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in the triangles ABC, GEF the sides about the equal angles are proportional, and those are corresponding sides which subtend the equal angles; [VI.4]
therefore
as AB is to BC,
so is GE to EF.
But
as AB is to BC,
so by hypothesis is DE to EF;
therefore
as DE is to EF,
so is GE to EF. [V.11]
