Proposition: Prop. 10.113: Square on Rational Straight Line applied to Apotome

(Proposition 113 from Book 10 of Euclid's “Elements”)

The (square) on a rational (straight line), applied to an apotome, produces as breadth a binomial whose terms are commensurable with the terms of the apotome, and in the same ratio. Moreover, the created binomial has the same order as the apotome.


Modern Formulation

(not yet contributed)

Proofs: 1

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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