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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)

1. Fitzpatrick, Richard: Euclid's "Elements of Geometry"

Adapted from CC BY-SA 3.0 Sources:

1. Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016