Mathematical Treasures - Widman's Commercial Arithmetic

Published in Leipzig in 1489, Behend und hüpsch Rechnung uff [auf] allen Kauffmanschafften (Nimble and Neat Calculation in all Trades) was the first printed commercial arithmetic book to appear in Germany. The author was Johannes Widman (ca.1460–1498), a graduate of the University of Leipzig who returned to the university to teach mathematics. Widman introduced the plus sign “+” and the minus sign “–” into the context of European mathematics. The title page for the 1508 edition is shown below, depicting merchants at a counting table. It is difficult to discern if the man at lower right is working on an abacus or writing on a slate board.

On the pages below, Widman provided three examples of galley division:

Left: 9803617524 ÷ 45678 = 214624 + 22452/45678

Right: 161143442 ÷ 2159 = 74638; 3900994564 ÷ 3986 = 978674.

The six pages below provide some situational word problems, including a problem involving a courier and another involving the will of a dying man, a will that requires a mathematical interpretation.

These images from its George Arthur Plimpton Collection are presented through the courtesy of the Columbia University Libraries.

Index to Mathematical Treasures