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Book IV   Proposition 12
I say next that it is also equiangular.

For, since
    the angle FKC is equal to the angle FLC,
and
    the angle HKL was proved double of the angle FKC,
and
    the angle KLM double of the angle FLC,
therefore
    the angle HKL is also equal to the angle KLM.

Similarly
    each of the angles KHG, HGM, GML can also be proved equal to each of the angles HKL, KLM;
therefore
    the five angles GHK, HKL, KLM, LMG, MGH are equal to one another.
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