Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes, sive Solutio problematis isoperometrici latissimo sensu accepti.
Lausanne & Geneva: Marc-Michel Bousquet, 1744.
1st Edition. Hardcover. 4to - over 9¾ - 12" tall. Very Good. Item #003720
4to (239 x 186 mm). , 322,  pp., including initial blank and final leaf of binder's instructions, title page printed in red and black with engraved vignette, woodcut head-piece and initial, 5 folding engraved plates bound at end. Contemporary mottled calf, spine with 5 raised bands gilt-decorated and gilt-lettered in compartments, red-dyed edges, original endpapers (minor soiling and rubbing of leather, upper board with loss of small patch of leather, lower spine partially chipped, wormtracks to inner boards and final flyleaf). Light even browning of text leaves, occasional minor spotting, light pale dampstaining to several pages, plates a bit more browned, a few wormholes to final two plates. Provenance: Charles François de Bicquilley* (wet stamp on title verso). Still a crisp and clean copy despite the light dampstaining. ----
FIRST EDITION. With the publication of this work, the calculus of variations came into being as a new branch of mathematics. Leonhard Euler (1707-1783) was "one of the most prolific and versatile mathematicians and founder of modern fluid dynamics. In the above book he presented his calculus of variations, derived from his studies of isoperimetrical curves, a method for finding the variation when the values of some or all the expressions are varied" (Dibner).
"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" (D.S.B.). 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" (DSB).
*Charles François de Bicquilley (1738-1814), French mathematician, author of a treatise on the calculation of probabilities and a pioneering work on mathematics applied to economics. Both Euler and Bicquilley won the Academy Grand Prize. Pages 208 and 211 contain faint ink corrections of equations, possibly by Bicquilley.
References: Horblit 28; Dibner 111; Sparrow 60; Norman 731; Roberts & Trent 104; Eneström, Die Schriften Eulers, 65; DSB IV, p.479. - Visit our website to see more images!
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