Daniel, Sohn von 3), 1700, 1782, Mathematiker u. Physiker; arbeitete über hydrodynam. Probleme u. schuf die Anfänge der kinet. Gastheorie.
(1700-1782) Swiss mathematical physicist who made important contributions to trigonometry and differential equations (differentiation). In hydrodynamics he proposed Bernoulli's principle, an early formulation of the idea of conservation of energy.
Bernoulli was born in Groningen in the Netherlands, the son of mathematician Johann Bernoulli. Having studied philosophy, logic, and medicine in Basel, Switzerland, he became professor of mathematics at the St Petersburg Academy, Russia, 1725–32, and professor of anatomy and botany at the University of Basel from 1733. During his career he won ten prizes from the French Academy, for papers on subjects which included marine technology, oceanology, astronomy, and magnetism.
Bernoulli’s Hydrodynamica 1738 is both a theoretical and practical study of equilibrium, pressure, and velocity in fluids. Bernoulli’s principle states that the pressure of a moving fluid decreases the faster it flows (which explains the origin of lift on the airfoil of an aircraft’s wing). Hydrodynamica also contains the first attempt at a thorough mathematical explanation of the behavior of gases by assuming they are composed of tiny particles, producing an equation of state that enabled Bernoulli to relate atmospheric pressure to altitude, for example. This was the first step toward the kinetic theory of gases achieved a century later.
Among his achievements in mathematics, Bernoulli demonstrated how differential calculus could be used in problems of probability. He did pioneering work in trigonometrical series and the computation of trigonometrical functions. Bernoulli also showed the shape of the curve known as the lemniscate.
Jakob, Bruder von 3), 1655, 1705, Mathematiker; hinterließ eine Darstellung der Wahrscheinlichkeitsrechnung.
(1654-1705) Swiss mathematician who with his brother Johann pioneered German mathematician Gottfried Leibniz’s calculus. Jakob used calculus to study the forms of many curves arising in practical situations, and studied mathematical probability (Ars conjectandi 1713); Bernoulli numbers are named for him.
Jakob Bernoulli’s papers on transcendental curves (1696) and isoperimetry (1700, 1701) contain the first principles of the calculus of variations. It is probable that these papers owed something to collaboration with Johann. His other great achievement was his treatise on probability, Ars Conjectandi, which contained both the Bernoulli numbers (a series of complex fractions) and the Bernoulli theorem.
Jakob Bernoulli was born in Basel. On a trip to England 1676 he met Irish physicist Robert Boyle and other leading scientists, and decided to devote himself to science. He became particularly interested in comets (which he explained by an erroneous theory 1681) and in 1682 began to lecture in mechanics and natural philosophy at the University of Basel. During the next few years he came to know the work of Leibniz and began a correspondence with him. In 1687 he was made professor of mathematics at Basel.
Johann, 1667, 1748, Mathematiker; förderte die Variationsrechnung u. die Theorie der Differentialgleichung.
(1667-1748) Swiss mathematician who with his brother Jakob Bernoulli pioneered German mathematician Gottfried Leibniz's calculus. He was the father of Daniel Bernoulli.
Johann also contributed to many areas of applied mathematics, including the problem of a particle moving in a gravitational field. He found the equation of the catenary 1690 and developed exponential calculus 1691.
Bernoulli was born in Basel and studied medicine, but became professor of mathematics at Groningen, the Netherlands, 1694–1705, and then at Basel. Both Johann and Jakob wrote papers on a wide variety of mathematical and physical subjects, and it is often difficult to separate their work, although they never published together.