If A : B = D : E, and B : C = E : F, then as shown in proposition V.22, ex aequali, A : C = D : F.
In Book VII ratios of three terms are used in proposition VI.33. In that proposition, a certain proportion A : B : C = E : F : G is shown. This multiterm proportion may be interpreted as an abbreviation for two proportions A : B = E : F and B : C = F : G. Then it follows ex aequali that A : C = E : G. 

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. 