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Mathematical Treasure: John Napier's Rabdologiae

Frank J. Swetz (Pennsylvania State University)

Rabdologiae (literally, Collection of Rods) was published in 1617, after Napier’s death. The work, in two volumes, describes the construction and mathematical use of “Napier’s rods.” The title page of Volume Two is shown above. In this volume, Napier elaborated on the use of the rods in problem solving.

Pages 6 and 7 provide strips of multiples from which Napier's rods or "bones" can be constructed. For a demonstration of multiplication using Napier’s rods, see “John Napier: His Life, His Logs, and His Bones” in Convergence. As you might guess, the method is based on the gelosia method of multiplication.

Page 20 shows a division problem, \(861094÷432\), in which the quotient is obtained by the use of galley division. On page 21, Napier would discuss the concept of decimal fractions.

On page 22, the division problem was repeated with the fractional part of the quotient now expressed in decimals, i.e. \({\frac{118}{432}}=0,273\) or \(0.273\)

In the Appendix, more attention was given to constructing a multiplication matrix.

A graphic plate was included to stress the correct placing of partial results in the appropriate columns.

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 (Pennsylvania State University), "Mathematical Treasure: John Napier's Rabdologiae," Convergence (September 2013)