Definition: 5.08: Proportion in Three Terms
And a proportion in three terms is the smallest (possible).
Modern Formulation
We say, the positive real numbers \(\alpha,\beta,\gamma\) are in a proportion in three terms, if they fulfil the proportion.
\[\frac\alpha\beta=\frac\beta\gamma.\]
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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"