page_title: John Napier
section_title: Advances in mathematics
hierarchical_section_title: John Napier / Advances in mathematics
caption_attribution_description: English: An ivory set of Napier's Bones from around 1650. An exhibit in the National Museum of Scotland.
context_page_description: John Napier of Merchiston, nicknamed Marvellous Merchiston, was a Scottish landowner known as a mathematician, physicist, and astronomer. He was the 8th Laird of Merchiston. His Latinized name was Ioannes Neper.
  John Napier is best known as the discoverer of logarithms. He also invented the so-called "Napier's bones" and made common the use of the decimal point in arithmetic and mathematics.
  Napier's birthplace, Merchiston Tower in Edinburgh, is now part of the facilities of Edinburgh Napier University. Napier died from the effects of gout at home at Merchiston Castle and his remains were buried in the kirkyard of St Giles. Following the loss of the kirkyard there to build Parliament House, he was memorialised at St Cuthbert's at the west side of Edinburgh.
context_section_description: His work, Mirifici Logarithmorum Canonis Descriptio (1614) contained fifty-seven pages of explanatory matter and ninety pages of tables of numbers related to natural logarithms (see Napierian logarithm). The book also has an excellent discussion of theorems in spherical trigonometry, usually known as Napier's Rules of Circular Parts. See also Pentagramma mirificum.
  Modern English translations of both Napier's books on logarithms and their description can be found on the web, as well as a discussion of Napier's bones and Promptuary (another early calculating device).
  His invention of logarithms was quickly taken up at Gresham College, and prominent English mathematician Henry Briggs visited Napier in 1615. Among the matters they discussed were a re-scaling of Napier's logarithms, in which the presence of the mathematical constant now known as e (more accurately, e times a large power of 10 rounded to an integer) was a practical difficulty. Neither Napier nor Briggs actually discovered the constant e; that discovery was made decades later by Jacob Bernoulli.
  Napier delegated to Briggs the computation of a revised table. The computational advance available via logarithms, the inverse of powered numbers or exponential notation, was such that it made calculations by hand much quicker. The way was opened to later scientific advances, in astronomy, dynamics, and other areas of physics.
  Napier made further contributions. He improved Simon Stevin's decimal notation. Lattice multiplication, used by Fibonacci, was made more convenient by his introduction of Napier's bones, a multiplication tool using a set of numbered rods.
  Napier may have worked largely in isolation, but he had contact with Tycho Brahe who corresponded with his friend John Craig. Craig certainly announced the discovery of logarithms to Brahe in the 1590s (the name itself came later); there is a story from Anthony à Wood, perhaps not well substantiated, that Napier had a hint from Craig that Longomontanus, a follower of Brahe, was working in a similar direction.
  It has been shown that Craig had notes on a method of Paul Wittich that used trigonometric identities to reduce a multiplication formula for the sine function to additions.
caption: An ivory set of Napier's Bones from around 1650
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