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Proposition: Prop. 10.107: Straight Line Commensurable With That Which Produces Medial Whole With Medial Area

(Proposition 107 from Book 10 of Euclid's “Elements”)

A (straight line) commensurable (in length) with a (straight line) which with a medial (area) makes a medial whole is itself also a (straight line) which with a medial (area) makes a medial whole.

• Let $AB$ be a (straight line) which with a medial (area) makes a medial whole, and let $CD$ be commensurable (in length) with $AB$.
• I say that $CD$ is also a (straight line) which with a medial (area) makes a medial whole.

Modern Formulation

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Table of Contents

Proofs: 1

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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