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tent of it : this induced them to endeavour 
to unravel the secret ; which they did with 
such success, that Leibnitz declared that 
the invention belonged to them as much as 
to himself. 
In 1607, James Bernoulli succeeded to 
the professorship of mathematics at Basil ; 
a trust which he discharged with great ap- 
plause; and his reputation drew a great 
number of foreigners from all parts to at- 
tend his lectures. In 1699, he was admitted 
a foreign member of the Academy of Sci- 
ences of Paris ; and in 1701, the same 
honour was conferred upon him by the 
Academy of Berlin : in both of which he 
published several ingenious compositions, 
about the years 1702, 3, and 4. He wrote 
also several pieces in the “ Acta Erudito- 
rum” of Leipsic, and in the “ Journal des 
Scjavans.” His intense application to study 
brought upon him the gout, and by degrees 
a slow fever, which put a period to his life 
the 16th of August 1705, in the 51st year of 
his age. Archimedes having found out the 
proportion of a sphere and its circumscrib- 
ing cylinder, ordered them to be engraven on 
his monument. In imitation of him, Bernoulli 
appointed that a logarithmic spiral curve 
should be inscribed on his tomb, with these 
words, “ Eadem mutata resurgo ;” in allu- 
sion to the hopes of the resurrection, which 
are in some measure represented by the 
properties of that curve, which he had the 
honour of disco vering. 
James Bernoulli had an excellent genius 
for invention, and elegant simplicity, as well 
as a close application. He was eminently 
skilled in all the branches of the mathema- 
tics, and contributed much to the promot- 
ing the new analysis, infinite series, &c. He 
carried to a great height the theory of the 
quadrature of the parabola ; the geometry 
of curve lines, of spirals, of cycloids, and 
epicycloids. His works, that had been pub- 
lished, were collected, and printed in 2 
volumes 4to. at Geneva in 1744. 
Bernoulli (John), the brother of 
James, last mentioned, and a celebrated 
mathematician, was born at Basil the 7th 
of August, 1667. His father intended him 
for trade ; but his own inclination was at 
first for tire Belles-Lettres, which however, 
like his brother, he left for mathematics. 
He laboured with his brother to discover 
the method used by Leibnitz, in his essays 
on the differential calculus, and gave the 
first principles of tiie integral calculus. 
Our author, with Messieurs Huygens and 
VOL I. 
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Leibnitz, was the first who gave the solu- 
tion of the problem proposed by James 
Bernoulli, concerning the catenary, or 
curve formed by a chain suspended by its 
two extremities. 
John Bernoulli was a member of most of 
the academies of Europe, and received as 
a foreign associate of that of Paris in 1699. 
After a long life spent in constant study 
and improvement of all the branches of the 
mathematics, he died full of honours the 1st 
of January, 1748, in the 81st year of his 
age. Of five sons which he had, three pur- 
sued the same sciences with himself. One 
of these died before him ; the two others, 
Nicolas and Daniel, he lived to see become 
eminent and much respected in the same 
sciences. 
The writings of this great man were dis- 
persed through the periodical memoirs of 
several academies, as well as in many se- 
parate treatises. And the whole of them 
were carefully collected and published at 
Lausanne and Geneva, 1742, in 4 volumes, 
4to. 
Bernoulli (Daniel), a celebrated phy- 
sician and philosopher, and son of John Ber- 
noulli last mentioned, was born at Gronin- 
gen, February the 9th, 1700, where his fa- 
ther was then professor of mathematics. 
He was intended by his father for trade, 
but his genius led him to other pursuits. 
He passed some time in Italy; and at 24 
years of age he declined the honour offered 
him of becoming president of an academy 
intended to have been established at Genoa. 
He spent several years with great credit at 
Petersburgh ; and in 1733 returned to 
Basil, where his father was then professor 
of mathematics ; and here our author suc- 
cessively filled the chair of physic, of natural 
and of speculative philosophy. 
' Daniel Bernoulli wrote a multitude of 
pieces, which have been published in the 
Memoirs of the Academy of Sciences at 
Paris, and in those of other academies. He 
gained and divided ten prizes from the 
Academy of Sciences, Which were contended 
for by the most illustrious mathematiciaus 
in Europe. The only person who has had 
similar success m the same line, is Eider, 
liis countryman, disciple, rival, and friend. 
His first prize he gained at 24 years of age. 
In 1734 he divided one with his father ; 
which hurt the family union ; for the father 
considered the contest itself as a want of 
respect; and the son did not sufficiently 
conceal that he thought (what was really 
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