JAMES, a celebrated mathematician, born at Basil the 27th of December 1654. Having taken his degrees in the university of Basil, 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

Daniel, a celebrated physician and philosopher, was born at Groningen, February 9, 1700. He was intended by his parents for trade, but his genius led him to different pursuits. He passed some time in Italy, and at 24 refused to be president of an academy meant to have been established at Genoa. He spent several years at St Petersburg with great credit; and in 1733 returned to Basil, where he successively filled the chair of physic, natural and speculative philosophy. In his first work, *Exercitationes Mathematicae*, he took the only title he then had, viz. "Son of John Bernoulli," and would never suffer any other to be added to it. This work appeared in Italy with the great inquisitor's privilege added to it, and it clasped Bernoulli in the rank of inventors. He gained or divided nine prizes, which were contended for by the most illustrious mathematicians in Europe, from the academy of sciences. The only man who has had success of the same kind is Euler, his countryman, disciple, rival, and friend. His first prize he gained at 24 years of age. In 1734 he divided one with his father; but this hurt the family union: for the father construed the contest itself into a want of respect; and the son did not sufficiently conceal that he thought (what was really the case) his own piece better than his father's. Besides this, he declared for Newton, against whom his father had contended all his life. In 1740, Mr Bernoulli divided the prize "On the Tides of the Sea" with Euler and Maclaurin. The academy at the same time crowned a fourth piece, whose only merit was that of being Cartesian; but this was the last public act of adoration paid by it to the authority of the author of the Vortices, which it had obeyed perhaps too long. In 1748, Mr Daniel Bernoulli succeeded his father in the academy of sciences, and was himself succeeded by his brother John; this place, since its first erection, i.e. 84 years, never having been without a Bernoulli to fill it. He was extremely respected at Basil; and to bow to Daniel Bernoulli, when they met him in the streets, was one of the first lessons which every father gave his child. He used to tell two little adventures, which he said had given him more pleasure than all the other honours he had received. He was travelling with a learned stranger, who, being pleased with his conversation, asked his name: "I am Daniel Bernoulli," answered he with great modesty; "And I," said the stranger (who thought he meant to laugh at him), "I am Isaac Newton." Another time he was giving a dinner to the famous Koenig the mathematician, who boasted, with a sufficient degree of self-complacency, of a difficult problem he had resolved with much trouble. Bernoulli went on doing the honours of his table; and, when they went to drink coffee, presented him with a solution of the problem more elegant than his own. He died in March 1782.