Then, since a straight line FE through the centre bisects a straight line AC not through the centre, it also cuts it at right angles; [III. 3]
therefore the angle FEA is right.
Again, since a straight line FE bisects a straight line BD, it also cuts it at right angles; [III. 3]
therefore the angle FEB is right.
But the angle FEA was also proved right;
therefore the angle FEA is equal to the angle FEB, the less to the greater: which is impossible.
Therefore AC, BD do not bisect one another.