Definition:Perturbed Proportion

Definition

As Euclid defined it:

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 V: Definition $18$)

That is, a perturbed proportion is an expression for the case when, there being three magnitudes $a, b, c$ and three others $A, B, C$:

$a : b = B : C$

$b : c = A : B$