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Mathematical Treasure: 16th-Century Libro de Abbaco

Frank J. Swetz (Pennsylvania State University)

Libro de Abbaco (1574) is an Italian manuscript compiled by a Giovanni Battista Cortona. Little is known about the author but it can safely be assumed he was an Italian businessman and/or merchant. Such books were usually made for reference or instructional purposes and some as “displays” of the author’s knowledge and ability. This one seems to be of the latter category. The cover of the Libro bears a decorative design.

The operation of addition is introduced by the summing of monetary transactions involving ducats, grossi, and piccolo, hardly instructive to a novice just learning arithmetic.

The presentation of the operation of multiplication is more didactical. Tables of “Multiplication Facts” are given along with examples.

The product of two multi-digit numbers is found employing the “downward algorithm.”

On the left page, two additional methods of multiplication are demonstrated: at the top, “per quadrilatero” (by the rectangle); below, “per gelosia” (by the grating). A discussion of division begins on the opposite page.

Here the author used his skill in employing the “galera” (galley) method to obtain quotients for two examples.

The later section of the manuscript provides examples of calculating commercial problems. In the problem on the right page, the phrase “per centro” can be discerned: it translates into English as “by the hundred” from which is derived the word “percent.”

These images were obtained through the courtesy of the Beinecke Rare Book and Manuscript Library, Yale University, reference no. MS655.

Index to Mathematical Treasures

Frank J. Swetz (Pennsylvania State University), "Mathematical Treasure: 16th-Century Libro de Abbaco," Convergence (July 2018)