Proposition: Prop. 10.033: Construction of Components of Major

(Proposition 33 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 rational, and the (rectangle contained) by them medial. fig033e

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