Napier (Neper), John

SUBJECT AREA: Electronics and information technology

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b. 1550 Merchiston Castle, Edinburgh, Scotland

d. 4 April 1617 Merchiston Castle, Edinburgh, Scotland

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Scottish mathematician and theological writer noted for his discovery of logarithms, a powerful aid to mathematical calculations.

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Born into a family of Scottish landowners, at the early age of 13 years Napier went to the University of St Andrews in Fife, but he apparently left before taking his degree. An extreme Protestant, he was active in the struggles with the Roman Catholic Church and in 1594 he dedicated to James VI of Scotland his Plaine Discovery of the Whole Revelation of St John, an attempt to promote the Protestant case in the guise of a learned study. About this time, as well as being involved in the development of military equipment, he devoted much of his time to finding methods of simplifying the tedious calculations involved in astronomy. Eventually he realized that by representing numbers in terms of the power to which a "base" number needed to be raised to produce them, it was possible to perform multiplication and division and to find roots, by the simpler processes of addition, substraction and integer division, respectively.

A description of the principle of his "logarithms" (from the Gk. logos, reckoning, and arithmos, number), how he arrived at the idea and how they could be used was published in 1614 under the title Mirifici Logarithmorum Canonis Descriptio. Two years after his death his Mirifici Logarithmorum Canonis Constructio appeared, in which he explained how to calculate the logarithms of numbers and gave tables of them to eight significant figures, a novel feature being the use of the decimal point to distinguish the integral and fractional parts of the logarithm. As originally conceived, Napier's tables of logarithms were calculated using the natural number e(=2.71828…) as the base, not directly, but in effect according to the formula: Naperian logx= 107(log e 107-log e x) so that the original Naperian logarithm of a number decreased as the number increased. However, prior to his death he had readily acceded to a suggestion by Henry Briggs that it would greatly facilitate their use if logarithms were simply defined as the value to which the decimal base 10 needed to be raised to realize the number in question. He was almost certainly also aware of the work of Joost Burgi.

No doubt as an extension of his ideas of logarithms, Napier also devised a means of manually performing multiplication and division by means of a system of rods known as Napier's Bones, a forerunner of the modern slide-rule, which evolved as a result of successive developments by Edmund Gunther, William Oughtred and others. Other contributions to mathematics by Napier include important simplifying discoveries in spherical trigonometry. However, his discovery of logarithms was undoubtedly his greatest achievement.

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Bibliography

Napier's "Descriptio" and his "Constructio" were published in English translation as Description of the Marvelous Canon of Logarithms (1857) and W.R.MacDonald's Construction of the Marvelous Canon of Logarithms (1889), which also catalogues all his works. His Rabdologiae, seu Numerationis per Virgulas Libri Duo (1617) was published in English as Divining Rods, or Two Books of Numbering by Means of Rods (1667).

Further Reading

D.Stewart and W.Minto, 1787, An Account of the Life Writings and Inventions of John Napier of Merchiston (an early account of Napier's work).

C.G.Knott (ed.), 1915, Napier Tercentenary Memorial Volume (the fullest account of Napier's work).

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