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Mathematical Treasure: Malcolm’s Arithmetick and Book-keeping

Frank J. Swetz (The Pennsylvania State University)

Alexander Malcolm (1685-1763) was a Scottish teacher of arithmetic and bookkeeping. He authored several books on these subjects; A New Treatise of Arithmetick and Book-keeping (1718) was one such book. The description of the text’s contents as provided on the title page reflects the instruction offered.

On page 64, the author introduced the “Rule of Five,” a compound proportion where five quantities are given and one must find an unknown sixth. While this rule is very old, it was seldom employed. The rule involving proportions that was most often applied in business situations was the “Rule of Three.” In his discussion on page 65, the author provided an example of application of the “Rule of Three” twice in order to solve a problem involving five given quantities and a sixth quantity to be found. In this problem, it is given that a weight (of cargo) of 25 stones moved 16 miles costs 15 £ 10 shillings; it is then required to find the cost of moving a load of 40 stones a distance of 9 miles. (The British unit of monetary currency, the pound, denoted by the abbreviation Lib. or the symbol £, was equivalent to 20 shillings in 1718. The British unit of weight measure, the stone, was and is equivalent to 14 pounds, not to be confused with the monetary units of the same name.)

This material is obtained through the courtesy of the University of California Libraries. A complete digital copy can be read on the UC Libraries’ Internet Archive.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Malcolm’s Arithmetick and Book-keeping," Convergence (July 2016)