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Mathematical Treasures - Benedetto da Firenze's Trattato d'arismetriche

Frank J. Swetz and Victor J. Katz


Benedetto da Firenze (1429 – 1479) was a respected Florentine maestro d’abaco. Here, on page 114 of his unpublished manuscript Trattato d’arismetricha (ca. 1460), a work on mercantile arithmetic, is a discussion of regula del chataina, the chain rule, used to compute exchange rates. This is not the chain rule you know from calculus, of course!

The two images below are of the same manuscript (Plimpton MS 193) of Boethius's Arithmetic as that above. They were added to this article in 2018. While the image above was prepared specifically for the Mathematical Association of America (MAA) by the Rare Book and Manuscript Library of the Columbia University Libraries, those below are presented courtesy of the Columbia University Libraries via Digital Scriptorium.

Benedetto da Firenze, or Benedict of Florence, was a noted mathematician of his city, known especially for his mercantile arithmetic, Trattato d’arismetricha (ca. 1460, Plimpton MS 193). Although highly valued for its content, the manuscript was never printed. It contains several classical problems of the times: grains of wheat on a chessboard, the hare and the hound, jealous husband, and the testament of the dying man.

The Arithmetic also considered geometry problems.

The images above have been obtained through the kind cooperation of the Rare Book and Manuscript Library of the Columbia University Libraries. These and more images may be accessed via Digital Scriptorium, a digital collection of medieval and early Renaissance manuscripts made available by a consortium of cooperating university libraries headed by the University of California, Berkeley. 

Index to Mathematical Treasures

Frank J. Swetz and Victor J. Katz, "Mathematical Treasures - Benedetto da Firenze's Trattato d'arismetriche," Convergence (January 2011)


Mathematical Treasures from the Smith and Plimpton Collections at Columbia University