LOGAR 
'though, by reafon of his natural refervednefs, he never 
published any thing to the world. But, whatever might 
have been in this, it is certain that the world is indebted 
for logarithms to baron Napier, who died in the year 
1618. This nobleman likevvife made confiderable im¬ 
provements in trigonometry; and the frequent numerical 
■computations he had occafion for in this branch, un¬ 
doubtedly contributed to his invention of the logarithms, 
that he might fave part of the trouble in thefe calcula¬ 
tions. His book, publiihed in ifirq, was intitled Mirijici 
Logarithmorum Canonis Defcriptio. At this time he did not 
publifli his method of conltrufting the numbers until the 
fenfe of the learned Hiould be known. In other refpefts 
the work is complete, containing all the logarithms of 
the natural numbers to the ufual extent of logarithmic 
tables; with the logarithmic fines, tangents, and fecants, 
for every minute'of the quadrant, directions for uiing the 
tables, &c. 
This work was publiihed in Latin; but was-afterwards 
tranllated into Englilh-by Mr. Edward Wright, inventor 
of the principles of what has been falfely called Merca¬ 
tor’s Sailing. The tranflation was fent to his lordlhip at 
Edinburgh, and returned with his approbation and fome 
few additions. It was publiihed in 1616, after Mr. Wright’s 
death, with a dedication to the Ealt-India Company, by his 
Ion Samuel Wright, and a preface by Mr. Briggs, who 
afterwards diftinguilhed himfelf fo much in bringing lo¬ 
garithms to perfection. In this tranflation, Mr. Briggs 
alio gave the delbription and draught of a fcale invented 
by Mr. Wright, as well as other methods invented by 
himfelf, for finding the intermediate proportional num¬ 
bers ; the logarithms already found having been only 
printed for fuch numbers as were the natural fines of each 
minute. Mr. Wright’s.tranflation was reprinted in 1618, 
with a new title-page, and the addition of 16 pages of new 
matter, “fiiowing the method of calculating triangles, as 
well as a method of finding out fuch lines and logarithms 
as are not to be found in the canons.” 
Next year John Speidftl publiihed his New Logarithms, 
in which were lome remedies for the inconveniences at¬ 
tending lord Napier’s method. The fame year alfo Ro¬ 
bert Napier, the baron’s fon, publiihed a new edition of 
his father’s book, entitled Canonis Logarithmorum Defcriptio ; 
with another concerning the method of conltrufting them, 
which the baron had promifed; together with fome other 
smifcellaneous pieces, which his lather had likewife com- 
poled along with Mr. Briggs. In 1620, alfo a copy of 
thefe works was printed at Lyons in one volume, by Bar¬ 
tholomew Vincent, a bockfeller there; but this publica¬ 
tion feem.s to 'nave been but little known, as Wingate, who 
carried ibgarithms to France four years after, is laid to 
have been the firlt who introduced them into that country. 
The kind of logarithms now in ufe were invented by 
Mr. Henry Briggs, profefior of geometry in Grefham col¬ 
lege, London, at the time they were firlt difcovered by 
Napier. As loon as the logarithms of Napier were pub- 
lilhed, Mr. Briggs direfted his attention to the ftudy and 
improvement of them; and his employment in this way 
■was announced in a letter to Mr. Ulher, afterwards the ce¬ 
lebrated archbilhop, in the year 1615. By him the fcale 
was changed, and o was made the logarithm of 1; but 
lord Napier informed Mr. Briggs that he had already 
thought of fuch a feheme, but chofe rather to publifli 
the logarithmic tables he had completed, and to let thofe 
alone until he Ihould have more leifure, as well as better 
health. At- an interview betwixt lord Napier and Mr. 
Briggs, the prefent plan feems to have been fettled ; and, 
in confequence of his lordlhip’s advice, Mr. Briggs made 
fome alteration in the method of conltrufting his tables 
from that which he had begun. A covrelpondence alfo 
took place betwixt his lordlhip and-Mr. Briggs, which 
continued during the lifetime of the former. It appears, 
however, that, whether Mr. Briggs thought of this alte¬ 
ration before lord Napier or nor, he certainly was the per¬ 
son who firlt publiflied it bo the world; and home refleo 
Vol.XII. No. 879. 
1 T H M S. 835 
tions have been thrown upon his lordlhip for not making 
any mention of the fliare which Mr. Briggs had in it. 
In 1617 Mr. Briggs publiihed his firlt thouland loga¬ 
rithms under the title of Logarithmorum Chilias Prima ; and 
in 1620 Mr. Edward Gunter publiihed lib canon of Tri¬ 
angles, containing the artificial or logarithmic fines and 
tangents for every minute, to feven places of figures be- 
fides the index; the logarithm of the radius being 10,000, 
•&c. Thefe were the firlt tables of logarithmic fines, tan¬ 
gents, See. which made their appearance upon the prefent 
plan; and in 1623 they were reprinted in his book de 
SeElore et Radio , along with the Chilias Prima of Mr. Briggs. 
The latne year Mr. Gunter applied thefe logarithms of 
numbers, fines, and tangents, to ftraight lines drawn 011 
a ruler; and with thele the proportions in common num¬ 
bers, as well as in trigonometry, were folved by the mere 
application of a pair or compaffes; a method founded upon 
■this property, that the logarithms of the terms of equal 
ratios are equally different. The inftrum.ent is now well 
known by the name of the two-feet Gunter’s fcale. By 
the fame methods he alfo greatly improved the feftor. He 
was alfo the firlt who uled the word cojine for the fine of 
the complement of an arc; and he introduced the ufe of 
•arithmetical complements into the logarithmical arithme¬ 
tic. He is faid alfo to have firlt luggelted the idea of the 
logarithmic curve, lo called becaule the fegments of its axis 
are the logarithms of the correlponding ordinates. 
The logarithmic lines were afterwards drawn in many 
other ways. Wingate, in 1627, drew them upon two 
fe pa rate rulers Hiding by each other, in order to fave 
the ufe of compaifes in refolving proportions. In 1627, 
alfo, they were applied by Mr. Oughtred to concentric 
circles; about 1650, in a fpiral form, by one Mr, Mil- 
burne of Yorklhire; and in 1657, they were applied o» 
the prefent Hiding-rule by Mr. Seth Partridge. 
The knowledge of logarithms was dift'uied in France 
by Mr. Edmund Wingate, as already related, though not 
carried originally thither by him. Two fmall trafts were 
publiflied by him in French, and afterwards an edition in 
Englifli, all printed in London. In the firlt of thefe he 
mentions the ufe of Gunter’s ruler; and in the other that 
of Briggs’s logarithms, with the canon of artificial lineS 
and tangents. There are likewife tables of thele fines, 
tangents, and logarithms, copied from Counter. 
From the time that Mr. Briggs firlt began to ftudy the 
nature of logarithms, he applied to the conftruftion of 
tables with fuch affiduity, that by the year 1624 he pub¬ 
liihed his Arithmetica Logarithmica, containing the loga¬ 
rithms of 30,000 natural numbers to fourteen places of 
figures befides the index ; viz. from 1 to 20,000, and from 
90,000 to ioo,ooo, together with the differences of the lo¬ 
garithms. According to fome, there was another chiliad, 
viz. from 100,000 to 101,000; but this does not feein to 
be well authenticated. In the preface to this work, lie- 
gives an account of the alteration made in the fcale by- 
lord Napier and himfelf; and earneftly folicits other pc-r- 
fons to undertake the talk of filling up the intermediate 
numbers; offering to give inftruftions, and to afford pa-? 
per ready ruled for the purpofe. He gives alfo inftruc- 
tions at large in the preface for the conftruftion of loga¬ 
rithmic tables'. Thus he hoped to get the logaritlmisof 
the other 70,000 natural numbers completed ; while he 
himfelf, being now pretty far advanced in years, might be¬ 
at liberty to apply to the canon of logarithmic lines. Sec. 
which was as much wanted by mathematicians as the- 
others. His willies were accomplilhed by Adrian Vlacq, 
or Flack, of Gouda in Holland, who completed the num¬ 
bers from 20 to 90,000 ; and thus the world was furuilhed. 
with the logarithms of all natural numbers from 1 to. 
100,000; but thofe of Vlacq were only done to ten places 
of figures. To thefe was added a table of artificial lines, 
tangents, and fecants, to every minute of the quadrant. Be¬ 
fides the great work already mentioned, Mr. Briggs com¬ 
pleted a table of logarithmic fines and tangents for the 100th 
part of every degree,to fourteen places oi figures befides the, 
4 index; 
