10 December 1999
EULER, Leonhard (1707-1783). Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes, sive Solutio problematis isoperometrici latissimo sensu accepti. Lausanne and Geneva: Marc-Michel Bousquet, 1744.
4o (239 x 190 mm). Title printed in red and black with engraved vignette, 5 folding engraved plates, woodcut head-piece and initial. (Marginal staining to first 2 leaves, light dampstaining throughout.) Late 18th-century half calf and speckled paper boards, edges red-sprinkled (rubbed, head of spine chipped).
FIRST EDITION. The Methodus contains Euler's researches in a branch of mechanics-related mathematical science that he founded, the calculus of variations. "Starting with several problems posed 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" (DSB). Of equal significance for the development of mechanical science is the first of two appendices, in which Euler applied the calculus of variations to several problems in the theory of elasticity. "In this appendix, which was in fact the first general work on the mathematical theory of elasticity, Euler studied bending and vibrations of elastic bands... and of a plate under different conditions... and deduced the famous Euler buckling formula, or Euler critical load, used to determine the strength of columns" (ibid.). Dibner Heralds of Science 111; Grolier/Horblit 28; Norman 731; Roberts & Trent pp. 104-5.
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