James, a celebrated mathematician, born at Baflil the 27th of December 1654. Having taken his degrees in the university of Baflil, he applied himself to divinity, not so much from inclination as complaisance to his father. He gave very early proofs of his genius for mathematics, and soon became a geometrician, without any assistance from masters, and at first almost without books: for he was not allowed to have any books of this kind; and if one fell by chance into his hands, he was obliged to conceal it, that he might not incur the reprimands of his father, who designed him for other studies. This severity made him... Bernouilli him choose for his device, Phaeton driving the chariot of the sun, with these words, "In initio patria sidera verba,"

"I traverse the stars against my father's inclination."

This had a particular reference to astronomy, the part of mathematics to which he at first applied himself.

But the precautions of his father did not avail, for he pursued his favourite study with great application. In 1676 he began his travels. When he was at Geneva, he fell upon a method to teach a young girl to write, though she had lost her sight when she was but two months old. At Bordeaux he compiled 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, which he afterwards translated into Latin. He went soon after to Holland, where he applied himself to the study of the new philosophy. After having visited Flanders and Brabant, he went to Calais, and passed over from thence to England. At London he contracted an acquaintance with all the most eminent men in the several sciences; and had the honour of being frequently present at the philosophical societies held at the house of the famous Mr Boyle. He returned to his native country in 1682; and he exhibited at Basle a course of experiments in natural philosophy and mechanics, which consisted of a variety of new discoveries. In 1682, he published his essay of a new system of comets; and the year following, his dissertation on the weight of air.

Mr Leibnitz, about this time, having published in the Acta Eruditorum at Leipzig some essay of his new Calculus differentialis, or infinitesimis partibus, but concealed the art and method of it; Mr Bernouilli, and one of his brothers, discovered, by the little which they saw, the beauty and extent of it: they endeavoured to unravel the secret; which they did with such success, that Mr Leibnitz declared, that the invention belonged to them as much as to himself. In 1687, the professorship of mathematics at Basle being vacant, Mr Bernouilli was appointed his successor. He discharged this trust with universal applause; and his reputation drew a great number of foreigners from all parts to hear his lectures. He had an admirable talent in teaching, and adapting himself to the different genius and capacity of his scholars. In 1699, he was admitted into the academy of sciences at Paris as a foreign member, and in 1701 the same honour was conferred upon him by the academy of Berlin. He wrote several pieces in the Acta Eruditorum of Leipzig, the Journal des Sciences, and the Histoire de l'Academie des Sciences. His studious application to the studies brought upon him the gout, and by degrees a slow fever, of which he died the 16th of August 1705, in the 38th year of his age.—Archimedes having found out the proportion of a sphere to a cylinder circumscribed about it, ordered it to be engraven upon his monument. In imitation of him, Mr Bernouilli appointed, that a spiral logarithmical curve should be inscribed upon his tomb, with these words, Eadem mutata resurgo; in allusion to the hopes of the resurrection, which are represented in some measure by the properties of the curve which he had the honour of discovering.