481 



BERNOULLI. 



Bernoulli, 

 Daniel. 



(Tiz. Daniel, the suojcct of the following article ; 

 John, who was doctor of laws and philosophy, and 

 professor of mathematics at Basle; and Nicholas, who 

 was professor of law at Bern, and afterwards profes- 

 sor of mathematics at Petersburg!),) inherited the ge- 

 nius of their father. 



The talents of John Bernoulli as a mathematician 

 were of the very first order ; and if they were sur- 

 passed by any of his cotemporaries, the superiority 

 could be claimed only by his brother and Sir Isaac 

 Newton. He is represented by those that knew him, 

 as just, sincere, and pious, possessed of much natu- 

 ral vivacity, and animated by a zeal and enthusiasm 

 which often rose to extravagance. 

 In the angry contention which he carried on with 

 his brother, we do not perceive any of those virtues 

 which posterity can be called to admire. In the vio- 

 lence of his temper, and in the intoxication of suc- 

 cess, we may find some apology for the vulgar sar- 

 casms which he lavished upon Taylor and Keill ; 

 but the rude abuse which he poured upon a brother, 

 superior to himself both in age and acquirements, and 

 to whom he was indebted for all his mathematical 

 knowledge, and the unnatural jealousy with which he 

 viewed the rising reputation of his son, will long con- 

 tinue to cast a shadow upon his name, and must be 

 permitted to remain upon record without either par- 

 don or palliation. 



During the whole of his life, he testified a sincere 

 belief in the Christian religion, the doctrines of which 

 he had studied with peculiar attention ; and in a 

 journal of the principal events of his life, which he 

 left behind him, there are numerous expressions of 

 the warmest gratitude for the kindness which the 

 Almighty had shewn him. During his stay in Hol- 

 land, his orthodoxy was called in question by the 

 Dutch theologians ; and he published several polemi- 

 cal dissertations in defence of his tenets, and particu- 

 larly an apology pro suafama, lionore et religione, 

 which he pronounced as rector of the university. 

 The controversy terminated in favour of Bernoulli ; 

 and the arm of the civil power was stretched out to 

 silence his adversaries. (/3) 



BERNOULLI, Daniel, a celebrated mathema- 

 tician and natural philosopher, was the son of John 

 Bernoulli, and was born at Groningcn on the 9th of 

 February 1700. The attention of young Bernoulli 

 was early directed by his father to the study of ma- 

 thematics ; but his first attempts, though promising 

 and successful, did not obtain that encouragement 

 and applause which a son might have expected from 

 the fond partiality of a father. Having one day re- 

 ceived a problem to resolve, he carried it into his 

 closet, examined it with attention, and returned with 

 the solution to his father, delighted with the success 

 of his first efforts, and anticipating the praise which 

 they deserved. Why did you not resolve it instant- 

 ly ?. was the oidy answer he received ; and the tone 

 and maimer in which it was spoken produced a tem- 

 porary dislike to the mathematical sciences. Having 

 refused to follow the profession of a merchant, to 

 which he was destined by his friends, he entered upon 

 the study of medicine, and went to Italy to perfect 

 himself in that important science, under the care of 

 Michelotti and Morgagni. His time, however, was 



chiefly occupied with mathematical pursuits , and In- 

 returned to his native country loaded with literary 

 honours, alter having refused, at the age of 21-, the 

 presidency of an academy which the republic of C. 

 noa was about to establish. In the following year he 

 accepted an invitation to the Academy of St Peters- 

 burgh ; and though he enjoyed, in this situation, a 

 handsome income, his affections were perpetually fixed 

 on his native country : He therefore determined to 

 have Russia ; but the court of St Petersburgh, unwil- 

 ling to sufler such a loss, increased lus appointments, 

 and settled upon him, during life, the half of his income, 

 with permission to retire. This generous conduct, 

 so seldom to be met with in the history of princes, 

 induced Bernoulli to remain in Russia, till the loss of 

 his health compelled him to return to the south of 

 Europe. In 17j-J, when he arrived at Basle, the 

 residence of his father, he was appointed professor of 

 medicine, and afterwards filled the chair of physics, 

 and of speculative philosophy, which he held at the 

 same time. 



The first work published by Bernoulli appeared 

 in 1721, under the title of Excrcitationes qucedam 

 Mathematical. This interesting production, which 

 was printed in Italy with the approbation of the In- 

 quisition, contained an able solution of the celebrated 

 equation of Ricati, and several ingenious observations 

 on recurring series, which conducted him, a few 

 years afterwards, to a new and elegant method of ap- 

 proximation, for determinate equations composed of 

 an infinite number of terms. 



His attention was next directed to mathematical 

 subjects, upon which he published several ingenious 

 and profound memoirs. In the Commentaries of St 

 Petersburgh for 1726, he gave the most complete 

 demonstration of the parallelogram of forces. This 

 demonstration, though long and abstruse, was inde- 

 pendent of the consideration of compound motion, 

 and consisted chiefly in proving the absurdity of eve- 

 ry other supposition. His memoir on the relation of 

 the centre of gravity, the centre of oscillation, and 

 the centre of forces ; his researches respecting the 

 oscillatory motion of a system of bodies placed along 

 a flexible thread ; and his determination of the direc- 

 tion and velocity of the two motions, display a ge- 

 nius of the first order, and have greatly contributed 

 to the advancement of theoretical mechanics. His 

 papers on these subjects will be found in the Comment. 

 Pctrop. vol. vi. p. 108. ; vol vii. p. lb'2. ; vol. ix. 

 p. 189. ; vol. xv. p. 97.; vol. xviii. p. 215. 



The problem of vibrating chords, which was par- 

 tially solved by Taylor in 17 It, and afterwards in a 

 more general form by DAlembert and Euler, by- 

 means of their new calculus of partial differences, was 

 the next subject that employed the genius of Ber- 

 noulli. He attempted to shew, that the method of 

 Taylor, though limited by the particular hypothesis 

 which he employ td, was as general in its nature as 

 that of D'Alembert and Euler, who had only the me- 

 rit of employing a new analysis. By considering the 

 decomposition of the real motion of a string into 

 the isochronous vibrations of the whole string and 

 its aliquot parts, he obtained a solution of the pro- 

 blem as extensive in its application as that which car> 

 be fairly drawn from the methods of D'Alembert and 



