COROLLARY 2.

The Proposition holds true of two ranks of magnitudes, of which each of the first rank has to a single magnitude the same ratio as each of the second rank has to another single magnitude.

[The Proposition holds true of two ranks of magnitudes (A, B, C, &c., and a, b, c, &c.), of which each of the first rank has to a single magnitude (X) the same ratio as each of the second rank has to another single magnitude (x).

PROP. XXV.

If four magnitudes of the same kind be proportionals: the greatest and least together are greater than the other two together.

THE ENUNCIATIONS,

SYSTEMATICALLY ARRANGED.

§ 1. From given Equimultiples to prove others.

1. A=ma, B=mb, C=mc, &c. | (A+B+C+&c.) =

§ 2. From given Equimultiples to prove Proportions: and vice versâ.

§ 3. From given Proportions (and Disproportions) to prove others involving the same Ratios.

§ 4. From given Equations (or Inequalities) to prove Proportions (or Disproportions): and vice versâ.

12. abcd::e:f:: &c. (a+c+e+&c.) : (b+d+f+&c.) :: a : b.