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
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Table of Contents
Proofs: 1
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References
Adapted from (subject to copyright, with kind permission)
 Fitzpatrick, Richard: Euclid's "Elements of Geometry"
Adapted from CC BYSA 3.0 Sources:
 Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016