Opening a new branch of mathematics

EULER, Leonhard.

Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes, sive Solutio problematis isoperometrici latissimo sensu accepti.

Lausanne & Geneva: Marc-Michel Bousquet, 1744.

1st Edition. Hardcover. Very Good. Item #002404

4to (236 x 189 mm). [4], 322, [2] 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 (plate IV misbound after plate V). Contemporary full calf, spine with 5 raised bands richly gilt in compartments and with red morocco label titled in gilt, red sprinkled edges (extremities little rubbed, top spine repaired, corners bumped). Light browning of text leaves, some worming to inner margin not affecting text, occasional light spotting of outer margins, bibliographic pencil notations to first free endpaper. Provenance: L. Jose Luiz de Souza (signed on title page).
Horblit 28; Dibner 111; Sparrow 60; Norman 731; Roberts & Trent 104; Enestrom 65; D.S.B. IV, p.479. 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" (D.S.B.).

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