For, if possible, let another straight line be so interposed, as FA, and let DG be drawn from the point D perpendicular to FA.
Then, since the angle AGD is right, and the angle DAG is less than a right angle, AD is greater than DG. [I. 19]
But DA is equal to DH;
therefore DH is greater than DG, the less than the greater: which is impossible.
Therefore another straight line cannot be interposed into the space between the straight line and the circumference.