or if
a : b : c = 1/f : 1/e : 1/d,
and if
a > c, then d > f,
but if
a = c, then d = f,
and if
a < c, then d < f.
By aid of these two propositions the following two are proved.
§ 55. Prop. 22. If there be any number of magnitudes, and as many others, which have the same ratio, taken two and two in order, the first shall have to the last of the first magnitudes the same ratio which the first of the others has to the last.