For on AB let the square AD be described;
therefore AD is medial.
And, since AB is commensurable in length with BC, while AB is equal to BD, therefore DB is also commensurable in length with BC;
so that DA is also commensurable with AC. [VI. 1, X. 11]
But DA is medial;
therefore AC is also medial. [X. 23, Por.]
Q. E. D.