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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. The method was based on lattice multiplication , and also called rabdology , a word invented by Napier.
The first device, which by then was already popularly used and known as Napier's bones, was a set of rods inscribed with the multiplication table. Napier coined the word rabdology (from Greek ῥάβδος [rhabdos], rod and λόγoς [logos] calculation or reckoning) to describe this technique. The rods were used to multiply, divide and even ...
John Napier of Merchiston (/ ˈ n eɪ p i ər / NAY-pee-ər; [1] Latinized as Ioannes Neper; 1 February 1550 – 4 April 1617), nicknamed Marvellous Merchiston, was a Scottish landowner known as a mathematician, physicist, and astronomer. He was the 8th Laird of Merchiston. John Napier is best known as the discoverer of logarithms.
The promptuary contains a lot more pieces than a set of Napier's Bones. A set of Napier's Bones with 20 rods is capable of multiplying numbers of up to 8 digits. An equivalent promptuary needs 160 strips. In the examples and illustrations below, N is set to 5 - that is, the illustrated promptuary can multiply numbers of up to 5 digits.
Napier imagined a point P travelling across a line segment P0 to Q. Starting at P0, with a certain initial speed, P travels at a speed proportional to its distance to Q, causing P to never reach Q. Napier juxtaposed this figure with that of a point L travelling along an unbounded line segment, starting at L0, and with a constant speed equal to ...
Use Napier's rules to solve the triangle ABD: use c and B to find the sides AD and BD and the angle ∠BAD. Then use Napier's rules to solve the triangle ACD: that is use AD and b to find the side DC and the angles C and ∠DAC. The angle A and side a follow by addition.
Pascal tried to create a smoothly functioning adding machine for use by his father initially, and later for commercialisation, while the adding machine in Schickard's design appears to have been introduced to assist in multiplication (through the calculation of partial products using Napier's bones, a process that can also be used to assist ...
Binary notation had not yet been standardized, so Napier used what he called location numerals to represent binary numbers. Napier's system uses sign-value notation to represent numbers; it uses successive letters from the Latin alphabet to represent successive powers of two: a = 2 0 = 1, b = 2 1 = 2, c = 2 2 = 4, d = 2 3 = 8, e = 2 4 = 16 and so on.