You are here

Mathematical Treasure: Commercial Arithmetic from Lombardy

Frank J. Swetz (The Pennsylvania State University)

The University of Pennsylvania Library manuscript designated Codex 468 comprises a Handbook of Commercial Arithmetic. Elaborately written, it originated in Lombardy and was probably written and owned by Giovanni Domenico Marchesi, ca. 1578. The codex begins with a series of diagrams explaining the basic operations of arithmetic and then proceeds to consider the mathematical solution schemes for a series of commercially related problems. Instructive diagrams are given.


Basic multiplication facts:

Multiplication algorithms for multi-digit factors, including both downward multiplication and the gelosia technique:

Basic division facts:

The “Galley” division algorithm:

On folio 11, the first leaf of text begins:

A selection of example problems and their solutions:

The images above were obtained through the kind cooperation of the University of Pennsylvania Libraries.

Index to Mathematical Treasures


Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Commercial Arithmetic from Lombardy," Convergence (February 2019)