Let the same construction as before be made.
Since then AB is the side of a rational plus a medial area, divided at C, therefore AC, CB are straight lines incommensurable in square which make the sum of the squares on them medial, but the rectangle contained by them rational. [X. 40]
Since then the sum of the squares on AC, CB is medial,
therefore DL is medial,
so that DM is rational and incommensurable in length with DE. [X. 22]
Again, since twice the rectangle AC, CB, that is MF, is rational, therefore MG is rational and commensurable with DE. [X. 20]
Therefore DM is incommensurable with MG; [X. 13]
therefore DM, MG are rational straight lines commensurable in square only;
therefore DG is binomial. [X. 36]
I say next that it is also a fifth binomial straight line.