For since, as BG is to C, so is EH to F,
inversely, as C is to BG, so is F to EH.
Since, then, as AB is to C, so is DE to F,
and, as C is to BG, so is F to EH,
therefore, ex aequali, as AB is to BG, so is DE to EH. [V. 22]
And, since the magnitudes are proportional separando, they will also be proportional componendo; [V. 18]
therefore, as AG is to GB, so is DH to HE.
But also, as BG is to C, so is EH to F;
therefore, ex aequali, as AG is to C, so is DH to F. [V. 22]