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
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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