Lemma: Lem. 10.053: Construction of Rectangle with Area in Mean Proportion to two Square Areas

(Lemma to Proposition 53 from Book 10 of Euclid's “Elements”)

Let $AB$ and $BC$ be two squares, and let them be laid down such that $DB$ is straight-on to $BE$. $FB$ is, thus, also straight-on to $BG$. And let the parallelogram $AC$ have been completed. I say that $AC$ is a square, and that $DG$ is in mean proportion to $AB$ and $BC$, and, moreover, $DC$ is in mean proportion to $AC$ and $CB$.


Modern Formulation

(not yet contributed)

Proofs: 1

Proofs: 1 2 3 4 5 6

Thank you to the contributors under CC BY-SA 4.0!



Adapted from (subject to copyright, with kind permission)

  1. Fitzpatrick, Richard: Euclid's "Elements of Geometry"