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Proposition: 7.33: Least Ratio of Numbers

(Proposition 33 from Book 7 of Euclid's “Elements”)

To find the least of those (numbers) having the same ratio as any given multitude of numbers.

• Let $A$, $B$, and $C$ be any given multitude of numbers.
• So it is required to find the least of those (numbers) having the same ratio as $A$, $B$, and $C$.

Modern Formulation

To find the reduced ratios of $\frac AB$ and $\frac BC,$ i.e. such that $A,$ $B$ and $C$ are mutually co-prime.

Table of Contents

Proofs: 1

Mentioned in:

Proofs: 1 2 3 4 5 6

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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