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btanty of wliich lie admired, the principles of which he de- 

 veloped, and the utility of which he difcavered, and promot- 

 ed to Aich a degree, that this great philofopher, whiltl he 

 claimed the hon-ur of the original invention, acknowledged 

 tlirit J. Dernouilli and his brother had a grcv.t fhare in the 

 advantage whicli the public derived from it, and that no 

 perfon had made a greater ufe of this invention than they, 

 and the marquis de I'Hofpital. In 1687, he was unanimoully 

 chofcn to fiicceed Peter Megerlin, as profefTor of mathema- 

 tics at Bafil, and he difeharged the duties of his office with 

 fr.ch rep itation, that he greatly contributed to the credit of 

 t'ne univerfity, and to the increafe of the number of lludents. 

 ]n 1699, he was elefted a foreign member of the academy 

 of fciences at Paris, and in I 701, of the academy of Berlin. 

 Tlie me- ' oirs of both thefe focicties were enriched by many 

 of his coinmunications. Several of his pieces were alfo pub- 

 lilTied in the Afta Eruditorum, and the Journal des Scavans. 

 The gout, brought on by unremitting application, produced 

 a fever, which terminated his life, Auguft 16, 1 705, in the 

 5 [ft year of his age.' He ordered a logarithmic fpiral to be 

 engraved on his tomb, with this motto, " Eadem miitata 

 refnrgo," I rife the fame, though changed. He was mar- 

 ried at the age of 30; and left one fon and a daughter. By 

 the exercife of extraordinary powers of invention, and per- 

 fevering application, he made many valuable difcoverics, 

 which improved the method of anah fis, the dodrine of in- 

 finite fcries, and the higher department of mathematical in- 

 veitigation ; fuch as the qindrature of the parabola, and the 

 jreometry of curve lines, of fpirals, cycloids and epicycloids. 

 His works, with their relpective titles, are enumerated in the 

 General Dictionary, to which we refer ; and they were col-' 

 lefted and p\iblifhed in 2 vols. 4to. at Geneva, in 1744. 

 The " Ars conjeftandi," or the art of forming probable 

 conjcflures concerning events that depend on chance, in 

 which he was engaged at the time of his death, and which 

 is not included in the above collettion, was printed at Balil, 

 in 1713, 4to. To this is added a treatife concerning infinite 

 feries. An extract from this valuable treatife, containing the 

 beft demonftration that has yet been given of Sir Ifaac New- 

 ton's famous binomial theorem, in the firll and fimpleft cafe 

 of it, or that of the integral and affirmative powers of the 

 binomial quantity a + i, left by its great inventor without a 

 demonftration, is included in the 3d volume of the " Scri- 

 ptores Logarithmici," for which we are indebted to baron 

 Maferes. 



Bernouilli, John, the brother of the preceding, and 

 no lefs celebrated as a mathematician, was born at Bafil, 

 July 27, 1667. At the age of 15, he commenced the ftudy 

 of philofophy, and foon after he was fent to Neufehatel to 

 learn the French language, and the principles of commerce ; 

 but preferring intellcftualpurfuits to a mercantile profeffion, 

 he returned home at the clofe of the year, for the profecu- 

 tion of his ftudies, and received the degree of doflor in phi- 

 lofophy in 1685. Inftructed by his elder brother in the firtl 

 rudiments of mathematics, he afterwards, viz. in 1684, when 

 he was only 17 years of age, concurred with him in invcf- 

 tigating and explaining the principl' -■: of Leibnitz's differen- 

 tial calculus. He alfo was one of the three mathematicians, 

 the two others being Huygens and Leibnitz, who folved the 

 problem of the catenary curve, propofed by his brother 

 James. In 1690, he fet out on his travels ; and in the pro- 

 grefs of them communicated the difcoveries of the new ana- 

 lyfis to Daniel le Clerc, and Fatio de Duillier, at Geneva, 

 and to the marquis de I'Hofpital at Paris. On his return to 

 own country, in 1692, he commenced a correfpondence 

 with Leibnitv;, which latted during the life of the latter. 

 Having declined the profefTordiip of niath?matics at 

 • Vol. IV. 



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"Wolfcnbuttle, which was offered him in 1693, he nndcr- 

 took, in 1695, ■* courfe of philofophical experiments at 

 Groningen, and was furniftied by the curators of the univer- 

 (ity with the neceilaiy apparatus. About this tim.e he dif- 

 covered, what has been called the mercurial phofphorus, oc- 

 cafioncd, as it is now known, by the fnflion of mercury 

 againft glafs, in a partial vacuum ; for which Frederic I. 

 king of Pruflia, honoured him with a gold medal, and with 

 the rank of member of the academy of fcicncts at Berlin. 

 He w;: alfo a member of the royal fociety of London, and 

 of other learned bodies. He fucceeded his brother James at 

 Bafil, in 17OJ, on which occafion he delivered a difcourfe, 

 " De Fatis Novi Analyfeos, ct GeometriE Sublimis," and 

 continued till his death in this fituation, though he was foli- 

 cited to remove to Leyden, Padua, and Groningen. He 

 collefted his works in 1743, and printed tliem at Laufanne, 

 in 4 vols. 410. His correfpondence was extenfive, and he 

 was much engaged in a controverfy with the Englifh ma- 

 thematicians concerning the invention of fluxions ; in another 

 with Renau, concerning the manoeuvring of (hips; and iit 

 another on mathematical fubjefts, with Jurin, Brook Taylor, 

 Keil, Pemberton, Herman, a: d Riccati. In 1730, he 

 gained a prize of the academy of fciences for a memoir on the 

 elliptic figure of the planets, and the motion of tl eir aphelia; 

 and in 1734, Ije received the half prize, jointly witH his 

 fon Daniel, from the fame academy, for a memoir on the 

 phyfical caufe of the inclination of the planetaiy orbits. 

 Bernouilli died January I, 1748, in the 8 1 ft year of hi* 

 age, and left four daughters and five fons, three of whom 

 were mathemattcians. Fontenelle's Eloges. Moreri. 



Bernouilli, John, fon of the preceding, was bom at 

 Bafil, January 17, 1695, ^"'^ '^'^'^ "^^ Pcteriburgh, July 26, 

 1726. He was licentiate of law, profefTor ot law at Berne; 

 afterwards profefibr of Mathematics at Pelerfburgh, and 

 member of the inftitute of Bologna. 



Bernouilli, Nicholas, nephew of the two preceding, 

 profefFor of mathematics at Padua, afterwards of logic, and 

 then of law at Bafil, member of the academy of fciences and 

 belles Icttres at Berlin, and alfo of the royal fociety of 

 I-,ondon, and of the inftitute at Bologna, was horn at Bafil, 

 Oftober 10, 1687, and died there, November 29, 1759. 



Bernouilli, Danifx, M.D. fon of John Bernouilli, was 

 born at Groninger, Feb. 9, 1700. Prefen-ing mathemati- 

 cal to commercial purfuits, he pafied the earlier part of his 

 life in Italy, and at the age of 24, declined the prefidency of 

 an academy about to be eftabliflied at Genoa, and in the fol- 

 lowing year accepted an iavitation to Peterfburgh, where 

 he fpent feveral years. On his return to Bafil, in 1733, he 

 was fucceffively profeflor of anatomy and botany, and of na- 

 tural and experimental philofophy ; and had the honour of 

 being s member of the academies of Peterfburgh, Paris, and 

 Berlin, and of the rcyal fociety of London. In 1724, he 

 publilhcd his " Exercitationes Mathematics;" and, in 1738, 

 his " Hydronamica." Many otiier pieces have been pub- 

 hfiied in the memoirs of the academy of fciences at Paris, 

 and in thofe of other focieties. He gained and divided ten 

 prizes from the Parifian academy ; and on the divifion of the 

 prize refpcdting the inclination of the planetai-y orbits, his 

 father expreifed diffatisfaftion ; more efpecially as Daniel 

 had embraced the Newtonian philofophy in preference to 

 that of Defcartes, to which he himfelf maintained h:s at- 

 tachment as long as he lived. In 1740, he divided the prize 

 on the tides with Euler and Maclaurin. At Bafd he was 

 much refpefted, not only as a man of diftingui(l;eil talents, 

 but for his fimple and modeft manners. Although he paid 

 external refpeft to the rehgion of his country, he was 

 charged by his paftors with an exceflivc freedom of opinion, 



I i which 



