METHODUS INVENIENDI LINEAS CURVAS: Maximi Minimive proprietate gaudentes, sive Solutio problematis isoperimetrici latissimo sensu accepti.

4to, pp. [ii], 322, [1] avis au relieur, [1] blank; with five folding leaves of plates; engraved vignette on title, headpiece, and initial; some light dustsoiling and foxing, principally marginal, in places, and wormtrace to a couple of gatherings, not affecting text but touching the edge of Plate III; otherwise clean and fresh throughout; with the stamp of the Royal Society of Edinburgh on title, front pastedown, and front free endpaper; in contemporary calf, rebacked; spine in compartments with raised bands, ruled in gilt, and with title in gilt and the crest of the Royal Society of Edinburgh at foot; boards bordered in gilt; somewhat worn but sound.

First edition of Euler's pioneering work on the calculus of variations, which constitutes the founding text of that branch of mathematics.

Euler had explored the subject of the shortest line between two points on a surface in a 1732 article (De linea brevissima in superficie quacunque duo quaelibet puncta jungente) but there he addressed individual cases separately. It was only in the Methodus Inveniendi that he attempted a systematic approach to general problems. "As the birthyear of the theory of the calculus of variations one usually considers 1744, the year in which Euler published his famous book Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes, sive Solutio problematis isoperimetrici latissimo sensu accepti (A method for discovering curved lines that enjoy a maximum or minimum property, or the solution of the isoperimetric problem taken in its widest sense). Thus Euler replaced 'art of invention' (ars inveniendi), a very popular term in the works of Tschirnhaus and in other works of Leibniz's time, by 'method of invention', a remarkable turn toward systematization... Euler's book also contains a fascinating collection of 66 problems. Carathéodory, the editor of the book as a volume of Euler's Works, said that it 'is one of the most beautiful mathematical works ever written. We cannot emphasize enough the extent to which that Lehrbuch over and over again served later generations as a prototype in the endeavour of presenting special mathematical material in its [logical, intrinsic] connection.'" (Kreysig).

From the library of the mathematician and historian of mathematics Alex Craik F.R.S.E. (1938-2019), sometime president of the Edinburgh Mathematical Society.

Erwin Kreysig, 'On the Calculus of Variations and Its Major Influences on the Mathematics of the First Half of Our Century, Pt 1', American Mathematical Monthly 101, (1994), 674-8; DSB IV, p. 479.