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Definition: Napier, John from Philip's Encyclopedia

Scottish mathematician. He developed 'Napier's bones', an early calculating apparatus, and logarithms (1614), a powerful mathematical technique.

Summary Article: Napier, John (1550-1617)
From The Hutchinson Dictionary of Scientific Biography

Place: United States of America

Subject: biography, maths and statistics, computing

Scottish mathematician who invented logarithmic tables.

Napier was born in Merchiston Castle, near Edinburgh, in 1550, into a family of influential landed nobility and statesmen who were staunchly attached to the Protestant cause. As a young boy he was educated chiefly at home, although he may have spent some time at the Edinburgh High School and, less probably, studying in France. At the age of 13 he was sent to St Salvator's College, in the University of St Andrews. There he studied mainly theology and philosophy, gained a reputation for his quick temper, and left without taking his degree. He may then have passed a few years studying on the continent. He was, at any rate, in Scotland in 1571. He built a castle at Gartnes, on the banks of the Endrick, and lived there with his wife, whom he married in 1572, until the death of his father in 1608 brought him the inheritance of Merchiston.

Napier was an aristocratic scientific and literary amateur. He never occupied any professional post in his life. But he became known as the ‘Marvellous Merchiston’ for his varied accomplishments. He made advances in scientific farming, especially by the use of salt as a fertilizer; he invented a hydraulic screw and revolving axle by means of which water could be removed from flooded coalpits and obtained the patent for its sole manufacture and use in 1597; he also published, in 1593, a violent denunciation of the Roman Catholic Church entitled A Plaine Discovery of the Whole Revelation of St John, a popular work that ran through several editions and was translated into French, Dutch, and German. He had scarcely a moment of idleness, and overwork - combined with the gout from which he suffered in his later years - brought him to his death, at Merchiston, on 4 April 1617.

Napier's favourite intellectual pursuit was astronomy, and it was via astronomy that he was led to make his great invention. He performed many calculations in the course of his observations and research. He found the lengthy calculations, involving the use of trigonometric functions (especially sines) a tiresome burden, and over the course of about 20 years the idea of logarithmic tables slowly gestated in his mind. In 1614 he explained his new invention and printed the first logarithmic table in the Mirifici logarithmorum canonis descriptio/Description of the Marvellous Canon of Logarithms. The word ‘logarithm’ he formed from the Greek logos (‘expression’) and arithmos (‘number’). The best statement of his invention, however, was given in the posthumously published Mirifici logarithmorum canonis constructio/Construction of the Marvellous Canon of Logarithms (1619).

Napier's publication was immediately recognized by mathematicians for the great advance that it was. In particular, it excited the English mathematician Henry Briggs, who went to Edinburgh in 1616 (and a couple of times thereafter) to discuss the new tables with Napier. Together they worked out improvements - such as the idea of using the base ten - and the result, Briggs's tables of 1617, was the production of the standard form of logarithmic tables in use until the advent of cheap electronic calculators.

Napier himself has a claim as the inventor of the first mechanical calculator, albeit one of a wholly primitive kind. His last work, Rabdologia (‘numeration by little rods’), was published in 1617. In it he explained his system of multiplying and dividing by the use of rods - usually made of bones or ivory, and hence known as Napier's bones - and showed also how square roots could be extracted by the manipulation of counters on a chessboard.

As a footnote, and a testament to the splendid practical inventiveness of the man, it should be remembered that it was Napier, too, who first used and then popularized the decimal point to separate the whole-number part from the fractional part of a number.

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