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.


Modern Formulation

(not yet contributed)

Proofs: 1

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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",, 2016