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Logarithm
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===Slide rules=== {{main|Slide rule}} Another critical application was the slide rule, a pair of logarithmically divided scales used for calculation. The non-sliding logarithmic scale, [[Gunter's rule]], was invented shortly after Napier's invention. [[William Oughtred]] enhanced it to create the slide ruleβa pair of logarithmic scales movable with respect to each other. Numbers are placed on sliding scales at distances proportional to the differences between their logarithms. Sliding the upper scale appropriately amounts to mechanically adding logarithms, as illustrated here: [[Image:Slide rule example2 with labels.svg|center|thumb|Schematic depiction of a slide rule. Starting from 2 on the lower scale, add the distance to 3 on the upper scale to reach the product 6. The slide rule works because it is marked such that the distance from 1 to {{mvar|x}} is proportional to the logarithm of {{mvar|x}}.|alt=A slide rule: two rectangles with logarithmically ticked axes, arrangement to add the distance from 1 to 2 to the distance from 1 to 3, indicating the product 6.]] For example, adding the distance from 1 to 2 on the lower scale to the distance from 1 to 3 on the upper scale yields a product of 6, which is read off at the lower part. The slide rule was an essential calculating tool for engineers and scientists until the 1970s, because it allows, at the expense of precision, much faster computation than techniques based on tables.<ref name="ReferenceA">{{Citation|last1=Maor|first1=Eli|title=E: The Story of a Number|publisher=[[Princeton University Press]]|isbn=978-0-691-14134-3|year=2009|at=sections 1, 13}}</ref>
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