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Proposition: Prop. 10.072: Sum of two Incommensurable Medial Areas give rise to two Irrational Straight Lines

(Proposition 72 from Book 10 of Euclid's “Elements”)

When two medial (areas which are) incommensurable with one another are added together, the remaining two irrational (straight lines) arise (as the square root of the total area) - either a second bimedial, or the square root of (the sum of) two medial (areas).

• For let the two medial (areas) $AB$ and $CD$, (which are) incommensurable with one another, have been added together.
• I say that the square root of area $AD$ is either a second bimedial, or 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