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Let $a, b, c$ and $A, B, C$ be magnitudes.

$a, b, c$ are in perturbed proportion to $A, B, C$ if and only if:

$a : b = B : C$
$b : c = A : B$

In the words of Euclid:

A perturbed proportion arises when, there being three magnitudes and another set equal to them in multitude, as antecedent is to consequent among the first magnitudes, so is antecedent to consequent among the second magnitudes, while, as the consequent is to a third among the first magnitudes, so is a third to the antecedent among the second magnitudes.

(The Elements: Book $\text{V}$: Definition $18$)