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

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,

C B

of

A B

itself as the cut line, the rectangle on

A B

and

A C

equals the rectangle on

A C

and

A C

together with the rectangle on

A B

and

C B

— but the rectangle on

A C

and

A C

is the square on

A C

by Definition II.1. Re-expressing the rectangle on

A B

and

C B

via II.1 again as the rectangle on

A C

,

C B

plus the rectangle on

C B

,

C B

(which is the square on

C B

, again by Definition II.1) and combining, we obtain: the rectangle on

A B

and

A C

equals the rectangle on

A C

and

C B

plus the square on

A C

. By Common Notion 2 the equality is preserved when rearranged.