Proposition: Prop. 10.006: Magnitudes with Rational Ratio are Commensurable
(Proposition 6 from Book 10 of Euclid's “Elements”)
If two magnitudes have to one another the ratio which (some) number (has) to (some) number then the magnitudes will be commensurable.
 For let the two magnitudes $A$ and $B$ have to one another the ratio which the number $D$ (has) to the number $E$.
 I say that the magnitudes $A$ and $B$ are commensurable.
Modern Formulation
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Table of Contents
Proofs: 1 Corollaries: 1
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
Propositions: 30 31 32 33 34 35 36 37 38 39 40
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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