B £ R 
BER'NO, abbotof Riclienou, in the diocefe of Con- 
ffnnce, who flourilhed abontthe year 1008, is celebrated 
as a poet, mufician, pliilofopher, and divine. He was the 
author of feveral treatifes'on mafic, particularly De Iniiru- 
mentis Mnficalibtis, which he dedicated to-Arrabon arch- 
■bifliop of Mentz. He alfo wrote De Menfura Mono- 
cliordi. But the mod celebrated of his works is a treatifc 
De Mufica feu Tonis. This trail is part of the Baliol 
-manufcript, and follows the Enchiridion of Odo : it con¬ 
tains a luminary of the doctrines delivered by Boetius, an 
explanation of the ecclelialtical tones, intermixed with fre¬ 
quent exhortations to piety, and the application of rnufic 
to religious purp'ofes. He was highly favoured by the 
emperor Henry II. for his great learning and piety ; and 
died in 104S. 
BERNON', a town of France, in the department of the 
Aube, and chief place of a canton, in the diftriel of Kr- 
vy : four miles fomh-eaft of Ervy. 
BERNOUL'L.I (James), a celebrated mathematician, 
born at Bali 1 , Dec. 27, 1654. Having taken his degrees 
in that univcrfity, he applied himfelf to divinity at the 
delire of his father, but againft his own inclination, which 
led him to allronomy and mathematics. He gave very 
early proofs of his genius for thefe fciences, and foon-be¬ 
came a geometrician, without a preceptor, and almoft 
without books; for, if one by chance fell into his hands, 
he was obliged to conceal it to avoid the difplcafure of his 
father, u ho deligned him for other (Indies. This fituation 
induced him to choofe for his device, Phaeton driving the 
chariot,of the fun, with thefe words, Invito patre Jidera 
verfo, “ I traverfe the liars againll my father’s will al¬ 
luding particularly to allronomy, to which he then chiefly 
applied himfelf. In 1676 he began his travels. When 
he was at Geneva, he fell upon a method to teach a young 
girl to write who had been blind from two month? old. 
At Bourdeaux he contpofed univerfal gnomonie tables ; 
but they were never publifhed. He returned from France 
to his own country in 16S0. About this time there ap¬ 
peared a comet, the return of which he foretold ; and 
wrote a fmall trendTe upon it. Soon after this he went 
into Holland, where he applied himfelf to the (duly of the 
new philofophy. Having vilired Flanders and Brabant, 
he palfed over to England ; where he formed an acquain¬ 
tance with the moll eminent men in the fciences, and at¬ 
tended their philofophical meetings. He returned to. his 
native country in 1682 ; and exhibited at Bafil a courfe of 
experiments in natural philofophy and mechanics, which 
confllled of a variety of new difeoveries. The fame year 
he publifhed his Elfayon hew Syflem of Comets; and the 
year following, his Dilfertation on the Weight of the Air. 
About this time Leibnitz having publifhed, in the AiSta 
Eruditorum at Leipfic, fome ellays on his new Calculus 
Dijfercntialis ; but, concealing the art and method of it, 
Mr. Bernoulli and his brother John difeovered, by tlie 
little which they law, the beauty and extent of it: this in¬ 
duced them to endeavour to unravel the fecret; which 
they did with fuch fuccefs, that Leibnitz declared that 
the invention" belonged to them as much as to -himfelf. In 
1687 James Bernoulli fucceeded to the profelforlhip of 
mathematics at Bafil 4 a trull which lie difeharged- with 
great applaufe. In 1699 lie was admitted a foreign mem¬ 
ber of tlie academy of fciences of Paris ; and in 1701 tlie 
fame honour was conferred upon him by tlie academy of 
Berlin : in both of which lie publifhed feveral ingenious 
compolitions, about tlie years 1702, 3, and 4. He wrote 
alfo feveral pieces in the Acla Eruditorum of Leiplic, and 
in tlie Journal des Scavans. His intenfe application to 
fhidy brought upon him tlie gout, and by degrees a (low 
fever, which put a period to his life the 16th of Align ft 
1705, in tlie 51ft year of his age. Archimedes, having 
found out the proportion of a fpliere and its circumfcrib- 
ing cylinder, ordered them to be engraven on his monu¬ 
ment : in imitation of him, Bernoulli appointed that a lo¬ 
garithmic fpiral curve Ihould be inferibed on his tomb, 
with thefe words, Eadcm mulata rejurgo ; in allufion to tlie 
Vol. II. No. in. 
B E R 917 
hopes of the refiifre<Eli6i>, which are in fome meafttre re- 
prefented by tlie properties of that curve, which lie had 
the honour of difeovering. He was eminently Iki 1 led in 
all the-branches-of-the mathematics, and contributed 
much to the promoting tlie new analylis, infinite lerics, 
&c. He carried to a great height tiie theory of tlie qua¬ 
drature of the parabola ; tlie geometry of curve lines, of 
fpirals, of cycloids and epicycloids. His works, that had 
been publilhed, w ere collected, and printed in 2 vols. 410. 
at Geneva in 1744. At tlie time of his death lie was occu¬ 
pied on a great work entitled Dc Arte Conjeclandi, which 
was publilhed in 410. in 1713. It contains'one of the bed 
and mud elegant introductions to Infinite Series, &c. 
Bernoulli (John), tlie brother of James above-men¬ 
tioned, and a celebrated mathematician, was born at Balil 
tlie 71in of Augud 1667. His father intended him for 
trade; but at the.fird his own inclination led him to 
the Belles-Lettres, which however, like his brother, lie 
left for mathematics. He was the fird, with Huygens and 
Leibnitz, who gave tlie dilution of the problem propofed 
by James Bernoulli, concerning tlie catenary, or curve 
formed by a chain fufpended by its two extremities. He 
had tlie degree of do6for of phyfic at Bafil, and two years 
afterward was named profeifor of mathematics in theuni- 
verfity of Groningen.- It was here that lie difeovered tlie 
mercurial phofphortis or luminous barometer; and where 
lie refolved the problem propofed by his brother concern¬ 
ing Ifoperimetricais. On tlie deatli of his brother James, 
tlie profeifor at Balil, the Academic Senate appointed him 
to fucceed his brother, without alfembling competitors, 
and contrary to tlie eftablifhed practice : an appointment 
which lie held during his whole life. I11 1714 vvas pub¬ 
lilhed his treatife on tlie Management of Ships ; and in 
1730, his memoir on tlie Elliptical Figure of the Planets 
gained tlie prize of tlie Academy of Sciences. The fame 
academy alio diyided tlie,.prize, for their quedion concern¬ 
ing the inclination of the planetary orbits, between him 
and his fon Daniel. John Bernoulli was a member of 
mod of tlie academies of Europe, and received as a foreign 
aiTbciate of that of Paris in 1699. After a long life (pent 
in condant dudy and improvement of all the branches of 
the mathematics, lie died full of honours the id of Janu¬ 
ary 1748, in the 8id year of his age. Of five foils which 
lie had, three purfued tlie fame fciences with himfelf. 
One of thefe died before him ; the two others, Nicholas 
and Daniel, lie lived to fee become eminent and -much re¬ 
flected. The writings of this great man were difperfed 
through the periodical memoirs of feveral academies, as 
well as in many feparate treatifes. And she whole of them 
were carefully collected and publilhed at Laufanne arid 
Geneva, 1742, in 4 vols. 410. 
Bernoulli (Daniel), a celebrated phylician and plii- 
lofopher, and fon of John Bernoulli above-mentioned, was 
born at Groningen Feb. 9, 1700. He palled fome time ir> 
Italy ; and sit twenty-four years of age he declined the ho¬ 
nour offered him of becoming prefident of an academy 
intended to have been eltabhfhed at,Genoa. He fpent i'e- 
veral years with great reputation at Peterfburgh ; and in 
1733 returned to Balil, where his father was then profei¬ 
for of mathematics ; and here he fucceliively filled tlie 
chair of phyfic, of natural and of fpeculativc philofophy, 
In his work Exercitationes Mathematicae, 1724, lie took 
the only title lie then had, viz. “Son of John Bernoulli,’’ 
and never would Tuffer any other to be added to it. 
This work vvas publilhed in Italy, while lie was on his tra¬ 
vels ; and it clalfed him in the rank of inventors - . In his 
work, Hydrodynamica, publilhed in 4to. at Argentoratum 
or Strafbourg, iji 1738, to the fame title vvas alfo added 
that of Med. Pi of. Bali!. He alfo wrote a multitude oi 
other pieces, which have been publilhed in tlie Mem. 
Acad, of Sciences at Paris, and in ihofe Of other acade¬ 
mies. He gained and divided ten prizes from tlie Acade¬ 
my of Sciences, which were contended for by the moil il- 
luftrious mathematicians in. Europe. Tile only perfon who 
had fimilar fuccefs, is Euler, his countryman, difcipl.e, 
