Definition: 5.01: Magnitude is Aliquot Part
(Definition 1 from Book 5 of Euclid's “Elements”)
A magnitude is a part of a(nother) magnitude, the lesser of the greater, when it measures the greater.
Modern Formulation
A positive real number \(\alpha > 0\) is called an aliquot part of another positive real number^{1} \(\beta\), if there exists a natural number \(k > 1\) such that^{2}
\[\beta=k\cdot \alpha.\]
Mentioned in:
Definitions: 1 2 3 4
Proofs: 5 6 7 8 9 10 11 12
Propositions: 13 14 15 16 17 18 19 20
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References
Bibliography
 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)
 Fitzpatrick, Richard: Euclid's "Elements of Geometry"
Footnotes