PROGRESSION — 2nd ed. (1778

PROGRESSION, in mathematics, is either arithmetical or geometrical. Continued arithmetic proportion is, where the terms do increase and decrease by equal differences and is called arithmetic progression:

thus $\left\{ \begin{array}{l} a, a+d, a+2d, a+3d, \&c. \\ a, a-d, a-2d, a-3d, \&c. \end{array} \right\}$ increasing } by the difference $d$ .

In numbers $\left\{ \begin{array}{l} 2, 4, 6, 8, 10, \&c. \\ 10, 8, 6, 4, 2, \&c. \end{array} \right\}$ increasing } by the difference $2$ .

Geometric Progression, or Continued Geometric Proportion, is when the terms do increase or decrease by equal ratios: thus,

$\left\{ \begin{array}{l} a, ar, arr, arrr, \&c. \\ a, \frac{a}{r}, \frac{a}{rr}, \frac{a}{rrr}, \&c. \end{array} \right\}$ increasing } from a continual } multiplication } by $r$ .

$\left\{ \begin{array}{l} 2, 4, 8, 16, 32, 64, \&c. \\ 64, 32, 16, 8, 4, 2, \&c. \end{array} \right\}$ increasing } from a continual } multiplication } by $2$ .

See the articles FLUXIONS, GEOMETRY, and SERIES.