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

Increasing, 1, 3, 5, 7, 9, &c. Decreasing, 18, 15, 12, 9, 6, &c.

Geometrical progression is when the terms increase or decrease by equal ratios, thus:

Increasing, 1, 2, 4, 8, 16, &c. Decreasing, 81, 27, 9, 3, 1, &c.

An harmonical progression is such, that of any three consecutive terms, the first is to the third as the difference between the first and second is to the difference between the second and third. The reciprocals of the arithmetical series, 1, 2, 3, 4, 5, &c., are \( \frac{1}{1}, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}, \ldots \), which forms an harmonical progression.