For on FE let the square DF be described, and let GD be completed.
Since then, as FE is to EG, so is FD to DG, [VI. 1]
and FD is the square on FE, and DG the rectangle DE, EG, that is, the rectangle FE, EG,
therefore, as FE is to EG, so is the square on FE to the rectangle FE, EG.
Similarly also, as the rectangle GE, EF is to the square on EF, that is, as GD is to FD, so is GE to EF.
Q. E. D.