Editing Location arithmetic (section)

{{Short description|One of three devices to aid arithmetic calculation described by John Napier in a treatise}}
{{Rabdology}}
{{cleanup |reason=Passages of how-to steps that read like a tutorial and use "we" and "you". |date=April 2020}}
'''Location arithmetic''' (Latin ''arithmetica localis'') is the additive (non-positional) [[binary arithmetic|binary]] [[numeral systems]], which [[John Napier]] explored as a computation technique in his treatise ''[[Rabdology]]'' (1617), both symbolically and on a [[chessboard]]-like grid.

Napier's terminology, derived from using the positions of counters on the board to represent numbers, is potentially misleading because the numbering system is, in facts, non-[[Positional notation|positional]] in current vocabulary.

During Napier's time, most of the computations were made on boards with tally-marks or [[jeton]]s. So, unlike how it may be seen by the modern reader, his goal was not to use moves of counters on a board to multiply, divide and find square roots, but rather to find a way to compute symbolically with pen and paper.

However, when reproduced on the board, this new technique did not require mental trial-and-error computations nor complex carry memorization (unlike base 10 computations). He was so pleased by his discovery that he said in his preface:

{{blockquote|it might be well described as more of a lark than a labor, for it carries out addition, subtraction, multiplication, division and the extraction of square roots purely by moving counters from place to place.{{ref|Napier}}}}