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again at his last solution, and to say whether he still thinks 

 it ri|{hi ; ami I declare that when I shall have published 

 nine, pretexts of precipitation will not be listened to.' 

 John Bernoulli answered, that he would not revise his solu- 

 tion, and tliut his time was letter employed in making new 

 discoveries. James Bernoulli replied, that if in three mi- 

 MttM he had solved the whole mystery, surely ti.r mimitrs 

 more would not much diminish the number of his new dis- 

 :.t. After some further communications, in the course 

 of which John Bernoulli sent the demonstration of bis solu- 

 tion to Leibnitz (who declined giving any positive opinion), 

 and declared that ho would say no more on the subject, 

 James Bernoulli published his own solutions, with those of 

 other problems, without demonstrations, in the TxMpzig Act* 

 for June, 1700. Ho also printed at Basle a letter to his 

 brother, in which he invites him to publish his method, and 

 sends his own solution, without demonstration. John Ber- 

 noulli, though now in possession of the true result, could 

 not see where he was wrong ; perhaps would not, for a ma- 

 terial part of this letter was suppressed at hit desire in the 

 posthumous edition of his brother's works. (It was re- 

 printed whole in 1792, as already mentioned.) John Ber- 

 noulli replied, by sending his own demonstration under 

 cover to the Academy of Sciences, at Paris, to be opened 

 no soon as his brother should send his. On this, James 

 Bernoulli (March, 1701) published his own solution at 

 Basle, and also in the Leipzig Acts with the demonstration. 

 Do L'Hopital and Leibnitz immediately admitted its correct- 

 ness, and made John Bernoulli acquainted with their 

 opinion. But no more was heard from the latter ; he con- 

 tinued obstinately silent as long as his brother was alive, 

 nor was it till 1706, after the death of James Bernoulli, that 

 he published an incorrect solution in the memoirs of the 

 academy. The inference is obvious, tha^t he suspected the 

 incorrectness of his own method, and was afraid to expose 

 it to the searching eye of his brother; but that when the 

 latter was dead, he did not fear that any other person in 

 Europe would be able to expose him. As late as 1718, he 

 published a correct solution, and admitted that he had been 

 mistaken; but he had not the fairness to a<l<l, that his 

 new solution was only that of his brother in another shape. 

 After the preceding account, which is now undisputed, 

 the reader will not be surprised to be told, that after the 

 deaths of Leibnitz and De L'HOpital, their bosom friend 

 John Bernoulli endeavoured to rob them both. He claimed 

 to be a contemporaneous inventor of a method of the former 

 (that which was called the dijftreniiatio de curva in cur- 

 vum), of which he had said in admiration, when it was firsl 

 produced, that ' the god of geometry had admitted Leibnitz 

 farther into his sanctuary than himself.' And here too, il 

 cither of the brothers can be said to have invented that me- 

 thod as well as Leibnitz, it was James Bernoulli. He also 

 advanced an absurd pretension to be the author of all that 

 was new in the Analyse, &c. of De L'Hopital, a claim which 

 merits no refutation. He was jealous of his own son, Da- 

 niel Bernoulli, who divided with him the prize of the aca- 

 demy of sciences in 1 734. and was displeased that he turned 

 Newtonian. The following anecdote is related by Con- 

 dorcct, we know not on what authority, but we believe it : 

 'One day he proposed to his son Daniel, then a youth, a 

 little problem to try his strength ; the boy took it With him, 

 solved it, and came back expecting some praise from his 

 father. You ought to have done it on Ike tpot was all the 

 observation made, and with a tone and gesture which hi* 

 son remembered to the latest day of his life.' The only in- 

 stance which has ever fallen within our reading, in which 

 John Bernoulli showed himself free from petty feeling, 

 was in his treatment of Eulcr, when the latter was his pupi 1 

 at Basle. Observing his talent for mathematics he cncou- 

 1 it, and gave him private lessons, in addition to those 

 of tlic public course. 



In thus displaying a character which appears to have no 

 one amiable point about it, we depart from the common 

 practice, which is never to admit, if by any softening it can 

 bo helped, that great intellect is not accompanied by great- 

 ness of mind in wther respects. But it is not pood to sub- 

 stitute falsehood (and coloured truth is falsehood) fop truth 

 and it i* n .t good for the living to know that literary or 

 itific. reputation covers moral obliquity as soon as ihc 

 grave has covered the body. D'Alembert, who. in the form 

 of an iloge, has written an excellent account of th<; mathe- 

 matical character of John Bernoulli, has dexterously evaded 

 the difficulty. 'Bernoulli was only known to me by his 



work* ; I owe to them almost entirely the little progress I 

 mve made in geometry. Not havini: had any kind !' :- 

 (iiaintanen with him, I am ignorant of the unintrrr.ttinif 

 details of hit prirate lifr.' Speaking ol tin- ci-lchr.itt-.i 

 >ute above related, he says, 'This altercation produced 

 wveral pieces in which bitterness seems to IUIM- taken the 

 dace of emulation ; but as one of the two must have been 

 n the wrong, one of the two must have been in a passion.' 

 He only forgets to state, what he himself knew as well as 

 any body, that the 'one of the two' was the subject of the. 

 tloge, and his protfgi for the time being. 



In concluding what we mean to say on the two brot! 

 who stood at the head of their family, we mny observe 

 that it is clear that both one and the other had pushed 

 their researches in the infinitesimal analysis tar beyond 

 the \\cvr of any other won of their time. New ton had 

 abandoned the sciences, and Ixiinnitz, the other inventor, 

 though he could decide between the right and the w i 

 would not commit himself by an opinion on the solution of 

 John Bernoulli only, but contented himself with Mating 

 that it seemed to him to be correct, but that he could not 

 give it sufficient attention to speak positively. Of tin- 

 brothers, the elder was certainly the deeper and the more 

 correct; the younger the quicker anil the more elegant. 

 The works of John Bernoulli, who lived much longer than 

 his brother, contain an immense mass of disc.Acry: but 

 there is no particular on which we could dwell for the benefit 

 of the general reader: the mathematician should consult 

 the doge of D'Alembert already alluded to. 



NICOLAS BERNOULLI II. (to distinguish him from his 

 cousin of the same name), the eldest son of John Ber- 

 noulli, was born January 27, 1695, at Oroninjen. He 

 came to Basle with his father in 1705, and studied at i!.e 

 university, where he formed an intimate friendship with 

 the afterwards celebrated Euler. In 1725 he was invited 

 to Petersburg by the Empress Catherine, with his brother 

 Daniel. But he had hardly time to do more than sh.r.v 

 that he had the talents of his family, when he died, July 

 2f>, 1 726, at Petersburg. For his (tors see Cnmm. A>-<i<l. 

 Petrop. v. ii., and for some memoirs of liis, see vol. i. There 

 are some of his memoirs in his father's works. (See the 

 ]1i"graphie Unirtrsclte.) 



DANIEL BERNOULLI, the second son of John, was born 

 at Groningen, February 9, 1700. His father at first in- 

 tended that he should apply himself to trade, but his ob- 

 jections to that course of life prevailed, and he was allowed 

 to study medicine. He had received some- instruction in 

 mathematics from his father ; we have already seen how. 

 After passing some years in Italy, professedly employed 

 upon medicine, but really upon mathematics, he returned 

 to Basle. He could not at this time have been actually 

 known as a mathematician by any decided effort of his own; 

 but it was sufficient that he was a Bernoulli, for we arc 

 told that before he was twenty-four years old he had refused 

 the presidency of the Academy of Sciences at Genoa. The. 

 following year he and his brother Nicolas were invited to St. 

 Petersburg, as already mentioned. He appears not to have 

 been well satisfied with the half savage court of K. 

 and had made up his mind to quit it ; but the empress, 

 who wished him to remain, increased his salary, and gave 

 him full liberty to retire on the half of it wneWevi 

 pleased. Thus obliged in honour to remain, he continued 

 at St. Petersburg till 17:!:t, when the state of his health 

 compelled him to return to his country. Here he obtained, 

 first a chair of medicine, and afterwards of natural philo- 

 sophy, to which was subsequently added one of metaphysics. 



He had published, in 1724, his first work, entitled / 

 citatimifs Mathematics", in the title-page of which he 

 styled himself 'son of John Bernoulli,' which title he 

 always afterwards continued. His succeeding essays mi 

 mechanics were the first in which mot inn is decom, 

 into that of translation and rotation. He afterwards en- 

 tered into the theory of compound oscillation.-, and is the 

 first who applied mathematics to a spec ies of considerations 

 which have since become of tin? greatest utility and singu- 

 larly extension application. His Hydrodynamique, pub- 

 lished in 1738, is the first work in which the motions of 

 fluids arc reduced fo a question of mathematics. It is in 

 one point like the subsequent work of Lagrange (the Me- 

 r-iiiiijiif .1na/i<Ji(/Hi') : in that woik the whole question is 

 P -lured t i the ie-i;!i> of one principle, which, in the work 

 of Daniel Bernoulli, is called the cvtim rrntinn of vis viva. 

 In the theory of probabilities ho introduced what is known 



