Proposition: 2.03: Rectangle is Sum of Square and Rectangle
(Proposition 3 from Book 2 of Euclid's “Elements”)
If a straight line is cut at random then the rectangle contained by the whole (straight line), and one of the pieces (of the straight line), is equal to the rectangle contained by (both of) the pieces, and the square on the aforementioned piece.
Modern Formulation
With \(b=AC\) and \(a=CB\), we have \(b+a=AB\), and this proposition is a geometric version of the algebraic identity: \[(b+a)\,a = b\,a+a^2.\]
Table of Contents
Proofs: 1
Mentioned in:
Proofs: 1
Thank you to the contributors under CC BYSA 4.0!
 Github:

 nonGithub:
 @Fitzpatrick
References
Adapted from (subject to copyright, with kind permission)
 Fitzpatrick, Richard: Euclid's "Elements of Geometry"
Adapted from CC BYSA 3.0 Sources:
 Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016