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Definitions 17 and 18

Def. 17. A ratio ex aequali arises when, there being several magnitudes and another set equal to them in multitude which taken two and two are in the same proportion, the first is to the last among the first magnitudes as the first is to the last among the second magnitudes. Or, in other words, it means taking the extreme terms by virtue of the removal of the intermediate terms.

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.

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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.

© 1997
D.E.Joyce
Clark University