The Liber abaci, which fills 459 printed pages, contains the most perfect methods of calculating with whole numbers and with fractions, practice, extraction of the square and cube roots, proportion, chain rule, finding of proportional parts, averages, **progressions**, even compound interest, just as in the completest mercantile arithmetics of our days.

(i.) Arithmetical **Progressions** such as 2, 5, 8, ...

The word " sequence," as defined in ï¿½ 58 (i.), includes **progressions** such as the arithmetical and geometrical **progressions**, and, generally, the succession of terms of a series.