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. * Let the [three] [rational]bookofproofs$2083 (straight lines) $A$, $B$, and $C$, (which are) commensurable in square only, be laid down. * And let, $D$, in mean proportion3 (straight line) to $A$ and $B$, have been taken [Prop. 6.13]. * And let it be contrived that as $B$ (is) to $C$, (so) $D$ (is) to $E$ [Prop. 6.12]. fig028e

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

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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