Definition: 5.11: Corresponding Magnitudes

These magnitudes are said to be corresponding1 (magnitudes): the leading to the leading (of two ratios), and the following to the following.

Modern Formulation

Given two ratios of positive real numbers. \[\frac\alpha\beta,\quad\frac\gamma\delta,\]

pairs of numbers \((\alpha, \gamma)\) and \((\beta,\delta)\) are called corresponding magnitudes.

Proofs: 1 2
Propositions: 3 4

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  1. Literally, "double".