For since, as AE is to EB, so is CF to FD,
therefore also, as the square on AE is to the rectangle AE, EB, so is the square on CF to the rectangle CF, FD;
therefore, alternately, as the square on AE is to the square on CF, so is the rectangle AE, EB to the rectangle CF, FD. [V. 16]
But the square on AE is commensurable with the square on CF;
therefore the rectangle AE, EB is also commensurable with the rectangle CF, FD.
If therefore the rectangle AE, EB is rational, the rectangle CF, FD is also rational, [and for this reason CD is a first bimedial]; [X. 37]
but if medial, medial, [X. 23, Por.] and each of the straight lines AB, CD is a second bimedial. [X. 38]