Since then, as AB is to CD, so is EF to QR,
and there have been described on AB, CD the similar and similarly situated figures KAB, LCD,
and on EF, QR the similar and similarly situated figures MF, SR,
therefore, as KAB is to LCD, so is MF to SR.
But also, by hypothesis, as KAB is to LCD, so is MF to NH;
therefore also, as MF is to SR, so is MF to NH. [V. 11]
Therefore MF has the same ratio to each of the figures NH, SR;
therefore NH is equal to SR. [V. 9]
But it is also similar and similarly situated to it;
therefore GH is equal to QR.
And, since, as AB is to CD, so is EF to QR,
while QR is equal to GH,
therefore, as AB is to CD, so is EF to GH.