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Proposition: Prop. 10.010: Construction of Incommensurable Lines

(Proposition 10 from Book 10 of Euclid's “Elements”)1

To find two straight lines incommensurable with a given straight line, the one (incommensurable) in length only, the other also (incommensurable) in square. * Let $A$ be the given straight line. * So it is required to find two straight lines incommensurable with $A$, the one (incommensurable) in length only, the other also (incommensurable) in square. fig010e

Modern Formulation

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Table of Contents

Proofs: 1

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References

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", https://proofwiki.org/wiki/Main_Page, 2016

Footnotes

  1. This whole proposition is regarded by Heiberg as an interpolation into the original text (translator's note). ↩