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Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes. Marcum-Michaelem Bosquet & Socios, Lausanne & Geneve 1744 - First edition of "Euler’s most valuable contribution to mathematics in which he developed the concept of the calculus of variations." (Norman). "This work displays an amount of mathematical genius seldom rivaled." (Cajori). "The book brought him immediate fame and recognition as the greatest living mathematician." (Kline). ?Horblit 28; Evans 9; Dibner 111; Sparrow 60; Norman 731."Starting with several problems solved by Johann and Jakob Bernoulli, Euler was the first to formulate the principal problems of the calculus of variations and to create general methods for their solution. In Methodus inveniendi lineas curvas he systematically developed his discoveries of the 1730’s (1739, 1741). The very title of the work shows that Euler widely employed geometric representations of functions as flat curves . Here he introduced, using different terminology, the concepts of function and variation and distinguished between problems of absolute extrema and relative extrema, showing how the latter are reduced to the former . (DSB). "In this book Euler extended known methods of the calculus of variations to form and solve differential equations for the general problem of optimizing single-integral variational quantities. He also showed how these equations could be used to represent the positions of equilibrium of elastic and flexible lines, and formulated the first rigorous dynamical variational principle." (Craig G. Fraser). "Basel had achieved enough glory in the history of mathematics through being the home of the Bernoullis, but she doubled her glory, when she produced LĂ©onard Euler." (Smith).Craig G. Fraser in: Landmarks Writings in Western Mathematics, chapter 12; Cajori, History of Mathematics, p. 234; Smith, History of Mathematics, pp. 520-21; Kline, Mathematical Thought from Ancient to Modern Times, p. 579. 4to (236 x 190 mm), pp. [2] [1] 2-322 [1] and five engraved folding plates. Contemporary calf, boards with some scratched, corners worn, capitals chipped, binding still firm and unrestored, internally fine and clean. [Attributes: First Edition] [Bookseller: SOPHIA RARE BOOKS]
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