BERNOULLI (James)

, a celebrated mathematician, born at Basil the 27th of December 1654. Having taken his degrees in that university, he applied himself to divinity at the entreaties of his father, but against his own inclination, which led him to astronomy and mathematics. He gave very early proofs of his genius for these sciences, and soon became a geometrician, without a preceptor, and almost without books; for if one by chance fell into his hands, he was obliged to conceal it, to avoid the displeasure 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:” alluding 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 Bourdeaux 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 Fngland; where he formed an acquaintance with the most eminent men in the sciences, and was frequent at their philosophical meetings. He | returned to his native country in 1682; and exhibited at Basil a course of experiments in natural philosophy and mechanics, which consisted 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 Disscrentialis, but concealing the art and method of it, Mr. Bernoulli 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 Leibnitz declared that the invention belonged 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 attend his lectures. In 1699 he was admitted 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 Eruditorum of Leipsic, and in the Journal des Sçavans. 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.— Archimedes having found out the proportion of a sphere and its circumscribing cylinder, 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, Eadem mutata resurgo; in allusion to the hopes of the resurrection, which are in some measure represented by the properties of that curve, which he had the honour of discovering.

James Bernoulli had an excellent genius 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, infinite 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 epicycloids.

His works, that had been-published, were collected, and printed in 2 volumes 4to, at Geneva in 1744. At the time of his death he was occupied on a great work entitled De Arte Conjectandi, which was published in 4to, in 1713. It contains one of the best and most elegant introductions to Infinite Series, &c. This posthumous work is omitted in the collection of his works above mentioned.