Proposition: Prop. 10.102: Square on Straight Line which produces Medial Whole with Medial Area applied to Rational Straight Line
(Proposition 102 from Book 10 of Euclid's “Elements”)
The (square) on that (straight line) which with a medial (area) makes a medial whole, applied to a rational (straight line), produces a sixth apotome as breadth.
* Let $AB$ be that (straight line) which with a medial (area) makes a medial whole, and $CD$ a rational (straight line).
* And let $CE$, equal to the (square) on $AB$, have been applied to $CD$, producing $CF$ as breadth.
* I say that $CF$ is a sixth apotome.
Modern Formulation
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Table of Contents
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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