How to use Briggs in a sentence
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.
There is a short " preface to the reader " by Briggs, and a description of a triangular diagram invented by Wright for finding the proportional parts.
Henry Briggs, then professor of geometry at Gresham College, London, and afterwards Savilian professor of geometry at Oxford, welcomed the Descriptio with enthusiasm.
Briggs accordingly visited Napier in 1615, and stayed with him a whole month.
William Lilly's account of the meeting of Napier and Briggs at Merchiston is quoted in the article NA Pier.Advertisement
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.
The date of publication is, however, fixed as 1617 by a letter from Sir Henry Bourchier to Usher, dated December 6, 1617, containing the passage- " Our kind friend, Mr Briggs, hath lately published a supplement to the most excellent tables of logarithms, which I presume he has sent to you."
The Canonis Descriptio on its publication in 1614, at once attracted the attention of Edward Wright, whose name is known in connexion with improvements in navigation, and Henry Briggs, then professor of geometry at Gresham College, London.
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."
The different editions of the Descriptio and Constructio, as well as the reception of logarithms on the continent of Europe, and especially by Kepler, whose admiration of the invention almost equalled that of Briggs, belong to the history of logarithms (q.v.).Advertisement
There is nothing to show whether the transcripts were sent to Briggs as intended and returned by him, or whether they were not sent to him.
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.
Briggs also used decimals, but in a form not quite so convenient as Napier.
The vertical line was printed by Oughtred and some of Briggs's successors.
Charles Augustus Briggs, tried for heresy for his inaugural address in 1891 as professor of biblical theology at Union Seminary, was acquitted by the presbytery of New York, but was declared guilty and was suspended from its ministry by the General Assembly of 1893.Advertisement
Dr Briggs remained a member of the Union Seminary faculty but left the Presbyterian Church to enter the Protestant Episcopal.
Briggs, The Messiah of the Apostles, p. 284 seq.; Sabatier, Les Origines litteraires et la composition de l'Apocalypse de St Jean (1887); Spitta, Die Offenbarung des Johannes untersucht (1889).
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.
In 1895 Briggs (Messiah of the Apostles, 1895) developed this theory to a still more extreme degree.
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.Advertisement
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.
Briggs's Logarithmorum chilias prima, which contains the first published table of decimal or common logarithms, is only a small octavo tract of sixteen pages, and gives the logarithms of numbers from unity to 1000 to 14 places of decimals.
Briggs's tract of 1617 is extremely rare, and has generally been ignored or incorrectly described.
Briggs continued to labour assiduously at the calculation of logarithms, and in 1624 published his Arithmetica logarithmica, a folio work containing the logarithms of the numbers from to 20,000, and from 00,000 to ioo,000 (and in some copies to roi,000) to 14 places of decimals.
He designates it, however, only a second edition of Briggs's Arithmetica logarithmica, the title running Arithmetica logarithmica sive Logarithmorum Chiliades centum,.Advertisement
The original calculation of the logarithms of numbers from unity to ror,000 was thus performed by Briggs and Vlacq between 1615 and 1628.
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."
During the last years of his life Briggs devoted himself to the calculation of logarithmic sines, &c. and at the time of his death in 1631 he had all but completed a logarithmic canon to every hundredth of a degree.
Briggs appreciated clearly the advantages of a centesimal division of the quadrant, and by dividing the degree into hundredth parts instead of into minutes, made a step towards a reformation in this respect, and but for the appearance of Vlacq's work the decimal division of the degree might have become recognized.
The calculation of the logarithms not only of numbers but also of the trigonometrical functions is therefore due to Briggs and Vlacq; and the results contained in their four fundamental works - A rithmetica logarithmica (Briggs), 1624; Arithmetica logarithmica (Vlacq), 1628; Trigonometria Britannica (Briggs), 1633; Trigonometria artificialis (Vlacq), 1633 - have not been superseded by any subsequent calculations.Advertisement
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.
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."
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.
Briggs pointed out in his lectures at Gresham College that it would be more convenient that o should stand for the logarithm of the whole sine as in the Descriptio, but that the logarithm of the tenth part of the whole sine should be Io,000,000,000.
Briggs could not but admit was by far the most convenient of all.Advertisement
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.
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."
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.
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.
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."Advertisement
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.
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.
As special attention has not been drawn to the fact that some copies have the " Admonitio " and some have not, different writers have assumed that Briggs did or did not know of the promise contained in the " Admonitio " according as it was present or absent in the copies they had themselves referred to, and this has given rise to some confusion.
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.
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.Advertisement
Which draught, with some alterations, he printing in 1614, it came forthwith into the hands of our author Briggs, and into those of Will.
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.
John Kepler, who has been already quoted in connexion with Craig's visit to Tycho Brahe, received the invention of logarithms almost as enthusiastically as Briggs.
In the following year, 1626, Denis Henrion published at Paris a Traicte des Logarithmes, containing Briggs's logarithms of numbers up to 20,001 to io places, and Gunter's log sines and tangents to 7 places for every minute.
In the same year de Decker also published at Gouda a work entitled Nieuwe Telkonst, inhoudende de Logarithmi voor de Ghetallen beginnende van r tot io,000, which contained logarithms of numbers up to io,000 to io places, taken from Briggs's Arithmetica of 1624, and Gunter's log sines and tangents to 7 places for every minute.'Advertisement
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.
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.
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.
If we consider only the logarithms of numbers, the main line of descent from the original calculation of Briggs and Vlacq is Roe, John Newton, Sherwin, Gardiner; there are then two branches, viz.
Babbage compared his table with the Tables du Cadastre, and Lefort has given in his paper just referred to most important lists of errors in Vlacq's and Briggs's logarithms of numbers which were obtained by comparing the manuscript tables with those contained in the Arithmetica logarithmica of 1624 and of 1628.
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.
The processes used by Briggs are explained by him in the preface to the Arithmetica Logarithmica (1624).
He then by means of a simple proportion deduced that log (I 00000 00000 00000 I)=o 00000 00000 00000 0 434 2 944 81 90325 1804, so that, a quantity 1.00000 00000 00000 x (where x consists of not more than seventeen figures) having been obtained by repeated extraction of the square root of a given number, the logarithm of I 00000 00000 00000 x could then be found by multiplying x by 00000 00000 00000 04342 To find the logarithm of 2, Briggs raised it to the tenth power, viz.
Briggs calculated in a similar manner log 6, and thence deduced log 3.
Briggs also gave methods of forming the mean proportionals or square roots by differences; and the general method of constructing logarithmic tables by means of differences is due to him.
The earlier methods proposed were, like those of Briggs, purely arithmetical, and for a long time logarithms were regarded from the point of view indicated by their name, that is to say, as depending on the theory of compounded ratios.
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.
Although the method is usually known by the names of Weddle and Hearn, it is really, in its essential features, due to Briggs, who gave in the Arithmetica logarithmica of 1624 a table of the logarithms of I + i r n up to r =9 to 15 places of decimals.
Several additions were made by Briggs to the original work of Ferishta, but he omitted the whole of the twelfth book, and various other passages which had been omitted in the copy from which he translated.
The general assembly, to which the case was appealed, suspended Dr Briggs in 1893, being influenced, it would seem, in part, by the manner and tone of his expressions - by what his own colleagues in the Union Theological Seminary called the " dogmatic and irritating " nature of his inaugural address.
Briggs 1 points out that the term "Hallelujah" (Praise ye Yah) is found at the close of Pss.
They are also selling a second-hand gasoline blower - 4 HP (made by Briggs & Stratton) for £ 250.
Nicholas Briggs ' music works well, blending into the story well without once becoming intrusive on the action of the story itself.
However, Mr Sharp is unsympathetic, blaming the Briggs children for his son contracting German measles.
I gave Mr Briggs a cross stitch picture I'd done for him to say thanks for everything he's done.
In it is the helmet of Major Robert Philipson, who rode into the church during service in search of one of Cromwell's officers, Colonel Briggs, to do vengeance on him.
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.
Charles Augustus Briggs, tried for heresy for his inaugural address in 1891 as professor of biblical theology at Union Seminary (in which he attacked the inerrancy of the Bible, held the composite character of the Hexateuch and of the Book of Isaiah and taught that sanctification is not complete at death), was acquitted by the presbytery of New York, but was declared guilty and was suspended from its ministry by the General Assembly of 1893.
He introduced the words cosine and cotangent, and he suggested to Henry Briggs, his friend and colleague, the use of the arithmetical complement (see Brigg's Arithmetica Logarithmica, cap. xv.).
I gave Mr Briggs a cross stitch picture I 'd done for him to say thanks for everything he 's done.
Elsie Briggs, a university lecturer, owned this 15th century house from 1958 until her death in 1988.
Sonya Blade's direct superior, Major Jackson Briggs (known simply as "Jax" to most) is a Special Forces officer and the first African American combatant to appear in the series.
Castle Rock's Greg Popovich and August "Joe" Briggs have a keen business sense and more importantly, a sharper nose and palate sense.
Tami Briggs' album My Piece I Give You is full of instrumental, Christian songs played on the harp.
Christian yoga instructors say this album is great for a yoga session and that Briggs' harp playing is heavenly.
A fairy demon, similar to the Nix, is featured in the Patricia Briggs Mercy Thompson series.
Patricia Briggs is a full-time author who lives with her husband and animals in the Pacific Northwest.
This LoveToKnow Science Fiction interview is the product of a long conversation with Patricia Briggs about her writing, her werewolves and her upcoming works.
Mercedes Thompson is the main character in Patricia Briggs' series beginning with the novel Moon Called.
A New York Times bestseller, Patricia Briggs breathes life into the wonderful and intricate world of werewolves in America, the coyote who lives among them and the wild and somewhat hairy adventures that Mercy gets herself into.
Love To Know Science Fiction would like to thank Ms. Briggs for her time and to wish her continued success in her writing career.
You can find a complete booklist of Patricia Briggs current and upcoming novels on her website.
Authors like Patricia Briggs, Kelley Armstrong and Kevin Anderson rely on their imaginations to create fantasy characters that others can enjoy.
Another series that incorporates dark fairies are Patricia Briggs Mercedes Thompson novels.
Urban fantasy continues to thrive under the competent hands of novelists like Jim Butcher, Patricia Briggs, Kim Harrison, Jaye Wells and Kelley Armstrong.