|Book VI Proposition 20|
BE, EC, GL, LH be joined.
the polygon ABCDE is similar to the polygon FGHKL, [1.14]
the angle BAE is equal to the angle GFL;
as BA is to AE, so is GF to FL.
ABE, FGL are two triangles having one angle equal to one angle and the sides about the equal angles proportional,
the triangle ABE is equiangular with the triangle FGL;
so that it is also similar;
the angle ABE is equal to the angle FGL.
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