He worked with Leonhard Euler on the equations bearing their names.
He taught at Basel University[?] for 26 years until his death. He was a contemporary and intimate friend of Euler, whose works are mentioned in the next chapter. He went to St. Petersburg in 1724 as professor of mathematics, but the roughness of the social life was distasteful to him, and he was not sorry when a temporary illness in 1733 allowed him to plead his health as an excuse for leaving. He then returned to Basel, and held successively chairs of medicine, metaphysics, and natural philosophy[?] there.
His earliest mathematical work was the Exercitationes (Mathematical Exercises), published in 1724, which contains a solution of the differential equation proposed by Riccati[?]. 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 Maclaurin, a prize was awarded by the French Academy: these three memoirs contain all that was done on this subject between the publication of 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 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 Boyle and Mariotte[?].
Had a bad relationship with his father. Upon both of them entering and tying for the win 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. Even though Daniel tried to reconcile (he did nothing wrong), his father carried the grudge until his death.
He died at Basel, where he was professor of physics, on March 17, 1782.