle FAC exterior to the triangle ABC is also equal to the two angle ABC, ACB; [I.32]
therefore
    the angle BAC is also equal to the angle FAC;
therefore
    each is right; [I.Def.10]
therefore
    the angle BAC in the semicircle BAC is right.

Being what it was required to prove.
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