# Bernoulli

**Bernoulli**or

**Bernouilli**both: bĕrno͞oyē´ [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.

*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,

*Johannis Bernoulli opera omnia.*His son,

*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.

*The Columbia Electronic Encyclopedia,* 6th ed. Copyright © 2023, Columbia University Press. All rights reserved.

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