In mathematics, he was the first to draw up a methodical treatment of mechanics with the aid of geometry; he first distinguished harmonic progression from arithmetical and geometrical progressions.
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.
(iii.) Scales of Notation lead, by considering, e.g., how to express in the scale of to a number whose expression in the scale of 8 is 2222222, to (iv.) Geometrical Progressions.
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.
The work which involves arithmetic progressions is Hypsicles ' On the Ascension of Stars.