Proposition: Prop. 10.034: Construction of Components of Side of Rational plus Medial Area

(Proposition 34 from Book 10 of Euclid's “Elements”)

To find two straight lines (which are) incommensurable in square, making the sum of the squares on them medial, and the (rectangle contained) by them rational. fig034e

Modern Formulation

(not yet contributed)

Proofs: 1

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