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.
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. [V. 16, X. 11]
Therefore, if the rectangle AE, EB is rational, the rectangle CF, FD will also be rational, [X. Def. 4] and if the rectangle AE, EB is medial, the rectangle CF, FD is also medial. [X. 23, Por.]