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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)

Table of Contents

Proofs: 1

Mentioned in:

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

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References

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", https://proofwiki.org/wiki/Main_Page, 2016