# Bernoulli

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Related to Jakob Bernoulli: Johann Bernoulli, Jacob Bernoulli

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## Bernouilli

(both: bĕrno͞oyē`), 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 calculuscalculus,
branch of mathematics that studies continuously changing quantities. The calculus is characterized by the use of infinite processes, involving passage to a limit—the notion of tending toward, or approaching, an ultimate value.
and of the calculus of variationscalculus of variations,
branch of mathematics concerned with finding maximum or minimum conditions for a relationship between two or more variables that depends not only on the variables themselves, as in the ordinary calculus, but also on an additional arbitrary relation, or
, he was the first to use the word integral in solving LeibnizLeibniz or Leibnitz, Gottfried Wilhelm, Baron von
, 1646–1716, German philosopher and mathematician, b. Leipzig.
'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 principleBernoulli's principle,
physical principle formulated by Daniel Bernoulli that states that as the speed of a moving fluid (liquid or gas) increases, the pressure within the fluid decreases.
, and anticipated the law of conservation of energy and the kinetic-molecular theory of gaseskinetic-molecular theory of gases,
physical theory that explains the behavior of gases on the basis of the following assumptions: (1) Any gas is composed of a very large number of very tiny particles called molecules; (2) The molecules are very far apart compared to their sizes,
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 following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## Bernoulli

a family of Swiss scientists whose ancestor, Jakob Bernoulli (died 1583), was an emigrant from Holland.

Jakob Bernoulli. Born Dec. 27, 1654, in Basel; died there on Aug. 16, 1705. Professor of mathematics at the University of Basel (1687).

Having become familiar in 1687 with the first memoir of G. W. Leibniz on differential calculus (1684), Bernoulli soon after brilliantly applied the new ideas to the investigation of the properties of a number of curves. Together with his brother Johann, Jakob laid the foundation for the variational calculus. In addition, the isoperimetric problem introduced and partially solved by Jakob was also of great importance, as was the solution Jakob found to the brachistochrone problem that had been posed by his brother Johann. He proved the so-called Bernoulli theorem—an important particular case of the law of large numbers. In connection with the calculation of the sum of identical powers of natural numbers, he discovered the so-called Bernoulli numbers. He also worked in the field of physics (the determination of the center of oscillation of objects and the drag of objects of various shapes moving in a liquid).

### WORKS

Opera omnia, vols. 1–2. Geneva, 1744.
Wahrscheinlichkeitsrechnung (Ars conjectandi), vols. 1–4. Leipzig, 1899. (Ostwald’s Klassiker der exakten Wissenschaften, fasc. 107–108.)
In Russian translation:
Chast’ chetvertaia sochineniia “Ars conjectandi.” St. Petersburg, 1913.
Johann Bernoulli. Born July 27, 1667, in Basel; died there Jan. 1, 1748. Younger brother of Jakob Bernoulli. Professor of mathematics at the University of Groningen (Holland) from 1695 and at the University of Basel from 1705. Honorary member of the St. Petersburg Academy of Sciences.
Johann was an active coworker of Leibniz in the development of differential and integral calculus, in which area he made a number of discoveries. He gave the first systematic account of differential and integral calculus, furthered the development of methods of solving ordinary differential equations, posed the classical problem of geodesic lines, and found the characteristic geometric property of these lines. (He later derived their differential equation.) The bitter argument over the solution of variational problems which flared up between Johann and Jakob Bernoulli to some extent contributed to the formulation of new problems in this field. Johann Bernoulli also contributed valuable work in mechanics: impact theory, the motion of objects in a resistant medium, and the study of kinetic energy.

### WORKS

Opera omnia, vols. 1–4. Lausanne-Geneva, 1742.
In Russian translation:
Izbr. soch. po mekhanike. Moscow-Leningrad, 1937.
Daniel Bernoulli. Born Jan. 29, 1700, in Groningen; died Mar. 17, 1782, in Basel. Son of Johann Bernoulli. Worked in physiology and medicine but mainly in mathematics and mechanics.
In the period from 1725 to 1733, Daniel worked in the St. Petersburg Academy of Sciences—first in the subdepartment of physiology, and then in the subdepartment of mechanics. Later he became an honorary member of the St. Petersburg Academy of Sciences and published 47 papers in its publications from 1728 to 1778. He was professor of physiology (1733) and mechanics (1750) at Basel. In mathematics, Daniel contributed a method of numerical solution of algebraic equations using reciprocal series ana works on ordinary differential equations, on the theory of probability (with application to population statistics and, in part, to astronomy), and on the theory of series. In his works (the last of them was the treatise Hydrodynamica [1738], written in St. Petersburg), Daniel derived the fundamental equation of stationary motion of an ideal fluid that bears his name. He also developed the kinetic representation of gases.

### WORKS

Hydrodynamica sive de viribus et motibus fluidorum commentarii. Strasbourg, 1738.

### REFERENCE

Rainov, T. I. “Daniil Bernulli i ego rabota ν Peterburgskoi akademii nauk.” Vestnik AN SSSR, 1938, nos. 7–8.
Among the other members of the Bernoulli family were Nikolaus Bernoulli (1687–1759), the nephew of Jakob and Johann, a professor of mathematics in Padua and Basel; Nikolaus Bernoulli (1695–1726), the son of Johann, a professor of mathematics in the St. Petersburg Academy of Sciences; and Jakob Bernoulli (1759–89), the nephew of Daniel, a member of the St. Petersburg Academy of Sciences and the author of valuable works in mechanics.