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First edition, rare, of this highly important collection of letters, all published here for the first time. "In 1845, P.H. Fuss published [the offered work]. It contained much of the correspondence between Leonhard Euler, Christian Goldbach, Nicolas Fuss, and several members of the Bernoulli family (Johann (I), Nicolas, and Daniel). More than 150 years later, Fuss' book continues to be one of our best sources for much of this correspondence. In addition to publishing the correspondence, Fuss included a short biography of Euler, and a list of all of Euler's known works. Fuss had uncovered several of these himself, and brought the number of Euler's publications to 756. This list would remain the standard catalog of Euler's works until Enestrom's Index was published in 1913" (Euler Archive). After Fuss's 'Notice sur la vie et les écrits d'Euler' and his 'Liste systématique des ouvrages d'Euler', the remainder of vol. 1 is devoted to the correspondence between Euler and Goldbach over the period 1729-63 (177 letters). This correspondence is notable particularly for its enthusiastic discussion of number-theoretic problems in a period when number theory was largely regarded as trivial or unimportant. It has been lauded as 'a jewel in the history of science of the eighteenth century' by Fellmann (Leonhard Euler, 2007, p. 36). Vol. 2 contains the correspondence between Johann I Bernoulli and Euler, 1728-46 (14 letters); between Johann's eldest son Nicolas II Bernoulli and Goldbach, 1721-25 (27 letters); between Johann's second son Daniel Bernoulli and Goldbach, 1725-50 (71 letters); from Daniel Bernoulli to Euler, 1726-53 (58 letters); from Daniel Bernoulli to Nicolas Fuss, 1773-8 (5 letters); and from Johann's nephew Nicolas I Bernoulli to Euler, 1742-3 (4 letters). The letters published here contain a wealth of important results in mathematics and physics, far too many for a brief summary. We mention only three. 1) 'Goldbach's conjecture,' that any even integer is the sum of two prime numbers, appears, for the first time in print, on p. 127 of vol.1, in the letter from Goldbach to Euler of 7 June 1742 (see Struik, Source Book in Mathematics, p. 47). One of the most famous unsolved problems in mathematics, this conjecture has been verified for all even numbers up to 4 x 10^18 but it is still unknown whether it holds in general. 2) Euler's famous 'polyhedral formula,' that the number of edges (A), faces (H) and vertices (S) of any polyhedron satisfy the relation H + S = A + 2 - Euler conjectured this formula in his letter to Goldbach of 14 November 1750 (p. 537 of vol. 1). He published a proof in the Commentarii of the Academy of Sciences two years later, marking the birth of the field of mathematics now known as topology. 3) Daniel Bernoulli's invention of the 'gamma function,' the first representation of an interpolating function of the factorial in the form of an infinite product, appears in his letter to Goldbach of 6 October 1729 (p. 325 of vol. 2). Some sources instead credit Euler with this discovery, referring to his letter to Goldbach written one week later (p. 3 of vol. 1), which gives a definition different from Bernoulli's. Euler gave a third definition in his letter to Goldbach of 8 January 1730 (p. 8 of vol. 1). The collection was edited by Paul Heinrich von Fuss (1798-1855), whose father Nicolas was married to the daughter of Euler's eldest son Johann Albrecht. Nicholas was Euler's assistant in St. Petersburg 1773-83, and permanent secretary to the Academy of Sciences there 1800-26, when he was succeeded in that post by his son Paul. Two vols., 8vo, pp. cxxi, 673, [1]; xxiii, 713, [1], with frontispiece portrait of Euler (vol. 1) and Daniel Bernoulli (vol. 2), eight folding plates of geometrical diagrams and eight facsimile letters (not included in the collation). Text in Latin, German and French. Late 19th century cloth (minor repairs to head of spines, occasional foxing), stamp of Royal Society of Edinburgh on titles. Seller Inventory # ABE-1587330624144
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