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Proposition: Prop. 10.008: Magnitudes with Irrational Ratio are Incommensurable

(Proposition 8 from Book 10 of Euclid's “Elements”)

If two magnitudes do not have to one another the ratio which (some) number (has) to (some) number then the magnitudes will be incommensurable.

• For let the two magnitudes $A$ and $B$ not have to one another the ratio which (some) number (has) to (some) number.
• I say that the magnitudes $A$ and $B$ are incommensurable.

Modern Formulation

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Table of Contents

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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