II.5 Proposition II.5
If a straight line be cut into equal and unequal segments, the rectangle contained by the unequal segments of the whole together with the square on the straight line between the points of section is equal to the square on the half.
Proof
Let AB be bisected at C (I.10) and cut unequally at D.
Describe on CB the square CEFB (I.46), join BE