Definition: 5.14: Composition of a Ratio
A composition of a ratio is a taking of the (ratio of the) leading plus the following (magnitudes), as one, to the following (magnitude) by itself.
Modern Formulation
In other words, given a ratio of positive real numbers \(\alpha,\beta\):
\[\frac\alpha\beta,\]
the composition of the ratio is given by
\[\frac{\alpha+\beta}\beta.\]
Mentioned in:
Corollaries: 1
Proofs: 2 3 4 5 6 7 8 9 10 11 12 13
Propositions: 14 15
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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"