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Proposition: Prop. 10.106: Straight Line Commensurable with that which produces Medial Whole with Rational Area

(Proposition 106 from Book 10 of Euclid's “Elements”)

A (straight line) commensurable (in length) with a (straight line) which with a rational (area) makes a medial whole is a (straight line) which with a rational (area) makes a medial whole. * Let $AB$ be a (straight line) which with a rational (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 rational (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