**John Napier** was a Scottish scholar who is best known for his invention of logarithms, but other mathematical contributions include a mnemonic for formulas used in solving spherical triangles and two formulas known as Napier's analogies.

- Archibald Napier was a justice-depute and was knighted in 1565.
- Before continuing we should comment on the spelling of John Napier.
- The name John is most easily dealt with as John Napier, and almost everyone else around his time, used the old spelling "Jhone".
- The forms Napeir, Nepair, Nepeir, Neper, Napare, Naper, Naipper are all seen but John Napier would most commonly have been written Jhone Neper at that time.
- Napier was educated at St Andrews University, entering the university in 1563 at the age of 13.
- Napier's name appears on the matriculation roll of St Salvator's College for 1563.
- We know that Napier spent some time at St Andrews University and he wrote himself many years later that it was in St Andrews that he first became passionately interested in theology.
- However Napier's name does not appear in the list of those being awarded degrees in the subsequent years so he must have left St Andrews to study in Europe before completing a degree.
- Napier did not acquire his knowledge of higher mathematics at St Andrews nor did he acquire his deep knowledge of classical literature there.
- It was in 1571 that Napier himself began to make arrangements for his own marriage but it was at nearly two years before that took place.
- Napier devoted himself to running his estates.
- Napier took 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 had been a fanatical Protestant from his days as an undergraduate at St Andrews.
- There were good reasons why Napier thought that a change in the religious situation in Scotland might occur, for there had, for some time, been rumours that Philip of Spain might invade Scotland.
- The Plaine Discovery of the Whole Revelation of St. John did gain Napier quite a reputation, not only within Scotland, but also on the Continent after the work was translated into Dutch, French and German.
- Napier's study of mathematics was only a hobby and in his mathematical works he writes that he often found it hard to find the time for the necessary calculations between working on theology.
- He is best known, however, for his invention of logarithms but his other mathematical contributions include a mnemonic for formulae used in solving spherical triangles, two formulae 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 and cube roots.
- Napier also found exponential expressions for trigonometric functions, and introduced the decimal notation for fractions.
- Much of Napier's work on logarithms seems to have been done while he was living at Gartness.
- Napier's discussion of logarithms appears in Mirifici logarithmorum canonis descriptio in 1614.
- Two years later an English translation of Napier's original Latin text was published, translated by Edward Wright.
- Unlike the logarithms used today, Napier's logarithms are not really to any base although in our present terminology it is not unreasonable (but perhaps a little misleading) to say that they are to base 1/e1/e1/e.
- Napier did not think of logarithms in an algebraic way, in fact algebra was not well enough developed in Napier's time to make this a realistic approach.
- Briggs did make the difficult journey from London to Edinburgh to see Napier in the summer of 1615 (would he have dreamed that now it takes 4 hours by train, rather than at least 4 days by horse and coach in those times).
- It happened one day as John Marr and the Lord Napier were speaking of Mr Briggs, "Oh! John," saith Merchiston, "Mr Briggs will not come now"; at the very instant one knocks at the gate, John Marr hastened down and it proved to be Mr Briggs to his great contentment.
- Briggs had suggested to Napier in a letter sent before their meeting that logs should be (in our terminology) to base 10 and Briggs had begun to construct tables.
- Briggs spent a month with Napier on his first visit of 1615, made a second journey from London to Edinburgh to visit Napier again in 1616 and would have made yet a third visit the following year but Napier died in the spring before the planned summer visit.
- Napier presented a mechanical means of simplifying calculations in his Rabdologiae published in 1617.
- The reason for publishing the work is given by Napier in the dedication, where he says that so many of his friends, to whom he had shown the numbering rods, were so pleased with them that they were already becoming widely used, even beginning to be used in foreign countries.
- Napier's numbering rods were made of ivory, so that they looked like bones which explains why they are now known as Napier's bones.
- It would be surprising if a man of such great an intellect as Napier did not appear rather strange to his contemporaries and, given the superstitious age in which he lived, strange stories began to circulate.
- Mark Napier suggests that John Napier deliberately played upon the primitive beliefs of his servants by going round with a cock which he had covered in soot.
- Napier, however, will be remembered for making one of the most important contributions to the advance of knowledge.
- In the preface to the Mirifici logarithmorum canonis descriptio, quoted above, Napier says he hoped that his logarithms will save calculators much time and free them from the slippery errors of calculations.

Born 1550, Merchiston Castle, Edinburgh, Scotland. Died 4 April 1617, Edinburgh, Scotland.

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Astronomy, Origin Scotland, Number Theory, Physics, Special Numbers And Numerals

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive