Proposition: Prop. 10.030: Construction of Rational Straight Lines Commensurable in Square Only When Square Differences Incommensurable

(Proposition 30 from Book 10 of Euclid's “Elements”)

To find two rational (straight lines which are) commensurable in square only, such that the square on the greater is larger than the (the square on) lesser by the (square) on (some straight line which is) incommensurable in length with the greater.

Modern Formulation

(not yet contributed)

Proofs: 1

Proofs: 1 2 3

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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