# Online Encyclopedia

# Daniel Bernoulli

**Daniel Bernoulli** (Groningen, February 9, 1700 - Basel, March 17, 1782) was a Dutch-born mathematician who spent much of his life in Basel, Switzerland. He worked with Leonhard Euler on the equations bearing their names. Bernoulli's principle is of critical use in aerodynamics. It is applicable to steady, inviscid, incompressible flow, along a streamline.

Born as the son of Johann Bernoulli, and nephew of Jakob Bernoulli, Daniel Bernoulli was by far the ablest of the younger Bernoullis. He is said to have had a bad relationship with his father. Upon both of them entering and tying for first place in a scientific contest at the University of Paris, Johann, unable to bear the "shame" of being compared to his offspring, banned Daniel from his house. Johann Bernoulli also tried to steal Daniel's book *Hydrodynamica* and rename it *Hydraulica*. Despite Daniel's attempts at reconciliation, his father carried the grudge until his death.

Daniel Bernoulli taught at the University of Basel for 26 years until his death. He was a contemporary and intimate friend of Euler. He went to St. Petersburg in 1724 as professor of mathematics, but did not like it there, and a temporary illness in 1733 gave him an excuse for leaving. He returned to Basel, where he held successively the chairs of medicine, metaphysics, and natural philosophy.

His earliest mathematical work was the *Exercitationes* (*Mathematical Exercises*), published in 1724, which contains a solution of the differential equation proposed by Jacopo Riccati (the Riccati equation). Two years later he pointed out for the first time the frequent desirability of resolving a compound motion into motions of translation and motions of rotation. His chief work is his *Hydrodynamique* (*Hydrodynamica*), published in 1738; it resembles Lagrange's *Méchanique Analytique* in being arranged so that all the results are consequences of a single principle, namely, in this case, the conservation of energy. This was followed by a memoir on the theory of the tides, to which, conjointly with the memoirs by Euler and Colin Maclaurin, a prize was awarded by the French Academy: these three memoirs contain all that was done on this subject between the publication of Isaac Newton's *Principia* and the investigations of Laplace. Bernoulli also wrote a large number of papers on various mechanical questions, especially on problems connected with vibrating strings, and the solutions given by Brook Taylor and by d'Alembert. He is the earliest writer who attempted to formulate a kinetic theory of gases, and he applied the idea to explain the law associated with the names of Robert Boyle and Edme Mariotte.

Daniel Bernoulli also was the author in 1738 of the "Exposition of a New Theory on the Measurement of Risk", *Econometrica* vol 22 (1954), pp23-36. - Stanford Encyclopaedia of Philosophy] which St. Petersburg paradox was the base of the economic theory of risk aversion, risk premium and utility

He died at Basel, where he was professor of physics, on March 17, 1782.

*Original entry based on the public domain Rouse History of Mathematics*