Proposition: Prop. 13.01: Area of Square on Greater Segment of Straight Line cut in Extreme and Mean Ratio

(Proposition 1 from Book 13 of Euclid's “Elements”)

If a straight line is cut in extreme and mean ratio then the square on the greater piece, added to half of the whole, is five times the square on the half.

For let the straight line $AB$ have been cut in extreme and mean ratio at point $C$, and let $AC$ be the greater piece.
And let the straight line $AD$ have been produced in a straight line with $CA$.
And let $AD$ be made (equal to) half of $AB$.
I say that the (square) on $CD$ is five times the (square) on $DA$.