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

and

as follows. From

draw

at right angles to

(I.11) with

equal to

. Through

draw

parallel to

(I.31), and through

,

,

in turn draw

,

,

parallel to

(I.31). Then the rectangle

on the lines

,

is divided by the parallels

,

into the three rectangles

on

,

;

on

,

; and

on

,

(Definition II.1). By Common Notion 2, the whole rectangle equals the sum of these parts:

. The argument generalises to any number of cuts on

.