Single-digit numbers are written in the bottom right triangle leaving the other triangle blank, while double-digit numbers are written with a digit on either side of the diagonal. The others hold the multiples of the single, namely twice the single, three times the single and so on up to the ninth square containing nine times the number in the top square. The first holds a single digit, which Napier called the 'single'. The squares contain a simple multiplication table. Each square except the top is divided into two halves by a diagonal line from the bottom left corner to the top right. A set of such bones might be enclosed in a carrying case.Ī rod's face is marked with nine squares. In some later designs, the rods are flat and have two tables or only one engraved on them, and made of plastic or heavy cardboard. Each rod is engraved with a multiplication table on each of the four faces. In Napier's original design, the rods are made of metal, wood or ivory and have a square cross-section. The board's left edge is divided into nine squares, holding the numbers 1 to 9. The complete device usually includes a base board with a rim the user places Napier's rods and the rim to conduct multiplication or division. Napier's bones are not the same as logarithms, with which Napier's name is also associated, but are based on dissected multiplication tables. Advanced use of the rods can extract square roots. ![]() Using the multiplication tables embedded in the rods, multiplication can be reduced to addition operations and division to subtractions. It was printed in Edinburgh and dedicated to his patron Alexander Seton. The method was based on lattice multiplication, and also called rabdology, a word invented by Napier. Napier's bones is a manually-operated calculating device created by John Napier of Merchiston, Scotland for the calculation of products and quotients of numbers.
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