BERNOULLI (JAmcs,) a celebrated mathematician, born at Basil, the 27th of December, 1654. Having taken his de grees in that university, he applied him self to divinity, at the entreaties of his fa ther, but against his own inclination, which led him to astronomy and mathe matics. He gave very early proofs of his genius for these sciences, and soon be came a geometrician, without a precep tor, and alinost without books; for if one 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 Boor 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 lie 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 1637, James Bernoulli succeeded to the professorship of mathematics at Basil; a trust which lie 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 Seavans." Llis 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 curve should be inscribed on his tomb, with these words, " Eadcm 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.