T H E
E L E M E N T S 
Book VI
Proposition 19

But
as BC is to BG;
so is the triangle ABC
to the triangle ABG; [VI.1]
therefore
the triangle ABC also has to the triangle ABG a ratio duplicate of that which BC has to EF.
But
the triangle ABG is equal to the triangle DEF;
therefore
the triangle ABC also has to the triangle DEF a ratio duplicate of that which BC has to EF.


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