Proposition: Prop. 10.013: Commensurable Magnitudes are Incommensurable with Same Magnitude
(Proposition 13 from Book 10 of Euclid's “Elements”)
If two magnitudes are commensurable, and one of them is incommensurable with some magnitude, then the remaining (magnitude) will also be incommensurable with it.
Modern Formulation
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Table of Contents
Proofs: 1
 Lemma: Lem. 10.13: Finding Pythagorean Magnitudes
Mentioned in:
Proofs: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
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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