Proposition: 2.02: Square is Sum of Two Rectangles
(Proposition 2 from Book 2 of Euclid's “Elements”)
(Proposition 2 from Book 2 of Euclid's “Elements”)
If a straight line is cut at random then the (sum of the) rectangle(s) contained by the whole (straight line), and each of the pieces (of the straight line), is equal to the square on the whole.
Modern Formulation
With \(a=AB\), \(b=AC\), \(C=CB\), we have $a=b+c$, in which case this proposition is a geometric version of the algebraic identity: \[a=b+c\Rightarrow a\,b+a\,c=a^2.\]
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