Proposition: Prop. 10.035: Construction of Components of Side of Sum of Medial Areas

(Proposition 35 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 medial, and, moreover, incommensurable with the sum of the squares on them.


Modern Formulation

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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