Napier's Bones

Timeline

1. 1617Edinburgh, Kingdom of Scotland · EdinburghNapier published Rabdologiæ in Latin, explaining how to perform multiplication, division, square roots, and cube roots using small rods inscribed with lattice-multiplication tables. He stated that one motive for publication was to establish priority of invention, since the bones were already in use. This book ran parallel to his 1614 treatise on logarithms, reducing complex operations to steps of addition and subtraction.
2. 1617–1650Western European mathematical and instrument workshops · Western EuropeThe bones were easy to make from wood, bone, or ivory and became pocket calculators for merchants, surveyors, and students. European instrument makers produced sets including rods for square roots, and Latin editions and translations brought the method into universities and practical arithmetic textbooks, making it one of the most widespread non-logarithmic calculating devices of the 17th century.
3. 1620–1642England and France · Western EuropeEdmund Gunter and William Oughtred turned logarithmic scales into sliding rulers, and the encyclopedic tradition often regards the bones as a precursor to the slide rule. Pascal's 1642 gear-driven adding machine represented a different route to mechanical carry. Napier's bones, logarithm tables, and early mechanical calculators together constituted the calculating toolkit of the pre-electronic era.
4. 1701European science museums and mathematics classrooms · EuropeIn the 18th and 19th centuries the bones still appeared in arithmetic manuals, but engineering and navigation calculations increasingly relied on the slide rule. In the 20th century, originals were mainly collected as history-of-science artifacts, while the lattice-multiplication principle continued to be used for demonstrations in mathematics education.