The rectangle contained by rational straight lines commensurable in square only is irrational, and the side of the square equal to it is irrational. Let the latter be called
medial.

For let the rectangle AC be contained by the rational straight lines AB, BC commensurable in square only; AC is irrational, and the side of the square equal to it is irrational; and let the latter be called medial.

For on AB let the square AD be described; therefore AD is rational. [X. Def. 4]