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Proposition: Prop. 10.109: Two Irrational Straight Lines arising from Medial Area from which Rational Area Subtracted

(Proposition 109 from Book 10 of Euclid's “Elements”)

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

• For let the rational (area) $BD$ have been subtracted from the medial (area) $BC$.
• I say that one of two irrational (straight lines) arise (as) the square root of the remaining (area), $EC$ - either a first apotome of a medial (straight line), or that (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