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Mathematical Treasure: Cuthbert Tunstall's De arte supputandi

Frank J. Swetz (The Pennsylvania State University)

De arte supputande libri quattuor was the first printed arithmetic published in England. The initial edition, published in 1522, was engraved by Hans Holbein. The edition shown below was published in Paris in 1529. The author, Cuthbert Tunstall (1474–1559), was a graduate of Oxford University. He based his work on the contents of available sources, principally Pacioli’s Summa. In later years, Augustus De Morgan (1806–1871) would comment on the excellence of this work.

Tunstall's 1522 (1529) arithmetic

Division problem in Cuthbert's arithmetic

On pages 60 and 61 (shown above), Tunstall discussed the operation of division. The illustrative problem on the bottom of page 61 (also shown below) is a galley division of 76859463820 by 1579. The format in which the quotient is presented is unusual for this time. The fractional remainder, 1397 / 1579, was given on the left, while the integral part of the quotient, 48676037, was written in the center of the computation; usually it was written outside the computation at the right or the left.

Division problem from page 61

The Special Collections staff at the Linderman Library of Lehigh University in Bethlehem, Pennsylvania, is pleased to cooperate with the Mathematical Association of America to exhibit this and other items from the Library’s holdings in “Mathematical Treasures.” In particular, Convergence would like to thank Lois Fischer Black, Curator, Special Collections, and Ilhan Citak, Archives and Special Collections Librarian, for their kind assistance in helping to make this display possible. You may use these images in your classroom; all other uses require permission from the Special Collections staff, Linderman Library, Lehigh University.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Cuthbert Tunstall's De arte supputandi," Convergence (January 2013), DOI:10.4169/loci003954