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Definition: 7.05: Multiple, Number Multiplying another Number

(Definition 5 and 15 from Book 7 of Euclid's “Elements”)

And the greater (number is) a multiple of the lesser (number) when it is measured by the lesser.

Modern Definition

See multiple.

Notes

• Euclid requires a multiple to be strictly greater than any of its divisors.
• Note that the modern definition of the multiple does not make this restriction.

Mentioned in:

Definitions: 1 2 3 4
Proofs: 5 6 7 8 9 10
Propositions: 11

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References

Bibliography

1. Landau, Edmund: "Vorlesungen über Zahlentheorie, Aus der Elementaren Zahlentheorie", S. Hirzel, Leipzig, 1927

Adapted from (subject to copyright, with kind permission)

1. Fitzpatrick, Richard: Euclid's "Elements of Geometry"