Bernoulli or Bernouilli both: bĕrno͞oyēˈ [key], name of a family distinguished in scientific and mathematical history. The family, after leaving Antwerp, finally settled in Basel, Switzerland, where it grew in fame. Jacob, Jacques, or James Bernoulli, 1654–1705, became professor at Basel in 1687. One of the chief developers both of the ordinary calculus and of the calculus of variations, he was the first to use the word integral in solving Leibniz's problem of the isochronous curve. He wrote an important treatise on the theory of probability (1713) and discovered the series of numbers that now bear his name, i.e., the coefficients of the exponential series expansion of x/(1-e−x). He was succeeded at Basel by his brother, Johann, Jean, or John Bernoulli, 1667–1748, who earlier had been professor at Gröningen and who was famous for his work in the field of integral and exponential calculus and was also a founder of the calculus of variations. He also contributed to the study of geodesics, of complex numbers, and of trigonometry. His collected works were published under the title Johannis Bernoulli opera omnia. His son, Daniel Bernoulli, 1700–1782, was a mathematician, physicist, and physician and has often been called the first mathematical physicist. He received his doctorate in medicine but became professor of mathematics at the St. Petersburg Academy in 1725. He was professor of anatomy and botany at Basel from 1733, later becoming professor of natural philosophy (physics). His greatest work was his Hydrodynamica (1738), which included the principle now known as Bernoulli's principle, and anticipated the law of conservation of energy and the kinetic-molecular theory of gases developed more than 100 years later. He also made important contributions to probability theory, astronomy, and the theory of differential equations (solving a famous equation proposed by Riccati). Among the other noted members of the family are Nicolaus Bernoulli, 1662–1716, brother of Jacob and Johann, who was professor of mathematics at St. Petersburg; Nicolaus Bernoulli, 1695–1726, son of Johann and brother of Daniel, also a mathematician; Johann Bernoulli, 1710–90, another son of Johann (1667–1748) and brother of Daniel, who succeeded his father in the chair of mathematics at Basel and also contributed to physics; his son, Johann Bernoulli, 1746–1807, who was astronomer royal at Berlin and also studied mathematics and geography; and Jacob Bernoulli, 1759–89, another son of Johann (1710–90), who succeeded his uncle Daniel in mathematics and physics at St. Petersburg but met an early death by drowning.

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