◀ ▲ ▶Branches / Geometry / Elements-euclid / Book--5-proportion / Definition: 5.02: Multiple of a Real Number

Definition: 5.02: Multiple of a Real Number

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

Modern Formulation

A positive real number \(\beta > 0\) is called a multiple of another positive real number¹ \(\alpha\), if there exists a natural number \(k > 1\) such that[^2] \[\beta=k\cdot \alpha.\]

Mentioned in:

Proofs: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
Propositions: 22 23 24 25 26 27

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References

Bibliography

1. Health, T.L.: "The Thirteen Books of Euclid's Elements - With Introduction and Commentary by T. L. Health", Cambridge at the University Press, 1968, Vol 1, 2, 3

Adapted from (subject to copyright, with kind permission)

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

Footnotes