Definition: 5.15: Separation of a Ratio
A separation of a ratio is a taking of the (ratio of the) excess by which the leading (magnitude) exceeds the following to the following (magnitude) by itself.
Modern Formulation
In other words, given a ratio of positive real numbers \(\alpha,\beta\) with \(\alpha > \beta\),
\[\frac\alpha\beta,\]
the separation of the ratio is given by
\[\frac{\alpha\beta}\beta.\]
Mentioned in:
Proofs: 1 2 3 4 5 6 7 8 9 10 11
Propositions: 12 13
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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"