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Proposition: Prop. 10.110: Two Irrational Straight Lines arising from Medial Area from which Medial Area Subtracted

(Proposition 110 from Book 10 of Euclid's “Elements”)

A medial (area) , incommensurable with the whole, being subtracted from a medial (area) , the two remaining irrational (straight lines) arise (as) the (square root of the area) - either a second apotome of a medial (straight line), or that (straight line) which with a medial (area) makes a medial whole.

• For, as in the previous figures, let the medial (area) $BD$, incommensurable with the whole, have been subtracted from the medial (area) $BC$.
• I say that the square root of $EC$ is one of two irrational (straight lines) - either a second apotome of a medial (straight line), or that (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