Proposition: Prop. 10.020: Quotient of Rational Numbers is Rational

Euclid's Formulation

If a rational (area) is applied to a rational (straight line) then it produces as breadth a (straight line which is) rational, and commensurable in length with the (straight line) to which it is applied. * For let the rational (area) $AC$ have been applied to the rational (straight line) $AB$, producing the (straight line) $BC$ as breadth. * I say that $BC$ is rational, and commensurable in length with $BA$.


Modern Formulation

(not yet contributed)

Proofs: 1

Proofs: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

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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