BERNOULLI. 



by chance fell into his hands, he was ob- 

 liged to conceal it, to avoid the displea- 

 sure of his father, who designed him for 

 other studies. This situation induced 

 him to choose for his device, Phaeton 

 driving the chariot of the sun, with these 

 words, Invito patre sidera verso, " I traverse 

 the stars against my father's will ;" allud- 

 ing particularly to astronomy, to which he 

 then chiefly applied himself. 



In 1676 he began his travels. When he 

 was at Geneva, he fell upon a method to 

 teach a young girl to write who had been 

 blind from two months old. At Bour- 

 deaux he composed universal gnomonic 

 tables ; but they were never published. 

 He returned from France.^to his own 

 country in 1680. About this time there 

 appeared a comet, the return of which he 

 foretold; and wrote a small treatise upon 

 it. Soon after this he went into Holland, 

 where he applied himself to the study 

 of the new philosophy. Having visited 

 Flanders and Brabant, he passed over to 

 England; where he formed an acquaint- 

 ance with the most eminent men in the 

 sciences, and was frequent at their philo- 

 sophical meetings. He returned to his 

 native country in 1682 ; and exhibited at 

 Basil a course of experiments in natural 

 philosophy and mechanics, which con- 

 sisted of a variety of new discoveries. 

 The same year he published his " Essay 

 on a new System of Comets ;" and the 

 year following, his " Dissertation on the 

 Weight of the Air." About this time 

 Leibnitz having published, in the Acta 

 Eruditorum at Leipsic, some essays on his 

 new "Calculus Differentialis," but con- 

 cealing the art and method of it, Mr. Ber- 

 noulli and his brother John discovered, 

 by the little which they saw, the beauty 

 and extent of it; this induced them to 

 endeavour to unravel the secret ; which 

 they did with such success, that Leib- 

 neitz declared that the invention be- 

 longed to them as much as to himself. 



In 1687, James Bernoulli succeeded to 

 the professorship of mathematics at Basil ; 

 a trust which he discharged with great 

 applause ; and his reputation drew a great 

 number of foreigners from all parts to at- 

 tend his lectures. In 1699, he was admit- 

 ted a foreign member of the Academy of 

 Sciences 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 Erudi- 

 torum" of Leipsic, and in the " Journal 

 des Savans." 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. Arch- 

 imedes having found out the proportion 

 of a sphere and its circumscribing cylin- 

 der, ordered them to be engraven on his 

 monument. In imitation of him, Bernoulli 

 appointed that a logarithmic spiral curvq 

 should be inscribed on his tomb, with 

 these words, " Eadem mutata resurgo;" 

 in allusion to the hopes of the resurrec- 

 tion, which are, in some measure, repre- 

 sented by the properties of that curve 

 which he had the honour of discovering. 



James Bernoulli had an excellent ge- 

 nius for invention, and elegant simplicity, 

 as well as a close application. He was 

 eminently skilled in all the branches of 

 the mathematics, and contributed much 

 to the promoting the new analysis, infi- 

 nite 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 epicy- 

 cloids. His works, that had been pub- 

 lished, were collected, and printed in two 

 volumes 4to. at Geneva, in 1744. 



BERNOULLI (John,) the brother of James, 

 last mentioned, and a celebrated mathe- 

 matician, was born at Basil the 7th of 

 August, 1667. His father intended him 

 for trade ; but his own inclination was at 

 first for the Belles-Lettres, which, how- 

 ever, like his brother, he left for mathe- 

 matics. 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 the integral 

 calculus. Our author, with Messieurs 

 Huygens and Leibnitz, was the first who 

 gave the solution of the problem propos- 

 ed by James Bernoulli, concerning the 

 catenary or curve formed by a chain sus- 

 pended by its two extremities. 



John Bernoulli was a member of most 

 of the academies of Europe, and receiv- 

 ed as a foreign associate of that of Paris 

 in 1669. After a long life spent in con- 

 stant 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 pursued the same 

 sciences with himself. One of these died 

 before him ; the two others, Nicolas 

 and Daniel, he lived to see become emi- 

 nent and much respected in the same 

 sciences. 



The writings of this great man were 

 dispersed through the periodical memoir* 

 of several academies, as weU as in many 



