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