Napier

John Napier

Born: 1550 in Edinburgh, Scotland
Died: 4 April 1617 in Edinburgh, Scotland

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Napier is best known for his invention of logarithms and for formulas used in solving spherical triangles.

Napier was educated at St Andrews University although he seems to have left without obtaining a degree. He then studied in Europe.

In 1571, Napier returned to Scotland and devoted himself to running his estate and taking part in the religious controversies of the time. He was a fervent Protestant and published, what he considered his most important work, the Plaine Discovery of the Whole Revelation of St. John (1593).

Napier's study of mathematics was only a hobby. He is best known, however, for his invention of logarithms but other mathematical contributions include a mnemonic for formulas used in solving spherical triangles, two formulas known as Napier's analogies used in solving spherical triangles and an invention called Napier's bones used for mechanically multiplying dividing and taking square roots. Napier also found exponential expressions for trigonometric functions, and introduced the decimal notation for fractions.

Napier's discussion of logarithms appears in Mirifici logarithmorum canonis descriptio in 1614. Unlike the logarithms used today Napier's logarithms are to base 1/e and involve a constant 10^7. Napier hoped that his logarithms would save astronomers much time and free them from the slippery errors of calculations. Laplace, 200 year later, agreed, saying that logarithms

by shortening the labours, doubled the life of the astronomer .

Napier presented a mechanical means of simplifying calculations in his Rabdologiae in 1617. He described a method of multiplication using rods with numbers marked off on them. Napier's rods were made of ivory, so that they looked like bones which explains why they are now known as Napier's bones. To multiply numbers the bones were placed side by side and the appropriate products read off.

Other Web sites:

Rice University, USA
Clarke University, USA

References:

  1. Dictionary of Scientific Biography
  2. Biography in Encyclopaedia Britannica
  3. C.G. Knott (ed.), Napier Tercentenary Memorial Volume (London, 1915).
  4. R Ayoub, What is a Naperian logarithm?, Amer. Math. Monthly 100 (1993), 351-364.
  5. M Napier, Memoirs of John Napier of Merchiston, his lineage, life, and times, with a history of the invention of logarithms (Edinburgh, 1904).
  6. D J Bryden, Napier's bones : a history and instruction manual (London, 1992). 
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JOC/EFR February 1996