Napier's bones

John Napier described them in Rabdologiae in 1617, the year he died. Each rod carries one column of the multiplication table, and every cell is split by a diagonal with the tens above it and the units below. Lay out the rods for the digits of the multiplicand, read off the row matching the multiplier, then add along the diagonals carrying as you go. The ivory gave them the name. The method does not abolish the addition, but it does abolish the need to know the table.

Napier had already given the world logarithms in 1614, and it was those — by way of Edmund Gunter's scale — that became the slide rule. Less noticed is that Rabdologiae also set out a location arithmetic on a chequered board that counts in base two: binary arithmetic eighty years before Leibniz, tucked into an appendix of a book about counting rods.

Wilhelm Schickard's calculating clock of 1623 was essentially Napier's rods rendered in gearwheels, which makes the bones an ancestor of both the slide rule and the mechanical calculator.