Then, since the angle FGC is right,
the angle FCG is acute; [I. 17]
and the greater angle is subtended by the greater side; [I. 19]
therefore FC is greater than FG.
But FC is equal to FB;
therefore FB is also greater than FG, the less than the greater: which is impossible.
Therefore FG is not perpendicular to DE.
Similarly we can prove that neither is any other straight line except FC;
therefore FC is perpendicular to DE.