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Proposition: Prop. 10.007: Incommensurable Magnitudes Have Irrational Ratio

(Proposition 7 from Book 10 of Euclid's “Elements”)

Incommensurable magnitudes do not have to one another the ratio which (some) number (has) to (some) number.

• Let $A$ and $B$ be incommensurable magnitudes.
• I say that $A$ does not have to $B$ the ratio which (some) number (has) to (some) number.

Modern Formulation

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Table of Contents

Proofs: 1

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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