For let the same construction as before be made.
Then, since AB is a first bimedial divided at C,
therefore AC, CB are medial straight lines commensurable in square only, and containing a rational rectangle, [X. 37]
so that the squares on AC, CB are also medial. [X. 21]
Therefore DL is medial. [X. 15 and 23, Por.]
And it has been applied to the rational straight line DE;
therefore MD is rational and incommensurable in length with DE. [X. 22]
Again, since twice the rectangle AC, CB is rational, MF is also rational.
And it is applied to the rational straight line ML;
therefore MG is also rational and commensurable in length with ML, that is, DE; [X. 20]
therefore DM is incommensurable in length with MG. [X. 13]
And they are rational;
therefore DM, MG are rational straight lines commensurable in square only;
therefore DG is binomial. [X. 36]
It is next to be proved that it is also a second binomial straight line.