Def. 18. A perturbed proportion arises when, there being three magnitudes and another set equal to them in multitude, antecedent is to consequent among the first magnitudes as antecedent is to consequent among the second magnitudes, while, the consequent is to a third among the first magnitudes as a third is to the antecedent among the second magnitudes.
| If A:B = D:E, and B:C = E:F, then as shown in proposition V.22, ex aequali, A:C = D:F. | |
| However, if G:H = M:N, and H:K = L:M, then a perturbed proportion holds as shown in proposition V.23, namely, G:K = L:N. |
Book V Introduction - Definitions V.14 through V.16 - Proposition V.1.