◀ ▲ ▶Branches / Geometry / Elements-euclid / Book-10-incommensurable-magnitudes / Proposition: Prop. 10.066: Straight Line Commensurable with Binomial Straight Line is Binomial and of Same Order

Proposition: Prop. 10.066: Straight Line Commensurable with Binomial Straight Line is Binomial and of Same Order

(Proposition 66 from Book 10 of Euclid's “Elements”)

A (straight line) commensurable in length with a binomial (straight line) is itself also binomial, and the same in order.

• Let $AB$ be a binomial (straight line), and let $CD$ be commensurable in length with $AB$.
• I say that $CD$ is a binomial (straight line), and (is) the same in order¹ as $AB$.

Modern Formulation

(not yet contributed)

Table of Contents

Proofs: 1

Thank you to the contributors under CC BY-SA 4.0!

Github:

non-Github:

@Fitzpatrick

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

Footnotes