Editing History of computing hardware (section)

=== Renaissance calculating tools===
Scottish mathematician and physicist [[John Napier]] discovered that the multiplication and division of numbers could be performed by the addition and subtraction, respectively, of the [[logarithm]]s of those numbers. While producing the first logarithmic tables, Napier needed to perform many tedious multiplications. It was at this point that he designed his '[[Napier's bones]]', an abacus-like device that greatly simplified calculations that involved multiplication and division.{{efn|A Spanish implementation of [[Napier's bones]] (1617), is documented in {{harvnb|Montaner|Simon|1887|pp=19–20}}.}}

[[File:Sliderule 2005.png|thumb|upright=1.15|left|A modern slide rule]]
Since [[real number]]s can be represented as distances or intervals on a line, the [[slide rule]] was invented in the 1620s, shortly after Napier's work, to allow multiplication and division operations to be carried out significantly faster than was previously possible.{{sfn|Kells|Kern|Bland|1943|p=92}} [[Edmund Gunter]] built a calculating device with a single logarithmic scale at the [[University of Oxford]]. His device greatly simplified arithmetic calculations, including multiplication and division. [[William Oughtred]] greatly improved this in 1630 with his circular slide rule. He followed this up with the modern slide rule in 1632, essentially a combination of two [[Gunter's scale|Gunter rule]]s, held together with the hands. Slide rules were used by generations of engineers and other mathematically involved professional workers, until the invention of the [[pocket calculator]].{{sfn|Kells|Kern|Bland|1943|p=82}}