Proposition: Prop. 10.097: Square on Apotome applied to Rational Straight Line

(Proposition 97 from Book 10 of Euclid's “Elements”)

The (square) on an apotome, applied to a rational (straight line), produces a first apotome as breadth. * Let $AB$ be an apotome, 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 first apotome.


Modern Formulation

(not yet contributed)

Proofs: 1

Proofs: 1 2 3

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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