|Book VI Proposition 7|
Therefore the triangle ABG is equianglar with the triangle DEF.
as DE is to BG, so is DE to EF. [VI.4]
as DE is to EF, so by hypothesis is AB to BC;
AB has the same ratio to each of the straight lines BC, BG; [V.11]
BC is equal to BG, [V.9]
the angle at C is also equal to the angle BGC. [I.5]
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