# Napier's Bones and the Genaille-Lucas Rulers

## Introduction

In 1617, John Napier published *Rabdologia*, a book that contained
a description of the rods that he had developed to aid in multiplication,
division, and the extraction of square roots. Napier's bones have since become
popular as a way of demonstrating multiplication to school students.
One problem with Napier's rules is that the user is required to perform
a number of additions and must keep track of the "carries" that occur during
these additions. In the late 1800's, a frenchman named Henri Genaille
invented an improved version of Napier's bones in response to a problem
posed by Edouard Lucas. The Genaille-Lucas rulers allow for multiplication
and division without the carries required by Napier's Bones.

This web page presents Napier's Bones and the Genaille Lucas ruler in
ready to print form. To use these documents, print them out on paper
or transparency stock, use a paper cutter to separate the strips, and
then have fun using them!

Note that the files are available in both postscript and PDF format. Free
software for viewing and printing PDF files is available from Adobe.

Note also that these figures were painstakingly drawn by hand. There is
every possibility that somewhere in he long process of doing this, I may
have made a mistake. Please contact the author if you find any errors.

Note added May 7, 2001. Jan Meyer identified two errors in the Genaille-Lucas
rulers. I've corrected these errors.

Unfortunately, I haven't yet written up any instructions on how to use
these. You'll want to refer to books lists at the bottom of this page
for more informatin. If you can think of any traditional "dead trees"
magazine or journal that might be intersted in this, I might be inspired
to sit down and write something up.

## Files to Download

## References

Aspray, William ed.,
*Computing Before Computers*, Iowa State University Press, 1990.
This book has been made available online in portable document format (PDF).

Behr, Achim, Extracting Square Roots by means of the Napier rods.

Gardner, Martin, *Knotted Doughnuts and Other Mathematical Entertainments*, W. H. Freeman, 1986.

Napier, John, * Rabdology*, translated by William Frank Richardson,
MIT Press, 1990.

Williams, M. R., *A History of Computing Technology, 2nd ed.*, IEEE Press, 1997.

This page and the postscript/pdf files that it links to are Copyright 2000,
Brian Borchers. You may reproduce these pages for personal or classroom
use, but you may not use these pages for any commercial purpose.

Return to the Brian Borchers Homepage