in general, denotes a regular advancing, or going forwards, in the same course and manner.

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:

\[ \begin{align*} \text{Thus} & \quad \{a, a+d, a+2d, a+3d, \ldots\}, \quad \text{&c. increasing} \\ \text{In numbers} & \quad \{1, 2, 4, 6, 8, 10, \ldots\}, \quad \text{&c. increasing} \end{align*} \]

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

\[ \begin{align*} \text{Increasing} & \quad \{a, ar, arr, arrr, \ldots\} \\ \text{Decreasing} & \quad \{a, \frac{a}{r}, \frac{a}{r^2}, \frac{a}{r^3}, \ldots\} \end{align*} \]

See the articles Fluxions, Geometry, and Series.