◀ ▲ ▶Branches / Geometry / Elements-euclid / Book--5-proportion / Definition: 5.06: Proportional Magnitudes

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

1. 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

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"