Definition: 5.16: Conversion of a Ratio
A conversion of a ratio is a taking of the (ratio of the) leading (magnitude) to the excess by which the leading (magnitude) exceeds the following.
Modern Formulation
In other words, given a ratio of positive real numbers \(\alpha,\beta\) with \(\alpha > \beta\),
\[\frac\alpha\beta,\]
the conversion of the ratio is given by
\[\frac\alpha{\alpha-\beta}.\]
Mentioned in:
Corollaries: 1
Proofs: 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
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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"
