Definition: 5.06: Proportional Magnitudes
And let magnitudes having the same ratio be called proportional.
Modern Formulation
Iif the positive real numbers $\alpha$ and $\beta$ have the same ratio as $\gamma$ and $\delta$ then they are proportional, formally
\[\frac\alpha\beta=\frac\gamma\delta.\]
Table of Contents
 Definition: Geometric Progression, Continued Proportion
Mentioned in:
Corollaries: 1 2 3
Definitions: 4 5 6 7
Proofs: 8 9 10 11 12 13 14 15 16 17
Propositions: 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
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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"