Let the same construction be made as before shown.
Then, since AB is a major straight line divided at C, AC, CB are straight lines incommensurable in square which make the sum of the squares on them rational, but the rectangle contained by them medial. [X. 39]
Since then the sum of the squares on AC, CB is rational,
therefore DL is rational;
therefore DM is also rational and commensurable in length with DE. [X. 20]
Again, since twice the rectangle AC, CB, that is, MF, is medial, and it is applied to the rational straight line ML,
therefore MG is also rational and incommensurable in length with DE; [X. 22]
therefore DM is also incommensurable in length with MG. [X. 13]
Therefore DM, MG are rational straight lines commensurable in square only;
therefore DG is binomial. [X. 36]