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Proposition: Prop. 10.003: Greatest Common Measure of Commensurable Magnitudes

(Proposition 3 from Book 10 of Euclid's “Elements”)

To find the greatest common measure of two given commensurable magnitudes. * Let $AB$ and $CD$ be the two given magnitudes, of which (let) $AB$ (be) the lesser. * So, it is required to find the greatest common measure of $AB$ and $CD$.

fig003e

Modern Formulation

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Table of Contents

Proofs: 1 Corollaries: 1

Mentioned in:

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