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Book III   Proposition 27
Now equal angles stand on equal circumferences, when thay are at the centers; [III.26] therefore
    the circumference BK is equal to the circumference EF.
But
    EF is equal to BC;
therefore
    BK is also equal to BC,
the less to the greater: which is impossible.

Therefore
    the angle BGC is not unequal to the angle EHF
therefore
    it is equal to it.

Being (part of) what it was required to prove.
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