Chapter II: JEAN BERNOULLI (1667-1748), brother of the preceding, was born at

Basel on the 27th of July 1667. After finishing his literary studies he was sent to Neuchatel to learn commerce and acquire the French language. But at the end of a year he renounced the pursuits of commerce, returned to the university of Basel, and was admitted to the degree of bachelor in philosophy, and a year later, at the age of 18, to that of master of arts. In his studies he was aided by his elder brother Jacques. Chemistry, as well as mathematics, seems to have been the object of his early attention; and in the year 1690 he published a dissertation on effervescence and fermentation. The same year he went to Geneva, where he gave instruction in the differential calculus to Nicolas Fatio de Duillier, and afterwards proceeded to Paris, where he enjoyed the society of N. Malebranche, J.D. Cassini, Philip de Lahire and Pierre Varignon. With the marquis de l'Hopital he spent four months studying higher geometry and the resources of the new calculus. His independent discoveries in mathematics are numerous and important. Among these were the exponential calculus, and the curve called by him the _linea brachistochrona_, or line of swiftest descent, which he was the first to determine, pointing out at the same time the relation which this curve bears to the path described by a ray of light passing through strata of variable density. On his return to his native city he studied medicine, and in 1694 took the degree of M.D. Although he had declined a professorship in Germany, he now accepted an invitation to the chair of mathematics at Groningen (_Commercium Philosophicum_, epist. xi. and xii.). There, in addition to the learned lectures by which he endeavoured to revive mathematical science in the university, he gave a public course of experimental physics. During a residence of ten years in Groningen, his controversies were almost as numerous as his discoveries. His dissertation on the "barometric light," first observed by Jean Picard, and discussed by Jean Bernoulli under the name of mercurial phosphorus, or mercury shining in vacuo (_Diss. physica de mercurio lucente in vacuo_), procured him the notice of royalty, and engaged him in controversy. Through the influence of Leibnitz he received from the king of Prussia a gold medal for his supposed discoveries; but Nicolaus Hartsoeker and some of the French academicians disputed the fact. The family quarrel about the problem of isoperimetrical figures above mentioned began about this time. In his dispute with his brother, in his controversies with the English and Scottish mathematicians, and in his harsh and jealous bearing to his son Daniel, he showed a mean, unfair and violent temper. He had declined, during his residence at Groningen, an invitation to Utrecht, but accepted in 1705 the mathematical chair in the university of his native city, vacant by the death of his brother Jacques; and here he remained till his death. His inaugural discourse was on the "new analysis," which he so successfully applied in investigating various problems both in pure and applied mathematics.

He was several times a successful competitor for the prizes given by the Academy of Sciences of Paris; the subjects of his essays being:--the laws of motion (_Discours sur les lois de la communication du mouvement_, 1727), the elliptical orbits of the planets, and the inclinations of the planetary orbits (_Essai d'une nouvelle physique celeste_, 1735). In the last case his son Daniel divided the prize with him. Some years after his return to Basel he published an essay, entitled _Nouvelle Theorie de la manoeuvre des vaisseaux_. It is, however, his works in pure mathematics that are the permanent monuments of his fame. Jean le Rond d'Alembert acknowledges with gratitude, that "whatever he knew of mathematics he owed to the works of Jean Bernoulli." He was a member of almost every learned society in Europe, and one of the first mathematicians of a mathematical age. He was as keen in his resentments as he was ardent in his friendships; fondly attached to his family, he yet disliked a deserving son; he gave full praise to Leibnitz and Leonhard Euler, yet was blind to the excellence of Sir Isaac Newton. Such was the vigour of his constitution that he continued to pursue his usual mathematical studies till the age of eighty. He was then attacked by a complaint at first apparently trifling; but his strength daily and rapidly declined till the 1st of January 1748, when he died peacefully in his sleep.

His writings were collected under his own eye by Gabriel Cramer,
professor of mathematics at Geneva, and published under the title of
_Johannis Bernoulli Operi Omnia_ (Lausan. et Genev.), 4 tom. 4to; his
interesting correspondence with Leibnitz appeared under the title of
_Gul. Leibnitii et Johannis Bernoulli Commercium Philosophicum et
Mathematicum_ (Lausan. et Genev. 1745), 2 tom. 4to.