We may state it more generally, thus:
If
a : b : c : d : e: ... = a′ : b′ : c′ : d′ : e′ : ... ,
then not only have two consecutive, but any two magnitudes on the first side, the same ratio as the corresponding magnitudes on the other. For instance—
a : c = a′ : c′; b : e = b′ : e′, &c.
Prop. 23 we state only in symbols, viz.:—
a : b : c : d : e : ... = 1/a′ : 1/b′ : 1/c′ : 1/d′ : 1/e′ ...,
then
a : c = c′ : a′,
b : e = e′ : b′,
and so on.