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

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parallel to either

A D

or

B E

(I.31), so that

C F

meets

D E

at

F

. The square

A D E B

is thereby divided into two rectangles:

A D F C

contained by

A D

and

A C

(and since

A D = A B

, this rectangle is contained by

A B

and

A C

, by Definition II.1), and

C F E B

contained by

C F

and

C B

(again,

C F = A B

, so this rectangle is contained by

A B

and

C B

). Their sum (Common Notion 2) is the whole square

A D E B

, which is the square on

A B

. Therefore the rectangle on

A B

and

A C

together with the rectangle on

A B

and

C B

equals the square on

A B

.