Napier publishes logarithms

Astronomers and navigators repeatedly faced long multiplications and divisions, often combined with trigonometric tables. John Napier investigated ways to reduce the labour and published a description of logarithms in 1614. His original construction involved quantities changing through motion and differed from familiar common logarithms. Its useful operational result was a correspondence between multiplication or division in one set of numbers and addition or subtraction in another.

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Users looked up logarithms, added or subtracted them, and used a table to recover the result. Lengthy calculations became simpler operations. Henry Briggs discussed the method with Napier and developed decimal logarithms suited to practical calculation. Producing the tables still demanded careful work, and printing errors had to be corrected. Individual calculators could now rely on shared published numerical resources whose accuracy required collective attention.

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Kepler and other astronomers adopted logarithmic tables, followed by navigators, surveyors, and engineers. Slide rules placed logarithmic scales on moving parts, allowing approximate multiplication and division through alignment. Before electronic calculators became common, tables and slide rules were regular instruments of technical education and work. Logarithms also entered the study of exponential growth, sound intensity, and measurement scales, extending a labour-saving method into a mathematical description of quantities.

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