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.


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