Mathematical Treasure: Flower of Reason for Merchants

Author(s):
Frank J. Swetz (The Pennsylvania State University)

This leather-bound manuscript is a businessman’s or merchant’s manual of information considered important to his trade activities. Written in Italian, it bears the title Fiore de ragione [Flower of Reason] and contains information on basic arithmetic and geometry. It includes as well records of accounts concerning land transfer in the region of Parma and expenses compiled in the boarding of young ladies. The entries cover the period from 1538 to 1638.

The first page of entries, shown below, is dated January 3, 1538, and concerns the writing of numbers using the “figures” 9, 8, 7, 6, 5, 4, 3, 2.

On the page below, the author demonstrates the multiplication of multi-digit numbers. Two products are found, 284 x 9 and 7824 x 25. The algorithm employed is the downward method popular today. Although there were several methods of multiplication in use at this time, this apparently was the author’s favorite.

Computations concerning a triangle are discussed on the page below.

On the page shown below, given a circle of radius 14 units, the circle’s circumference is determined to be 44 units. The value for $\pi$ used is 22/7.

The images above are supplied through the courtesy of Amherst College Archives and Special Collections. You may use them in your classroom; for permission to use them for any other purpose, please contact the Amherst College Library.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Flower of Reason for Merchants," Convergence (May 2017)