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Exercitationes Quaedam Mathematicae
Venice: Domenico Lovisa, 1724. A fine copy, printed on thick paper, of Daniel Bernoulli's first mathematical publication. In 1724 Bernoulli published [with the help of Christian Goldbach] his Exercitationes mathematicae in Venice, which attracted so much attention that he was called to the St. Petersburg Academy [where he met with Leonhard Euler].
This treatise combined four separate works dealing, respectively, with the game of faro, the outflow of water from the openings of containers, Riccati's differential equation, and the lunulae (figures bounded by two circular arcs). The discussions on Jacopo Riccati's differential equation were initiated in 1724 by the problem presented by Riccati in the Supplementa to the Acta eruditorum....Bernoulli demonstrated that Riccati's special differential equation axn dx + u2dx = b du could be integrated through separation of the variables for the values n =-4c/2c ± 1), where c takes on all integral values-positive, negative, and zero....In the first part of the Exercitationes..., dealing with faro, Bernoulli furnished data on recurrent series that later proved to have no practical application....[but] was evidence of his early interest in the work on the theory of probability done by his predecessors Montmort and De Moivre, which had been nourished by discussions with his cousin Nikolaus I. (DSB). 4to: 260 x 190 mm. Contemporary vellum. Provenance: Engraved book plate of George Frederick Nott (1767 1841) to front paste down. Pp. 96 and 1 engaved plate. Printed on thich paper. A very fine and clean copy.
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