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
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References
Adapted from (subject to copyright, with kind permission)
 Fitzpatrick, Richard: Euclid's "Elements of Geometry"
Adapted from CC BYSA 3.0 Sources:
 Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016