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)
 Fitzpatrick, Richard: Euclid's "Elements of Geometry"
Adapted from CC BYSA 3.0 Sources:
 Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016