Book 10
115
Again, let the square on D be equal to the rectangle B, C; therefore the square on D is irrational. [deduction from X. 20]
115
Therefore D is irrational; [X. Def. 4] and it is not the same with any of the preceding, for the square on none of the preceding, if applied to a rational straight line, produces C as breadth.
115
Similarly, if this arrangement proceeds ad infinitum, it is manifest that from the medial straight line there arise irrational straight lines infinite in number, and none is the same with any of the preceding. Q. E. D.
