|Book VI Proposition 20|
the angle BAM is equal to the angle GFN, and
the angle ABM is equal to the angle FGN, therefore
the remaining angle AMB is also equal to the ramaining angle FNG; [I.32]
the triangle ABM is equiangular with the triangle FGN.
Similarly we can prove that
the triangle BMC is also equiangular with the triangle GNH.
as AM is to MB, so is FN to NG, and
as BM is to MC, so is GN to NH;
so that, in addition, ex aequali,
as AM is to MC, so is FN to NH.
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