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Proposition: Prop. 10.070: Straight Line Commensurable with Side of Sum of two Medial Areas

(Proposition 70 from Book 10 of Euclid's “Elements”)

A (straight line) commensurable (in length) with the square root of (the sum of) two medial (areas) is (itself also) the square root of (the sum of) two medial (areas).

• Let $AB$ be the square root of (the sum of) two medial (areas), and (let) $CD$ (be) commensurable (in length) with $AB$.
• We must show that $CD$ is also the square root of (the sum of) two medial (areas).

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