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Napier sentence examples

napier
  • JOHN NAPIER (1550-1617), Scottish mathematician and inventor of logarithms, was born at Merchiston near Edinburgh in 1550, and was the eighth Napier of Merchiston.

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  • The first Napier of Merchiston, "Alexander Napare," acquired the Merchiston estate before the year 1438, from James I.

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  • His son, John Napier of Rusky, the third of Merchiston, belonged to the royal household in the lifetime of his father.

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  • His eldest son, Archibald Napier of Edinbellie, the fourth of Merchiston, belonged to the household of James IV.

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  • His eldest son was Archibald, seventh of Merchiston, and the father of John Napier, the subject of this article.

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  • In 1549 Archibald Napier, at the early age of about fifteen, married Janet, daughter of Francis Bothwell, and in the following year John Napier was born.

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  • About 1565 he was knighted at the same time as James Stirling, his colleague, whose daughter John Napier subsequently married.

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  • As already stated, John Napier was born in 1550, the year in which the Reformation in Scotland may be said to have commenced.

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  • The names of nearly all Napier's classfellows can be traced as becoming determinantes in 1566 and masters of arts in 1568; but his own name does not appear in the lists.

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  • About the end of the year 1579 his wife died, leaving him one son, Archibald (who in 1627 was raised to the peerage by the title of Lord Napier), and one daughter, Jane.

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  • A few years afterwards he married again, his second wife being Agnes, daughter of Sir James 1 The descent of the first Napier of Merchiston has been traced to "Johan le Naper del Counte de Dunbretan," who was one of those who swore fealty to Edward I.

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  • The legend with regard to the origin of the name Napier was given by Sir Alexander Napier, eldest son of John Napier, in 1625, in these words: "One of the ancient earls of Lennox in Scotland had issue three sons: the eldest, that succeeded him to the earldom of Lennox; the second, whose name was Donald; and the third, named Gilchrist.

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  • This committee consisted of six members, two barons, two ministers and two burgesses - the two barons selected being John Napier of Merchiston and James Maxwell of Calderwood.

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  • These interviews took place in October 15 93, and on the 29th of the following January Napier wrote to the king the letter which forms the dedication of the Plaine Discovery.

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  • The full title of this first work of Napier's is given below.'

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  • 2 Napier's Plaine Discovery is a serious and laborious work, to which he had devoted years of care and thought.

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  • Napier lived in the very midst of fiercely contending religious factions; there was but little theological teaching of any kind, and the work related to what were then the leading political and religious questions of the day.

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  • Set foorth by John Napier L.

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  • The second edition in English appeared at Edinburgh in 1611, and in the preface to it Napier states he intended to have published an edition in Latin soon after the original publication in 1593, but that, as the work had now been made public by the French and Dutch translations, besides the English editions, and as he was "advertised that our papistical adversaries wer to write larglie against the said editions that are alreadie set out," he defers the Latin edition "till having first seene the adversaries objections, I may insert in the Latin edition an apologie of that which is rightly done, and an amends of whatsoever is amisse."

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  • After the publication of the Plaine Discovery, Napier seems to have occupied himself with the invention of secret instruments of war, for in the Bacon collection at Lambeth Palace there is a document, dated the 7th of.

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  • June 1596 and signed by Napier, giving a list of his inventions for the defence of the country against the anticipated invasion by Philip of Spain.

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  • This work contains the first announcement of logarithms to the world, the first table of logarithms and the first use of the name logarithm, which was invented by Napier.

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  • In 1617 Napier published his Rabdologia, 4 a duodecimo of one hundred and fifty-four pages; there is prefixed to it as preface a dedicatory epistle to the high chancellor of Scotland.

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  • The method which Napier terms "Rabdologia" consists in the use of certain numerating rods for the performance of multiplications and divisions.

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  • These rods, which were commonly called "Napier's bones," will be described further on.

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  • John Napier died on the 4th of April 1617, the same year as that in which the Rabdologia was published.

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  • It has been usually supposed that John Napier was buried in St Giles's church, Edinburgh, which was certainly the burialplace of some of the family, but Mark Napier (Memoirs, p. 426) quotes Professor William Wallace, who, writing in 1832, gives strong reasons for believing that he was buried in the old church of St Cuthbert.

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  • It is nowhere else recorded that Napier suffered from the gout.

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  • It has been stated that Napier's mathematical pursuits led him to dissipate his means.

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  • Briggs was greatly excited by Napier's invention and visited him at Merchiston in 1615, staying with him a whole month; he repeated his visit in 1616 and, as he states, "would have been glad to make him a third visit if it had pleased God to spare him so long."

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  • 2 In this treatise (which was written before Napier had invented the name logarithm) logarithms are called "artificial numbers."

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  • Macdonald at Edinburgh in 1889, and that there is appended to this edition a complete catalogue of all Napier's writings, and their various editions and translations, English and foreign, all the works being carefully collated, and references being added to the various public libraries in which they are to be found.

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  • Napier's priority in the publication of the logarithms is unquestioned and only one other contemporary mathematician seems to have conceived the idea on which they depend.

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  • When Napier published the Canonis Descriptio England had taken no part in the advance of science, and there is no British author of the time except Napier whose name can be placed in the same rank as those of Copernicus, Tycho Brahe, Kepler, Galileo, or Stevinus.

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  • Napier lived, too, not only in a wild country, which was in a lawless and unsettled state during most of his life, but also in a credulous and superstitious age.

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  • Like Kepler and all his contemporaries he believed in astrology, and he certainly also had some faith in the power of magic, for there is extant a deed written in his own handwriting containing a contract between himself and Robert Logan of Restalrig, a turbulent baron of desperate character, by which Napier undertakes "to serche and sik out, and be al craft and ingyne that he dow, to tempt, trye, and find out" some buried treasure supposed to be hidden in Logan's fortress at Fastcastle, in consideration of receiving one-third part of the treasure found by his aid.

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  • Of this singular contract, which is signed, "Robert Logane of Restalrige" and "Jhone Neper, Fear of Merchiston," and is dated July 1594, a facsimile is given in Mark Napier's Memoirs.

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  • As the deed was not destroyed, but is in existence now, it is to be presumed that the terms of it were, riot fulfilled; but the fact that such a contract should have been drawn up by Napier himself affords a singular illustration of the state of society and the kind of events in the midst of which logarithms had their birth.

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  • After Napier's death his manuscripts and notes came into the possession of his second son by his second marriage, Robert, who edited the Constructio; and Colonel Milliken Napier, Robert's lineal male representative, was still in the possession of many of these private papers at the close of the 18th century.

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  • On one occasion when Colonel Napier was called from home on foreign service, these papers, together with a portrait of John Napier and a Bible with his autograph, were deposited for safety in a room of the house at Milliken, in Renfrewshire.

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  • Fortunately, however, Robert Napier had transcribed his father's manuscript De Arte Logistica, and the copy escaped the fate of the originals in the manner explained in the following note, written in the volume containing them by Francis, seventh Lord Napier: "John Napier of Merchiston, inventor of the logarithms, left his manuscripts to his son Robert, who appears to have caused the following pages to have been written out fair from his father's notes, for Mr Briggs, professor of geometry at Oxford.

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  • An account of the contents of these manuscripts was given by Mark Napier in the appendix to his Memoirs of John Napier, and the manuscripts themselves were edited in their entirety by him in 1839 under the title De Arte Logistica Joannis Naperi Merchistonii Baronis Libri qui supersunt.

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  • The treatise occupies one hundred and sixty-two pages, and there is an introduction by Mark Napier of ninety-four pages.

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  • The transcripts are entirely in the handwriting of Robert Napier himself, and the two notes that have been quoted prove that they were made from Napier's own papers.

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  • The title, which is written on the first leaf, and is also in Robert Napier's writing, runs thus: "The Baron of Merchiston his booke of Arithmeticke and Algebra.

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  • Napier uses abundantes and defectivae for positive and negative, defining them as meaning greater or less than nothing ("Abundantes sunt quantitates majores nihilo: defectivae sunt quantitates minores nihilo").

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  • Napier may thus have been the first to use the expression "quantity less than nothing."

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  • Among the Merchiston papers is a thin quarto volume in Robert Napier's writing containing a digest of the principles of alchemy; it is addressed to his son, and on the first leaf there are directions that it is to remain in his charter-chest and be kept secret except from a few.

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  • The principle of "Napier's bones" may be easily explained by imagir:ing ten rectangular slips of cardboard, each divided into nine squares.

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  • the figures as written down are 12510 6255 14595 1534560 Napier's rods or bones consist of ten oblong pieces of wood or other material with square ends.

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  • These rules were published in the Canonis Descriptio (1614), and Napier has there given a figure, and indicated.a method, by means of which they may be proved directly.

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  • Robert Napier says that these results would have been reduced to order and demonstrated consecutively but for his father's death.

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  • Only one of the four analogies is actually given by Napier, the other three being added by Briggs in the remarks which are appended to Napier's results.

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  • These examples show that Napier was in possession of all the conventions and attributes that enable the decimal point to complete so symmetrically our system of notation, viz.

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  • Napier thus had complete command over decimal fractions and the use of the decimal point.

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  • Briggs also used decimals, but in a form not quite so convenient as Napier.

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  • There seems but little doubt that Napier was the first to make use of a decimal separator, and it is curious that the separator which he used, the point, should be that which has been ultimately adopted, and after a long period of partial disuse.

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  • The office, Mark Napier states, is repeatedly mentioned in the family charters as appertaining to the "pultre landis" near the village of Dene in the shire of Linlithgow.

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  • The pultrelands and the office were sold by John Napier in 1610 for 1700 marks.

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  • With regard to the spelling of the name, Mark Napier states that among the family papers there exist a great many documents signed by John Napier.

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  • His own children, who sign deeds along with him, use every mode except Napier, the form now adopted by the family, and which is comparatively modern.

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  • The form "Neper" is the oldest, as John, third Napier of Merchiston, so spelt it in the 15th century.

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  • Napier frequently signed his name "Jhone Neper, Fear of Merchiston."

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  • The bibliography of Napier's workattached to W.

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  • Napier's three mathematical works are reprinted by N.

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  • Sir William Francis Patrick Napier >>

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  • At the same time, if the Basuto were eager for cattle, the Boers were eager for land; and their encroachments on the territories of the Basuto led to a proclamation in 1842 from Sir George Napier, the then governor of Cape Colony, forbidding further encroachments on Basutoland.

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  • In 1849, however, Moshesh was unwillingly induced by Sir Harry to surrender his claims to part of the territory recognized as his by the Napier treaty.

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  • Lord Napier b.

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  • The passage of the Bidassoa "was a general's not a soldiers' battle" (Napier).

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  • Napier, History of War in the Peninsula and South of France (London, 1828-1840); C. W.

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  • The regent Moray, the marquess of Montrose, and Napier of Merchiston were buried within its walls and are commemorated by monuments, and among the memorial tablets is one to R.

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  • Merchiston Academy, housed in the old castle of Napier, the inventor of logarithms, is another institution conducted on English public school lines.

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  • This had been followed by an intimation from the governor of the Cape (MajorGeneral Sir George Napier) inviting the emigrants to return to the colony, and stating that whenever he thought it desirable he should take military possession of the port.

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  • They had declared themselves a free and independent state under the title of " The Republic of Port Natal and adjacent countries," 1 and sought (September 1840) from Sir George Napier at the Cape an acknowledgment of their independence by Great Britain.

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  • The Boers, however, strongly resented the contention of the British that they could not shake off British nationality though beyond the bounds of any recognized British possession, nor were they prepared to see their only port garrisoned by British troops, and they rejected Napier's overtures.

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  • Napier, therefore, on the 2nd of December 1841, issued a proclamation in which he stated that in consequence of the emigrant farmers refusing to be treated as British subjects and of their attitude towards the Kaffir tribes he intended resuming military occupation of Port Natal.

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  • In April 1842 Lord Stanley (afterwards 14th earl of Derby), then secretary for the colonies in the second Peel Administration, wrote to Sir George Napier that the establishment of a colony in Natal would be attended with little prospect of advantage, but at the same time stated that the pretensions of the emigrants to be regarded as an independent community could not be admitted.

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  • Passing over the invention of logarithms by John Napier, and their development by Henry Briggs and others, the next author of moment was an Englishman, Thomas Harriot, whose algebra (Artis analyticae praxis) was published posthumously by Walter Warner in 1631.

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  • Among the English histories of Florence, Napier's Florentine History (6 vols., London,1846-1847) and A.Trollope's History of the Commonwealth of Florence (4 vols., London, 1865) are not without value although out of date.

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  • A few years later he rendered similar conspicuous services in the course of the Sind campaign, when his help was utilized by Napier in the process of subduing the frontier tribes, a large number of whom acknowledged the Aga's authority as their spiritual head.

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  • The first editor was Sydney Smith, then Jeffrey for many years, and later editors were Macvey Napier, William Empson, Sir G.

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  • Elsner, and, in the presence of other metals, by Napier and others.

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  • Sir Charles Napier >>

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  • Under this method might be classed the expositions of Luther, Osiander, Striegel, Flacius, Gerhard and Calovius; and English writers such as Napier, Mede and Newton.

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  • - Napier Brothers' capstan.

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  • His aim was as definite as that of Thucydides, or Schiller, or Napier or any other writer who has made his subject a particular war; only he determined to treat it in a certain way.

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  • Many of the white farmers in this district, unlike their fellows dwelling farther north, were willing to accept British rule, and this fact induced Mr Justice Menzies, one of the judges of Cape Colony then on circuit at Colesberg, to cross the Orange and proclaim (October 1842) the country British territory, a proclamation disallowed by the governor, Sir George Napier, who, nevertheless, maintained that the emigrant farmers were still British subjects.

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  • The period of Jeffrey's editorship extended to about twenty-six years, ceasing with the ninetyeighth number, published in June 1829, when he resigned in favour of Macvey Napier.

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  • X yos, word, ratio, and &pc0,u6s, number), in mathematics, a word invented by John Napier to denote a particular class of function discovered by him, and which may be defined as follows: if a, x, m are any three quantities satisfying the equation a^x = m, then a is called the base, and x is said to be the logarithm of m to the base a.

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  • The invention of logarithms has been accorded to John Napier, baron of Merchiston in Scotland, with a unanimity which is rare with regard to important scientific discoveries: in fact, with the exception 01 the tables of Justus Byrgius, which will be referred to further on, there seems to have been no other mathematician of the time whose mind had conceived the principle on which logarithms depend, and no partial anticipations of the discovery are met with in previous writers.

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  • The first announcement of the invention was made in Napier's Mirifici Logarithmorum Canonis Descriptio..

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  • Napier's logarithms are not the logarithms now termed Napierian or hyperbolic, that is to say, logarithms to the base e where e= 2.7182818 ...; the relation between N (a sine) and L its logarithm, as defined in the Canonis Descriptio, being N=10 7 e L/Ip7, so that (ignoring the factors re, the effect of which is to render sines and logarithms integral to 7 figures), the base is C".

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  • Napier's logarithms decrease as the sines increase.

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  • If 1 denotes the logarithm to base e (that is, the so-called "Napierian " or hyperbolic logarithm) and L denotes, as above, " Napier's " logarithm, the connexion between 1 and L is expressed by L = r o 7 loge 10 7 - 10 7 / or e t = I 07e-L/Ia7 Napier's work (which will henceforth in this article be referred to as the Descriptio) immediately on its appearance in 1614 attracted the attention of perhaps the two most eminent English mathematicians then living - Edward Wright and Henry Briggs.

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  • The former translated the work into English; the latter was concerned with Napier in the change of the logarithms from those originally invented to decimal or common logarithms, and it is to him that the original calculation of the logarithmic tables now in use is mainly due.

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  • Both Napier and Wright died soon after the publication of the Descriptio, the date of Wright's death being 1615 and that of Napier 1617, but Briggs lived until 1631.

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  • He at once saw the value of logarithms as an aid to navigation, and lost no time in preparing a translation, which he submitted to Napier himself.

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  • The preface to Wright's edition consists of a translation of the preface to the Descriptio, together with the addition of the following sentences written by Napier himself: " But now some of our countreymen in this Island well affected to these studies, and the more publique good, procured a most learned Mathematician to translate the same into our vulgar English tongue, who after he had finished it, sent the Coppy of it to me, to bee seene and considered on by myselfe.

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  • Briggs accordingly visited Napier in 1615, and stayed with him a whole month.

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  • William Lilly's account of the meeting of Napier and Briggs at Merchiston is quoted in the article NA Pier.

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  • calculations he had made, and suggested to Napier the advantages) that would result from the choice of io as a base, an improvement which he had explained in his lectures at Gresham College, and on which he had written to Napier.

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  • Napier said that he had already thought of the change, and pointed out a further improvement, viz., that the characteristics of numbers greater than unity should be positive and not negative, as suggested by Briggs.

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  • Inl,1616 Briggs again visited Napier and showed him the work he had accomplished, and, he says, he would gladly have paid him a third visit in 1617 had Napier's life been spared.

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  • It was published, probably privately, in 1617, after Napier's death,' and there is no author's name, place or date.

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  • The first calculation or publication of Briggian or common logarithms of trigonometrical functions was made in 1620 by Edmund Gunter, who was Briggs's colleague as professor of 1 It was certainly published after Napier's death, as Briggs mentions his " librum posthumum."

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  • It now remains to refer in more detail to the invention itself and to examine the claims of Napier and Briggs to the capital improvement involved in the change from Napier's original logarithms to logarithms to the base ro.

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  • Napier, however, did not live to keep this promise.

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  • The proposed work was published in 1619 by Robert Napier, his second son by his second marriage, under the title Mirifici logarithmorum canonis constructio...

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  • In the preface Robert Napier says that he has been assured from undoubted authority that the new invention is much thought of by the ablest mathematicians, and that nothing would delight them more than the publication of the mode of construction of the canon.

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  • It is important to notice that in the Constructio logarithms are called artificial numbers; and Robert Napier states that the work was composed several years (aliquot annos) before Napier had invented the name logarithm.

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  • Passing now to the invention of common or decimal logarithms, that is, to the transition from the logarithms originally invented by Napier to logarithms to the base io, the first allusion to a change of system occurs in the "Admonitio " on the last page of the Descriptio (1614), the concluding paragraph of which is " Verum si huius inventi usum eruditis gratum fore intellexero, dabo fortasse brevi (Deo aspirante) rationem ac methodum aut hunc canonem emendandi, aut emendatiorem de novo condendi, ut ita plurium Logistarum diligentia,limatior tandem et accuratior, quam unius opera fieri potuit, in lucem prodeat.

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  • Briggs in the short preface to his Logarithmorum chilias (1617) states that the reason why his logarithms are different from those introduced by Napier " sperandum, ejus librum posthumum, abunde nobis propediem satisfacturum."

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  • The " liber posthumus " was the Constructio (1619), in the preface to which Robert Napier states that he has added an appendix relating to another and more excellent species of logarithms, referred to by the inventor himself in the Rabdologia, and in which the logarithm of unity is o.

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  • These extracts contain all the original statements made by Napier, Robert Napier and Briggs which have reference to the origin of decimal logarithms. It will be seen that they are all in perfect agreement.

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  • He wrote also to Napier at once; and as soon as he could he went to Edinburgh to visit him, where, as he was most hospitably received by him, he remained for a whole month.

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  • When they conversed about the change of system, Napier said that he had perceived and desired the same thing, but that he had published the tables which he had already prepared, so that they might be used until he could construct others more convenient.

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  • Rejecting therefore, those which he had prepared already, Briggs began, at Napier's advice, to consider seriously the question of the calculation of new tables.

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  • In the following summer he went to Edinburgh and showed Napier the principal portion of the logarithms which he published in 1624.

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  • It has been thought necessary to give in detail the facts relating to the conversion of the logarithms, as unfortunately Charles Hutton in his history of logarithms, which was prefixed to the early editions of his Mathematical Tables, and was also published as one of his Mathematical Tracts, has charged Napier with want of candour in not telling the world of Briggs's share in the change of system, and he expresses the suspicion that " Napier was desirous that the world should ascribe to him alone the merit of this very useful improvement of the logarithms."

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  • There seems, however, no ground whatever for supposing that Briggs meant to express anything beyond his hope that the reason for the alteration would be explained in the posthumous work; and in his own account, written seven years after Napier's death and five years after the appearance of the work itself, he shows no injured feeling whatever, but even goes out of his way to explain that he abandoned his own proposed alteration in favour of Napier's, and, rejecting the tables he had already constructed, began to consider the calculation of new ones.

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  • The facts, as stated by Napier and Briggs, are in complete accordance, and the friendship existing between them was perfect and unbroken to the last.

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  • Briggs assisted Robert Napier in the editing of the " posthumous work," the Constructio, and in the account he gives of the alteration of the logarithms in the Arithmetica of 1624 he seems to have been more anxious that justice should be done to Napier than to himself; while on the other hand Napier received Briggs most hospitably and refers to him as " amico mihi longe charissimo."

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  • His prejudice against Napier naturally produced retaliation, and Mark Napier in defending his ancestor has fallen into the opposite extreme of attempting to reduce Briggs to the level of a mere computer.

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  • It is probable, therefore, that Briggs's copy contained no reference to the change, and it is even possible that the "Admonitio " may have been added after Briggs had communicated with Napier.

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  • It may also be remarked that the date frequently assigned to Briggs's first visit to Napier is 1616, and not 1615 as stated above, the reason being that Napier was generally supposed to have died in 1618 until Mark Napier showed that the true date was 1617.

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  • When the Descriptio was published Briggs was fiftyseven years of age, and the remaining seventeen years of his life were devoted with steady enthusiasm to extend the utility of Napier's great invention.

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  • The only other mathematician besides Napier who grasped the idea on which the use of logarithm depends and applied it to the construction of a table is Justus Byrgius (Jobst Biirgi), whose work Arithmetische and geometrische Progress-Tabulen ...

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  • was published at Prague in 1620, six years after the publication of the Descriptio of Napier.

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  • As regards priority of publication, Napier has the advantage by six years, and even fully accepting Bramer's statement, there are grounds for believing that Napier's work dates from a still earlier period.

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  • The power of io, which occurs as a factor in the tables of both Napier and Byrgius, was rendered necessary by the fact that the decimal point was not yet in use.

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  • 560; de Morgan's article on " Tables " in the English Cyclopaedia; Mark Napier's Memoirs of John Napier of Merchiston (1834), p. 39 2, and Cantor's Geschichte der Mathematik, ii.

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  • the case of both tables, the connexion between N a number and L its " logarithm " is N = (e 1)L (Napier), L = (I.

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  • Napier gives logarithms to base e ', Byrgius gives antilogarithms to base (I.coo')='a.

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  • There is indirect evidence that Napier was occupied with logarithms as early as 3594, for in a letter to P. Criigerus from Kepler, dated September 9, 1624 (Frisch's Kepler, vi.

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  • This story, though obviously untrue in some respects, gives valuable information by connecting Dr Craig with Napier and Longomontanus, who was Tycho Brahe's assistant.

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  • Dr Craig was John Craig, the third son of Thomas Craig, who was one of the colleagues of Sir Archibald Napier, John Napier's father, in the office of justice-depute.

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  • Between John Craig and John Napier a friendship sprang up which may have been due to their common taste for mathematics.

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  • Now Mark Napier found in the library of the university of Edinburgh a mathematical work bearing a sentence in Latin which he translates, " To Doctor John Craig of Edinburgh, in Scotland, a most illustrious man, highly gifted with various and excellent learning, professor of medicine, and exceedingly skilled in the mathematics, Tycho Brahe bath sent this gift, and with his own hand written this at Uraniburg, 2d November 1588."

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  • was the result of many years of labour and thought, 1 undertaken with this special object, and it would seem that Napier had seen some prospect of success nearly twenty years before the publication of the Descriptio.

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  • The " new invention in Denmark " to which Anthony Wood refers as having given the hint to Napier was probably the method of calculation called prosthaphaeresis (often written in Greek letters irpooOa4aipeats), which had its origin in the solution of spherical triangles.

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  • An account has now been given of Napier's invention and its publication, the transition to decimal logarithms, the calculation of the tables by Briggs, Vlacq and Gunter, as well as of the claims of Byrgius and the method of prosthaphaeresis.

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  • to Napier's Descriptio in order to describe its reception on the continent, and to mention the other logarithmic tables which were published while Briggs was occupied with his calculations.

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  • This erroneous estimate was formed when he had seen the Descriptio but had not read it; and his opinion was very different when he became acquainted with the nature of logarithms. The dedication of his Ephemeris for 1620 consists of a letter to Napier dated the 28th of July 1619, and he there congratulates him warmly on his invention and on the benefit he has conferred upon astronomy generally and upon Kepler's own Rudolphine tables.

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  • He says that, although Napier's book had been published five years, he first saw it at Prague two years before; he was then unable to read it, but last year he had met with a little work by Benjamin Ursinus 4 containing the substance of the method, and he at once recognized the importance of what had been effected.

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  • This letter was written two years after Napier's death (of which Kepler was unaware), and in the same year as that in which the Constructio was published.

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  • In the same year (1620) Napier's Descriptio (1614) and Constructio (1619) were reprinted by Bartholomew Vincent at Lyons and issued together.5 Napier calculated no logarithms of numbers, and, as already stated, the logarithms invented by him were not to base e.

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  • In 1624 Benjamin Ursinus published at Cologne a canon of logarithms exactly similar to Napier's in the Descriptio of 1614, only much enlarged.

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  • The interval of the arguments is io", and the results are given to 8 places; in Napier's canon the interval is 1', and the number of places is 7.

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  • At the end, Napier's table is reprinted, but to two figures less.

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  • It will be seen that this title is different from that of Napier's work of 1614; many writers have, however, erroneously given it as the title of the latter.

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  • The invention of logarithms and the calculation of the earlier tables form a very striking episode in the history of exact science, and, with the exception of the Principia of Newton, there is no mathematical work published in the country which has produced such important consequences, or to which so much interest attaches as to Napier's Descriptio.

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  • For more detailed information relating to Napier, Briggs and Vlacq, and the invention of logarithms, the reader is referred to the life of Briggs in Ward's Lives of the Professors of Gresham College (London, 1740); Thomas Smith's Vitae quorundam eruditissimorum et illustrium virorum (Vita Henrici Briggii) (London, 1707); Mark Napier's Memoirs of John Napier already referred to, and the same author's Naperi libri qui supersunt (1839); Hutton's History; de Morgan's article already referred to; Delambre's Histoire de l'Astronomie moderne; the report on mathematical tables in the Report of the British Association for 1873; and the Philosophical Magazine for October and December 1872 and May 1873.

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  • It may be remarked that the date usually assigned to Briggs's first visit to Napier is 1616 and not 1615 as stated above, the reason being that Napier was generally supposed to have died in 1618; but it was shown by Mark Napier that the true date is 1617.

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  • .," which contains reprints of Napier's Descriptio of 1614, Kepler's writings on logarithms (1624-1625), &c. In 1889 a translation of Napier's Constructio of 1619 was published by Walter Rae Macdonald.

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  • Some valuable notes are added by the translator, in one of which he shows the accuracy of the method employed by Napier in his calculations, and explains the origin of a small error which occurs in Napier's table.

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  • Appended to the Catalogue is a full and careful bibliography of all Napier's writings, with mention of the public libraries, British and foreign, which possess copies of each.

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  • Also, although logarithms have been spoken of as to the base e, &c., it is to be noticed that neither Napier nor Briggs, nor any of their successors till long afterwards, had any idea of connecting logarithms with exponents.

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  • Napier's original work, the Descriptio Canonis of 1614, contained, not logarithms of numbers, but logarithms of sines, and the relations between the sines and the logarithms were explained by the motions of points in lines, in a manner not unlike that afterwards employed by Newton in the method of fluxions.

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  • An account of the processes by which Napier constructed his table was given in the Constructio Canonis of 1619.

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  • These methods apply, however, specially to Napier's own kind of logarithms, and are different from those actually used by Briggs in the construction of the tables in the Arithmetica Logarithmica, although some of the latter are the same in principle as the processes described in an appendix to the Constructio.

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  • Besides Napier and Briggs, special reference should be made to Kepler (Chilias, 1624) and Mercator (Logarithmotechnia, 1668), whose methods were arithmetical, and to Newton, Gregory, Halley and Cotes, who employed series.

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  • The first of a series of ephemerides, calculated on these principles, was published by him at Linz in 1617; and in that for 1620, dedicated to Baron Napier, he for the first time employed logarithms. This important invention was eagerly welcomed by him, and its theory formed the subject of a treatise entitled Chilias Logarithmorum, printed in 1624, but circulated in manuscript three years earlier, which largely contributed to bring the new method into general use in Germany.

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  • "The vigorous following of a beaten enemy was not a prominent characteristic of Lord Wellington's warfare," as Napier says.

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  • Some account of the latter is given by Napier Malcolm in his book Five Years in a Persian Town (London,1905), pp. 87-89 and 186.

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  • The point separating the integers from the decimal fractions seems to be the invention of Bartholomaeus Pitiscus, in whose trigonometrical tables (1612) it occurs and it was accepted by John Napier in his logarithmic papers (1614 and 1619).

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  • See Ward, Lives of the Gresham Professors, and Whewell's biography prefixed to the 9th volume of Napier's edition of Barrow's Sermons.

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  • Tyers, &c.; far above all, of course, the unique Life by James Boswell, first published in 1791, and subsequently encrusted with vast masses of Johnsoniana in the successive editions of Malone, Croker, Napier, Fitzgerald, Mowbray Morris (Globe), Birrell, Ingpen (copiously illustrated) and Dr Birkbeck Hill (the most exhaustive).

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  • Napier, The Franks Casket (Oxford, 1901); G.

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  • Napier's Historical Notices of Swinconibe and Ewelme (1858).

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  • Many of the most important improvements in the construction of ships, especially steam vessels, are due to the enterprise and skill of the Clyde shipbuilders, who, from the time of Robert Napier of Shandon (1791-1876), who built and engined the first steamers for the Cunard Company, formed in 1840, have enjoyed an unrivalled reputation for the construction of leviathan liners, both as regards mechanical appliances and the beauty and convenience of the internal arrangements.

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  • Among his officers we see the names of Napier, Ramsay, Haliburton and Polwarth.

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  • Henry's men marauded on the Border, but a force which James summoned to Fala Moor (3 rst of October 1542) contained but one lord who would march with him - Napier of Merchistoun.

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  • Lang; Miss Shield's King over the Water and Martin Haile's James Francis Stuart (the old Chevalier); Omond's Lord Advocates of Scotland; Willcock's The Great Marquess (of Argyll); Napier's Lives of Montrose and Dundee; Clarke and Foxcroft's Life of Bishop Burnet; Sir Herbert Maxwell's Robert Bruce and Book of Douglas, with all Sir W.

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  • W., being the site of a Roman settlement; Merchiston Hall, to the N.W., was the birthplace of Admiral Sir Charles Napier.

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  • In 1843 the Mahommedan rulers of Sind, known as the " meers " or amirs, whose only fault was that they would not surrender their Annexa- independence, were crushed by Sir Charles Napier.

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  • Before reinforcements could come out from England, with Sir Charles Napier as commanderin-chief, Lord Gough had restored his own reputation by the crowning victory of Gujrat, which absolutely destroyed the Sikh army.

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  • Both General Jacob and Sir Charles Napier had prophesied that the Mutiny would take place.

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  • Victoria Park, in the heart of the town, contains a monument to Admiral Napier.

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  • The appearance of the combined British, Austrian and Russian fleets, under Sir Charles Napier, off Beirut (Aug.

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  • Nine days earlier Sir Charles Napier had appeared with a British squadron off Alexandria and, partly by persuasion, partly by threats, had induced Mehemet Ali to submit to the sultan and to send back the Ottoman fleet, in return for a guarantee of the hereditary pashalik of Egypt.

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  • Till 1813 it was in the hands of Major de Bosset, a Swiss in the British service, who displayed an industry and energy in the repression of injustice and development of civilization only outdone by the despotic vigour of Sir Charles Napier, who held the same office for the nine years from 1818 to 1827.

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  • James Mill, who was intimately acquainted with him, says (in a letter to Napier of November 1818) that he knew not a better man, and on the occasion of his death published a highly eulogistic notice of him in the Morning Chronicle.

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  • From the conquest of Sind by the British troops under the command of General Sir Charles Napier in 1843 up to 1854 no diplomatic intercourse occurred worthy of note between the British and Baluch states.

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  • Pedro in Oporto from July 1832 to July 1833, when the duke of Terceira and Captain Charles Napier, who had succeeded Sartorius, effected a daring and successful diversion which resulted in the capture of Lisbon (July 24, 1833).

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  • Miguel (4 vols., Lisbon, 1841-1849); Sir C. Napier, An Account of the War ....

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  • p. ci.; Napier and Stevenson, Crawford Charters, pp. 118 -120; D.N.B., s.v.

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  • This, however, failed to influence the emperor, and the English government at length saw that they must have recourse to arms. In July 1867, therefore, it was resolved to send an army into Abyssinia to enforce the release of the captives, under Sir Robert Napier (1st Baron Napier of Magdala).

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  • Lord Ellenborough often said that a general mutiny of the native army was the only real danger with which the British empire in India was threatened, and his warning was solemnly repeated by Sir Charles Napier.

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  • There are statues of George IV., Napier, Havelock and Gordon.

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  • In 1833 Whiteside married Rosetta, daughter of William Napier, and sister of Sir Joseph Napier (1804-1882), lord chancellor of Ireland.

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  • The incident created great excitement in England, but in 1857 the British government sent Sir Francis Napier to Washington to take Crampton's place.

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  • In deciding on war the British government relied on the capacity of its fleet, which was entrusted to the command of Sir Charles Napier, to strike a great blow in the Baltic. The fleet was despatched with extraordinary rejoicings, and amidst loud and confident expressions of its certain triumph.

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  • The expedition, entrusted to Sir Robert Napier, afterwards Lord Napier of Magdaia, was fitted out at great expense, and was rewarded with complete success.

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  • Two main lines leave the town, one following the west coast, the other an inland route to Napier.

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  • Charles Napier deserves praise for creating a truly hateful villain, sneering and snarling his way through the film in a hilariously over-the-top manner.

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  • Homework Once the children come home, Dad supervises the homework, using logarithms invented by John Napier of Edinburgh.

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  • logarithms invented by John Napier of Edinburgh.

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  • Specialist music indexes - at Napier these are in print format RILM (Répertoire international de la littérature musicale) Covers mainly classical music.

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  • mutinous spirit exhibited itself in the native army, which Napier was determined to put down.

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  • While abroad young Napier escaped some perils that existed at home.

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  • He is module leader for the Teaching at University module, designed to introduce postgraduates to teaching and available to Napier postgraduate students.

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  • sellout season of the play Freak Winds with Marshall Napier and Roxane Wilson.

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  • useful to consider within Napier's Educational Research Network.

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  • In the criminal court of Scotland, the earl of Argyll, hereditary justice-general of the kingdom, sometimes presided in person, but more frequently he delegated his functions; and it appears that in 1561 Archibald Napier was appointed one of the justice-deputes.

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  • no equal); and calling Donald into his presence commanded him, in regard to his worthy service, and in augmentation of his honour, to change his name from Lennox to Napier, and gave him the lands of Gosford, and lands in Fife, and made him his own servant, which discourse is confirmed by evidences of mine, wherein we are called Lennox alias Napier."

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  • In the preface to the appendix containing the local arithmetic he states that, while devoting all his leisure to the invention of these abbreviations of calculation, and to examining by what methods the toil of calculation might be removed, in addition to the logarithms, rabdologia and promptuary, he had hit upon a certain tabular arithmetic, whereby the more troublesome operations of common arithmetic are performed on an abacus or chess-board, and which may be regarded as an amusement A facsimile of this document is given by Mark Napier in his Memoirs of John Napier (1834), p. 248.

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  • Il mourut l'an 1616, et fut enterre hors la Porte Occidentale d'Edinbourg, dans l'Eglise de Sainct Cudbert.'" There can be no doubt that Napier's devotion to mathematics was not due to old age and the gout, and that he died in 1617 and not in 1616; still these sentences were written within eighteen years of Napier's death, and their author seems to have had some special sources of information.

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  • The logarithms introduced by Napier in the Descriptio are not the same as those now in common use, nor even the same as those now called Napierian or hyperbolic logarithms. The change from the original logarithms to common or decimal logarithms was made by both Napier and Briggs, and the first tables of decimal logarithms were calculated by Briggs, who published a small table, extending to 1000, in 1617, and a large work, Arithmetica Logarithmica, 1 containing logarithms of numbers to 30,000 and from 90,000 to Ioo,000, in 1624.

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  • (See Logarithm.) Napier's Descriptio of 1614 contains no explanation of the manner in which he had calculated his table.

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  • Napier deliberately set himself to abbreviate multiplications and divisions - operations of so fundamental a character that it might well have been thought that they were in rerum natura incapable of abbreviation; and he succeeded in devising, by the help of arithmetic and geometry alone, the one 1 The title runs as follows: Arithmetica Logarithmica, sive Logarithmorum chiliades triginta....

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  • In that article it is mentioned that a Scotsman in 1594 in a letter to Tycho Brahe held out some hope of logarithms; it is likely that the person referred to is John Craig, son of Thomas Craig, who has been mentioned as one of the colleagues of John Napier's father as justice-depute.

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  • Considering the time in which he lived, Napier is singularly free from superstition: his Plaine Discovery relates to a method of interpretation which belongs to a later age; he shows no trace of the extravagances which occur everywhere in the works of Kepler; and none of his writings contain allusions to astrology or magic.

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  • They were given to Francis, the fifth Lord Napier, by William Napier of Culcreugh, Esq., heir-male of the above-named Robert.

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  • These treatises were probably composed before Napier had invented the logarithms or any of the apparatuses described in the Rabdologia; for they contain no allusion to the principle of logarithms, even where we should expect to find such a reference, and the one solitary sentence where the Rabdologia is mentioned ("sive omnium facillime per ossa Rhabdologiae nostrae") was probably added afterwards.

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  • It -is worth while to notice that this reference occurs in a chapter "De Multiplicationis et Partitionis compendiis miscellaneis," which, supposing the treatise to have been written in Napier's younger days, may have been his earliest production on a subject over which his subsequent labours were to exert so enormous an influence.

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  • Apart from the interest attaching to these manuscripts as the work of Napier, they possess an independent value as affording evidence of the exact state of his algebraical knowledge at the time when logarithms were invented.

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  • In multiplications or divisions of any length it is generally convenient to begin by forming a table of the first nine multiples of the multiplicand or divisor, and Napier's bones at best merely provide such a table, and in an incomplete form, for the additions of the two figures in the same parallelogram have to be performed each time the rods are used.

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  • Nothing shows more clearly the rude state of arithmetical knowledge at the beginning of the 17th century than the universal satisfaction with which Napier's invention was welcomed by all classes and regarded as a real aid to calculation.

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  • Napier also describes in the Rabdologia two other larger rods to facilitate the extraction of square and cube FIG.

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  • Besides the logarithms and the calculating rods or bones, Napier's name is attached to certain rules and formulae in spherical trigonometry.

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  • "Napier's rules of circular parts," which include the complete system of formulae for the solution of right-angled triangles, may be enunciated as follows.

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  • "Napier's analogies" are the four formulae - tan (A +B) cos = cos l(a - b) cotzC, tan2(A - B) - sin(a - b)cot2C; a (a+b) sine (a+b) tan a(a +b) = cos(A - B) tan1c, tan2(a - b) = s in(A - B) tan2c.

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  • The work left by Napier is, however, rough and unfinished, and it is uncertain whether he knew of the other formulae or not.

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  • To Napier seems to be due the first use of the decimal point in arithmetic. Decimal fractions were first introduced by Stevinus in his tract La Disme, published in 1585, but he used cumbrous exponents (numbers enclosed in circles) to distinguish the different denominations, primes, seconds, thirds, &c. Thus, for example, he would have written 123.456 as 123@4050603.

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  • In the Rabdologia Napier gives an "Admonitio pro Decimali Arithmetica," in which he commends the fractions of Stevinus and gives an example of their use, the division of 861094 by 43 2.

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  • The hereditary office of king's poulterer (Pultrie Regis) was for many generations in the family of Merchiston, and descended to John Napier.

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  • He has been sometimes erroneously called "Peer of Merchiston," and in the 1645 edition of the Flamm Discovery he is so styled (see Mark Napier's Memoirs, pp. 9 and 173, and Libri qui supersunt, p. xciv.).

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  • The principal authorities for Montrose's career are Wishart's Res gestae, eec. (Amsterdam, 5647); Patrick Gordon's Short Abridgment of Britane's Distemper (Spalding Club); and the comprehensive work of Napier, Memorials of Montrose, is abundantly documented, containing Montrose's poetry, in which is included his celebrated lyric "My dear and only love."

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  • Finally, in deference to the strongly urged views of Sir George Napier, Lord Stanley, in a despatch of the 13th of December, received in Cape Town on the 23rd of April 1843, consented to Natal becoming a British colony.

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  • Napier held his Moslem ally in great esteem, and entertained a very high opinion of his political acumen and chivalry as a leader and soldier.

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  • See also the Selected Correspondence of Macvey Napier (1877); the sketch of Jeffrey in Carlyle's Reminiscences, vol.

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  • The work is a small quarto containing fifty-seven pages of explanatory matter and a table of ninety pages (see Napier, John).

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  • In an " Adm onitio " on the seventh page Napier states that, although in that place the mode of construction should be explained, he proceeds at once to the use of the logarithms, " ut praelibatis prius usu, et rei utilitate, caetera aut magis placeant posthac edenda, aut minus saltem displiceant silentio sepulta."

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  • We may infer therefore that as early as 1594 Napier had communicated to some one, probably John Craig, his hope of being able to effect a simplification in the processes of arithmetic. Everything tends to show that the invention of logarithms 2 See Mark Napier's Memoirs of John Napier of Merchiston (1834), p. 362.

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  • In Scotland the secret of the Cumbernauld band came out; Montrose, Napier and other friends were imprisoned on the strength of certain ambiguous messages to Charles, and on the 27th of July, being called before parliament, Montrose said - " My resolution is to carry with me honour and fidelity to the grave."

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  • Napier 's subsequent career was no less distinguished, but punctuated by spells of retirement on half-pay.

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  • Damian has also appeared in two sellout season of the play Freak Winds with Marshall Napier and Roxane Wilson.

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  • There were several ideas here that may be useful to consider within Napier 's Educational Research Network.

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  • Number 32: the Hoyland and Napier families now share this home.

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  • After a shoot-out at a chemical plant between the police and a band of thugs working for a local organized crime ring, Jack Napier, having fallen into a vat of chemicals, is transformed into the Joker.

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