NAPIER
, or Neper (John), baron of Merchiston in Scotland, inventor of the logarithms, was the eldest son of Sir Archibald Napier of Merchiston, and born in the year 1550. Having given early indications of great natural parts, his father was careful to have them cultivated by a liberal education. After going through the ordinary course of education at the university of St. Andrew's, he made the tour of France, Italy, and Germany. On his return to his native country, his literature and other fine accomplishments soon rendered him conspicuous; he however retired from the world to pursue literary researches, in which he made an uncommon progress, as appears by the several useful discoveries with which he afterwards favoured mankind. He chiefly applied himself to the study of mathematics; without however neglecting that of the Scriptures; in both of which he discovered the most extensive knowledge and profound penetration. His Essay upon the book of the Apocalypse indicates the most acute| investigation; though time hath discovered that his calculations concerning particular events had proceeded upon fallacious data. But what has chiefly rendered his name famous, was his great and fortunate discovery of logarithms in trigonometry, by which the ease and expedition in calculation have so wonderfully assisted the science of astronomy and the arts of practical geometry and navigation. Napier, having a great attachment to astronomy, and spherical trigonometry, had occasion to make many numeral calculations of such triangles, with sines, tangents, &c; and these being expressed in large numbers, they hence occasioned a great deal of labour and trouble: To spare themselves part of this labour, Napier, and other authors about his time, set themselves to find out certain short modes of calculation, as is evident from many of their writings. To this necessity, and these endeavours it is, that we owe several ingenious contrivances; particularly the computation by Napier's Rods, and several other curious and short methods that are given in his Rabdologia; and at length, after trials of many other means, the most complete one of logarithms, in the actual construction of a large table of numbers in arithmetical progression, adapted to a set of as many others in geometrical progression. The property of such numbers had been long known, viz, that the addition of the former answered to the multiplication of the latter, &c; but it wanted the necessity of such very troublesome calculations as those above mentioned, joined to an ardent disposition, to make such a use of that property. Perhaps also this disposition was urged into action by certain attempts of this kind which it seems were made elsewhere; such as the following, related by Wood in his Athenæ Oxonienses, under the article Briggs, on the authority of Oughtred and Wingate, viz, “That one Dr. Craig a Scotchman, coming out of Denmark into his own country, called upon John Neper baron of Marcheston near Edinburgh, and told him among other discourses of a new invention in Denmark (by Longomontanus as 'tis said) to save the tedious multiplication and division in astronomical calculations. Neper being solicitous to know farther of him concerning this matter, he could give no other account of it, than that it was by proportionable numbers. Which hint Neper taking, he desired him at his return to call upon him again. Craig, after some weeks had passed, did so, and Neper then shewed him a rude draught of that he called Canon Mirabilis Logarithmorum. Which draught, with some alterations, he printing in 1614, it came forthwith into the hands of our author Briggs, and into those of William Oughtred, from whom the relation of this matter came.”
Whatever might be the inducement however, Napier published his invention in 1614, under the title of Logarithmorum Canonis Descriptic, &c, containing the construction and canon of his logarithms, which are those of the kind that is called hyperbolic. This work coming presently to the hands of Mr. Briggs, then Professor of Geometry at Gresham College in London, he immediately gave it the greatest encouragement, teaching the nature of the logarithms in his public lectures, and at the same time recommending a change in the scale of them, by which they might be advantageously altered to the kind which he afterwards computed himself, which are thence called Briggs's Logarithms, and are those now in common use. Mr. Briggs also presently wrote to lord Napier upon this proposed change, and made journeys to Scotland the two following years, to visit Napier, and consult him about that alteration, before he set about making it. Briggs, in a letter to archbishop Usher, March 10, 1615, writes thus: “Napier lord of Markinston hath set my head and hands at work with his new and admirable logarithms. I hope to see him this summer, if it please God; for I never saw a book which pleased me better, and made me more wonder.” Briggs accordingly made him the visit, and staid a month with him.
The following passage, from the life of Lilly the astrologer, contains a curious account of the meeting of those two illustrious men. “I will acquaint you (says Lilly) with one memorable story related unto me by John Marr, an excellent mathematician and geometrician, whom I conceive you remember. He was servant to King James and Charles the First. At first when the lord Napier, or Marchiston, made public his logarithms, Mr. Briggs, then reader of the astronomy lectures at Gresham College in London, was so surprised with admiration of them, that he could have no quietness in himself until he had seen that noble person the lord Marchiston, whose only invention they were: he acquaints John Marr herewith, who went into Scotland before Mr. Briggs, purposely to be there when these two so learned persons should meet. Mr. Briggs appoints a certain day when to meet at Edinburgh; but failing thereof, the lord Napier was doubtful he would not come. It happened one day as John Marr and the lord Napier were speaking of Mr. Briggs; ‘Ah, John (said Marchiston), Mr. Briggs will not now come.’ At the very instant one knocks at the gate; John Marr hasted down, and it proved Mr. Briggs to his great contentment. He brings Mr. Briggs up into my lord's chamber, where almost one quarter of an hour was spent, each beholding other almost with admiration before one word was spoke. At last Mr. Briggs began: ‘My lord, I have undertaken this long journey purposely to see your person, and to know by what engine of wit or ingenuity you came first to think of this most excellent help into astronomy, viz, the logarithms; but, my lord, being by you found out, I wonder no body else found it out before, when now known it is so easy.’ He was nobly entertained by the lord Napier; and every summer after that, during the lord's being alive, this venerable man Mr. Briggs went purposely into Scotland to visit him.”
Napier made also considerable improvements in spherical trigonometry &c, particularly by his Catholic or Universal Rule, being a general theorem by which he resolves all the cases of right-angled spherical triangles in a manner very simple, and easy to be remembered, namely, by what he calls the Five Circular Parts. His Construction of Logarithms too, beside the labour of them, manifests the greatest ingenuity. Kepler dedicated his Ephemerides to Napier, which were published in the year 1617; and it appears from many passages in his letter about this time, that he accounted Napier to be the greatest man of his age in the particular department to which he applied his abilities.|
The last literary exertion of this eminent person was the publication of his Rabdology and Promptuary, in the year 1617; soon after which he died at Marchiston, the 3d of April in the same year, is the 68th year of his age.—The list of his works is as follows:
1. A Plain Discovery of the Revelation of St. John; <*>593.
2. Logarithmorum Canonis Descriptio; 1614.
3. Mirifici Logarithmorum Canonis Constructio; et eorum ad Naturales ipsorum numeros habitudines; una cum appendice, de alia eaque præstantiore Logarithmorum specie condenda. Luibus accessere propositiones ad triangula sphærica faciliore calculo resolvenda. Una cum Annotationibus aliquot doctissimi D. Henrici Briggii in eas, & memoratam appendicem. Published by the author's son in 1619.
4. Rabdologia, seu Numerationis per Virgulas, libri duo; 1617. This contains the description and use of the Bones or Rods; with several other short and ingenious modes of calculation.
5. His Letter to Anthony Bacon (the original of which is in the archbishop's library at Lambeth), intitled, Secret Inventions, Profitable and Necessary in these days for the Defence of this Island, and withstanding Strangers Enemies to God's Truth and Religion; dated June 2, 1596.
Napier's Bones, or Rods, an instrument contrived by lord Napier, for the more easy performing of the arithmetical operations of multiplication, division, &c. These rods are five in number, made of Bone, ivory, horn, wood, or pasteboard, &c. Their faces are divided into nine little squares (fig. 7, pl. 16); each of which is parted into two triangles by diagonals. In these little squares are written the numbers of the multiplication-table; in such manner as that the units, or right-hand figures, are found in the right-hand triangle: and the tens, or the left-hand figures, in the left-hand triangle; as in the figure.
To Multiply Numbers by Napier's Bones. Dispose the rods in such manner, as that the top figures may exhibit the multiplicand; and to these, on the left-hand, join the rod of units: in which seek the right-hand figure of the multiplier: and the numbers corresponding to it, in the squares of the other rods, write out, by adding the several numbers occurring in the same rhomb together, and their sums. After the same manner write out the numbers corresponding to the other figures of the multiplier; disposing them under one another as in the common multiplication; and lastly add the several numbers into one sum.
| 5978 |
| 937 |
| 41846 |
| 17934 |
| 53802 |
| 5601386 |
To perform Division by Napier's Bones. Dispose the rods so, as that the uppermost figures may exhibit the divisor; to these on the left-hand, join the rod of units. Descend under the divisor, till you meet those figures of the dividend in which it is first required how oft the divisor is found, or at least the next less num ber, which is to be subtracted from the dividend; then the number corresponding to this, in the place of units, set down for a quotient. And by determining the other parts of the quotient after the same manner, the division will be completed.
| 5978) | 5601386 | (937 |
| 53802 | ||
| 22118 | ||
| 17934 | ||
| 41846 | ||
| 41846 |
For example; suppose the dividend 5601386, and the divisor 5978; since it is first enquired how often 5978 is found in 56013, descend under the divisor (fig. 8) till in the lowest series you find the number 53802, approaching nearest to 56013; the former of which is to be subtracted from the latter, and the figure 9 corresponding to it in the 10d of units set down for the quotient. To the remainder 2211 join the following figure 8 of the dividend; and the number 17934 being found as before for the next less number to it, the corresponding number 3 in the rod of units is to be set down for the next figure of the quotient. After the same manner the third and last figure of the quotient will be found to be 7; and the whole quotient 937.
