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 \(\alpha > \beta\),


the separation of the ratio is given by


Proofs: 1 2 3 4 5 6 7 8 9 10 11
Propositions: 12 13

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  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"