BERNOULLI, DANIEL, a celebrated mathema tician and natural philosopher, was the son of John Bernoulli, and was born at Groningen 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 only answer he received ; and the tone manner 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 he returned to his native country loaded with literary honours, after having refused, at the age of 21•, the presidency of an academy which the republic of Ge 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 leave Russia ; but the court of St Petersburgh, unwil ling to suffer such a loss, increased his 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 17S3, 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 172-•, under the title of Exercitationes quredam Mathematiew. 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. Petrop. vol. vi. p. 108. ; vol vii. p. 162. ; vol. ix. p. 189. ; vol. xv. p. 97.; vol. xviii. p.
The problem of vibrating chords, which was par tially solved by Taylor in and afterwards in a more general form by D'Alembert 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 skew, that the method of Taylor, though limited by the particular hypothesis which he employed, 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 can be fairly drawn from the methods of D'Alembert and.