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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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