BERNOULLI 579 mechanical science which attracted much at- tention. In 1687 he was appointed professor of mathematics in the university of Basel, and engaged in profound mathematical investiga- tions, particularly in the development of the theory of the differential and integral calculus which had been devised by Leibnitz. In 1699 he was chosen member of the French academy, the first foreigner ever elected, and in 1701 became member of the Berlin academy. He directed that the logarithmic spiral, of which he had demonstrated the properties, should be engraved upon his tombstone with the motto : Eddem rnutatd resurgo. After his death his treatise entitled Ars Conjectandi was published (1713). It was one of the earliest works on the theory of probabilities. His collected works were published at Geneva in 1744 (2 vols. 4to). II. John, brother of the preceding, born July 27, 1667, died Jan. 1, 1748. He was educated at the university of Basel, studied medicine, and in 1690 published a dissertation on effer- vescence and fermentation. But he soon turned his attention to mathematics. In 1690 he went to Geneva, and travelled in France, where he made the acquaintance of Male- branche, De 1'IIOpital, and other men of sci- ence. He returned to Basel in 1692, and was appointed in 1695 professor of mathematics at Groningen. In 1696 he proposed for solution the following problem: "To find the curve on which a material point will fall from one given point to another in the least possible time." It was solved by his brother James and others, and James proposed in return an- other problem in regard to the solution of which there was a long controversy between the two brothers. John exhibited unreason- able jealousy of his brother, and was not equal to him as a mathematician. He, however, suc- ceeded him as professor of mathematics at Basel, and remained in that position till his death. He was also jealous of his son Daniel, and had controversies with many of the scien- tific men of his day ; but he was the instructor of Euler and the friend of Leibnitz, with whom he carried on a long correspondence, published at Lausanne and Geneva (2 vols., 1745). He aided with his brother in the development of the calculus, investigated many curious ques- tions in physics, and contributed greatly to the advancement of mathematical science. He ad- dressed many papers to the different scientific bodies of Europe, which were collected by Cra- mer (4 vols. 4to, Lausanne and Geneva, 1742), and was a member of the academies of Paris, Berlin, and St. Petersburg, of the royal so- ciety of London, and of the institute of Bologna. His works were published at Geneva in 1742 (1 vol. 4to). III. Daniel, second son of the pre- ceding, born in Groningen, Feb. 9, 1700, died in Basel, March 17, 1782. He received in- struction from his father in mathematics, and studied medicine for some years in Italy. While there he distinguished himself by a paper upon a question of geometry, and at the age of 24 was offered the presidency of an academy of sciences which had just been founded at Genoa. The following year he was appointed professor of mathematics at St. Petersburg, where he remained till 1733, when he was appointed first professor of botany and anatomy, and afterward of natural philosophy and meta- physics, in the university of Basel. In 1748 he succeeded his father as member of the academy of sciences at Paris, and ten times obtained the prizes of that body. He made many new and ingenious applications of mathematical science in mechanics, astronomy, and hydrau- lics, and in 1760 wrote a paper on inoculation in which he introduced a new principle in- to the theory of probabilities. He resigned his professorship in 1777, suffered much from asthma during the latter part of his life, and was finally found one morning by his servant dead in his bed. Among his works are : Exer- citationes yucedam Mathematices (4to, Venice, 1724) ; ffydrodynamica, sen de Viribus et Moti- bus Fluidorum (4to, Strasburg, 1738); and a work on the physicid cause of the inclination of the axes and orbits of planets with reference to the solar equator. IV. Nicholas, elder bro- ther of the preceding, born in Basel, Jan. 27, 1695, died in St. Petersburg, July 26, 1726. He travelled in France and Italy, and was then appointed professor at St. Petersburg with his brother. V. John, brother of the preceding, born in Basel, May 18, 1710, died July 17, 1790. He studied law and mathematics, in 1743 was appointed professor of eloquence at Basel, and in 1748 succeeded his father as professor of mathematics there. He was a member of the academy of sciences of Berlin and of Paris, and received three prizes from the French acad- emy. VI. John, son of the preceding, born in Basel, Nov. 4, 1744, died July 13, 1807. He studied at Basel and Neufchatel, devoting him- self especially to astronomy, mathematics, and philosophy. At the age of 19 he was appoint- ed astronomer of the Berlin academy, and afterward director of the mathematical class. He published Recueil pour let astronom.es (3 vols., Berlin, 1772-'6), Lettres astronomiyues (1781), and 6 vols. of his own travels, besides a collection of travels in 15 vols. VII. James, brother of the preceding, born in Basel, Oct. 17, 1759, died in St. Petersburg, July 13, 1789. When his uncle Daniel became infirm, he as- sumed at the age of 21 his duties as professor of natural philosophy, but was not chosen his successor, the appointment being made by lot. At the age of 29 he was appointed professor of mathematics in St. Petersburg, and mar- ried there a granddaughter of Enler. Two months afterward he died of apoplexy while bathing in the Neva. VIII. Nicholas, nephew of the first James and John, horn in Basel, Oct. 10, 1687, died Nov. 29, 1759. He edited the An Conjectandi of his uncle James, and solved several of the geometrical problems proposed by his uncle John. He was professor of mathematics at Padua from 1716 to 1722,
