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.).
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.
For Mr Henrie Briggs, Professor of Geometrie at Oxforde."
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.
Briggs seems to have used the notation all his life, but in writing it, as appears from manuscripts of his, he added also a small vertical line just high enough to fix distinctly which two figures it was intended to separate: thus he might have written 63 0957379.
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.
Dr Briggs remained a member of the Union Seminary faculty but left the Presbyterian Church to enter the Protestant Episcopal.
Briggs, American Presbyterianism (New York, 1885).
Briggs, Study of Holy Scripture (1899), especially ch.
Briggs, Bishop Asbury (London, 1874); W.
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).
Briggs, "The Case of the Abbe Loisy," Expositor (London, April 1905), and C. A.
Briggs and F.
200, and Briggs on Ps.
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.
Briggs George S.
Degree (in 1630) corresponded with Henry Briggs and other mathematicians.
Briggs, whose influence has been due in part to a large and varied body of work (Biblical Study, 1883, and many articles and volumes since) and in part to his organization of united critical, international and interconfessional labour, the chief fruits of which have been the Hebrew Lexicon (based on Gesenius, and edited by F.
Briggs, General Introduction to the Study of Holy Scripture (1889); G.
Briggs Study of Holy Scripture (Edinburgh, 1899), ch.
(" Our Lord's use of the Old Testament "); Briggs, op. cit.
Among more recent works and articles should be mentioned Briggs, Messianic Prophecy; Giesebrecht, Die Berufsbegabung der alttestamentlichen Propheten; Volz, Die vorexilische Jahwe-Prophetie u.
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.
2 He brought with him some 1 Dr Thomas Smith thus describes the ardour with which Briggs studied the Descriptio: " Hunc in deliciis habuit, in sinu, in manibus, in pectore gestavit, oculisque avidissimis, et mente attentissima, iterum iterumque perlegit, ...
William Lilly's account of the meeting of Napier and Briggs at Merchiston is quoted in the article NA Pier.
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."
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.
Briggs had himself been engaged in filling up the gap, and in a lettex to John Pell, written after the publication of Vlacq's work, and dated October 25, 1628, he says: " My desire was to have those chiliades that are wantinge betwixt 20 and 90 calculated and printed, and I had done them all almost by my selfe, and by some frendes whom my rules had sufficiently informed, and by agreement the busines was conveniently parted 'amongst us; but I am eased of that charge and care by one Adrian Vlacque, an Hollander, who hathe done all the whole hundred chiliades and printed them in Latin, Dutche and Frenche, moo bookes in these 3 languages, and hathe sould them almost all.
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.
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.
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.
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."
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.
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.
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.
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.