You are here

Mathematical Treasure: Flemish Commercial Arithmetic

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

Premiers fondaments de l’arithméticque ou du ciffre …, circa 1600, is a Flemish commercial arithmetic manuscript (Plimpton MS 229). It is richly illuminated. The first page promises to teach the fundamental rules of arithmetic, working with ciphers and their operations and further special rules such as “The Rule of Three,” here described also as “The Golden Rule.”

Folio 1 of a Flemish commercial arithemtic manuscript, circa 1600

The operation of subtraction is defined, discussed, and illustrated with an example:

Folio 7 (verso) of a Flemish commercial arithemtic manuscript, circa 1600

Folio 8 of a Flemish commercial arithemtic manuscript, circa 1600

The “species” of fractions is explained as a part of arithmetic. Note the use of the terms “numerator” and “denominator.”

Folio 23 of a Flemish commercial arithemtic manuscript, circa 1600

Applications of special computational rules are explained and demonstrated.

Folio 64 of a Flemish commercial arithemtic manuscript, circa 1600

Folio 85 of a Flemish commercial arithemtic manuscript, circa 1600

A section of the Arithmetic is devoted to the computation of interest.

Folio 123 (verso) of a Flemish commercial arithemtic manuscript, circa 1600

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 (The Pennsylvania State University), "Mathematical Treasure: Flemish Commercial Arithmetic," Convergence (June 2018)

Dummy View - NOT TO BE DELETED