◀ ▲ ▶Branches / Geometry / Elements-euclid / Book-10-incommensurable-magnitudes / Proposition: Prop. 10.012: Commensurability is Transitive Relation

Proposition: Prop. 10.012: Commensurability is Transitive Relation

Euclid's Formulation

(Magnitudes) commensurable with the same magnitude are also commensurable with one another.

• For let $A$ and $B$ each be commensurable with $C$.
• I say that $A$ is also commensurable with $B$.

Modern Formulation

(not yet contributed)

Table of Contents

Proofs: 1

Mentioned in:

Proofs: 1 2 3 4 5 6 7 8 9 10 11 12 13 14

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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