St. Petersburg: Imprimerie de l'Académie Impériale des Scienes, 1752.
1st Edition. Soft cover. 4to - over 9¾ - 12" tall. Very Good. Item #003805
4to (239 x 205 mm).  6-92 pp., folding engraved plate bound at the end. Contemporary marbled paper wrappers (paper over spine with ca. 5 cm split and slightly chipped). Text with even light age-toning, unobtrusive faint dampstaining in places, small hole in blank fore-margin of leaf E2. Provenance: Bureau de Longitude (faint inkstamp to title page), small shelf-mark sticker on front wrapper. A very good, unsophisticated copy. ----
EXCEPTIONALLY RARE FIRST EDITION of Clairaut's epochal work on the lunar orbit, "the first approximate resolution of the three-body problem in celestial mechanics" (DSB). The treatment of the movement of the moon's apogee in Newton's Principia was deficient, with the result that doubts were cast on the validity of Newton's system as a whole. Clairaut, along with d'Alembert and Euler, sought to complete the analytical description. "In 1849 Clairaut established that the difference between theory and observation was due to the fact that he and others solving the corresponding differential equation had restricted themselves to the first approximation. When he calculated the second approximation, it was satisfactorily in accordance with the observed data. Euler did not at once agree. To put his doubts at rest, he advised the St. Petersburg Academy to announce a competition on the subject. Euler soon determined that Clairaut was right, and on Euler's recommendation, his composition received the prize of the Academy" (A.P. Youschkevitch in DSB IV under Euler).
The book is very rare. Athough there are 15 copies listed in OCLC/WorldCat, no other copy has sold at auction since 1936 according to RareBookHub.
References: Poggendorff I, 447; DSB III, p. 283; not in Norman; Honeyman 701 (2nd edition only). - Visit our website to see more images!
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