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FD has been drawn parallel to GE, one of the sides of the triangle AGE,
therefore, proportionally,
as ED is to DA,
so is GF to FA. [VI.2]
But it was also proved that,
as CE is to ED, so is BG to GF;
therefore,
as CE is to ED, so is BG to GF,
and
as ED is to DA, so is GF to FA.
