Source — Euclid's Elements, encoded as an rrxiv paper

the square

(I.46), join

, and through

draw

parallel to

or

(I.31), meeting

at

and

at

. Through

draw

parallel to

or

(I.31), and through

draw

parallel to

or

(I.31). As in II.5, the complement

equals the complement

(I.43). Adding the square

(which is the square on

) to both of

(the rectangle on

,

) shows that the rectangle

together with the square on

equals the gnomon plus the small square, which is the square

on

. Hence

as required.