Proposition: Prop. 10.099: Square on Second Apotome of Medial Straight Line applied to Rational Straight Line
(Proposition 99 from Book 10 of Euclid's “Elements”)
The (square) on a second apotome of a medial (straight line), applied to a rational (straight line), produces a third apotome as breadth.
* Let $AB$ be the second apotome of a medial (straight line), 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 third apotome.
Modern Formulation
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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