|Book IV Proposition 4|
since the angle ABD is equal to the angle CBD,
the right angle BED is also equal to the right angle BFD,
EBD, FBD are two triangles having two angles equal to two angles and one side equal to one side, namely that subtending one of the equal angles, which is BD, common to the triangles; therefore
they will also have the remaining sides equal to the remaining sides; [I.26] therefore
DE is equal to DF.
For the same reason
DG is also equal to DF.
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