Proposition: Prop. 10.028: Construction of Components of Second Bimedial

(Proposition 28 from Book 10 of Euclid's “Elements”)

To find (two) medial (straight lines), containing a medial (area) , (which are) commensurable in square only.

Modern Formulation

(not yet contributed)

Proofs: 1

  1. Lemma: Lem. 10.028.1: Finding Two Squares With Sum Also Square
  2. Lemma: Lem. 10.028.2: Finding Two Squares With Sum Not Square

Proofs: 1 2
Propositions: 3 4

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"

Adapted from CC BY-SA 3.0 Sources:

  1. Prime.mover and others: "Pr∞fWiki",, 2016