Lausanne & Geneva: Marci-Michaelis Bousquet, 1742. First edition.
An exceptionally fine and complete copy with both the portraits which often lack, from the collection of Robert Honeyman. “Bernoulli published only one book, Théorie de la manoeuvre des vaisseaux (1714) and apart from this, his dissertation De motu musculorum (1694) and one or two minor pieces, all his work was contributed to journals (189 papers are collected here) or were first published in these volumes, i.e. 59 of his lectures and the Hydraulica in volume IV [appearing here for the first time in print], which was written in competition with his son Daniel.” (Roger Gaskell).
❧Honeyman 293 (this copy, sold for $1,500 in 1978); Norman 217; Stanitz 55; Arnoud de Vitry 55.
“The first volume is primarily devoted to problems in geometry and the early calculus, but also contains papers on muscular mechanics, the resistance of solids, and a geometrical demonstration of the motion of pendulums and projectiles in resisting and unresisting media. Volumes two and three are almost totally devoted to problems of mechanics, the first of these containing his theoretical essay on the maneuvering of vessels and related papers, as well as numerous contributions on the analysis of trajectories. His discourse on the laws governing the communication of movement opens volume three, which also contains his essay on celestial mechanics. The last volume contains contributions on the curvature of elastic plates, his mechanico-dynamical propositions, and problems in dynamics. Most important, its appearance in this volume represents the first printing of the Hydraulica, which was written in competition with his son, Daniel.
“Johann Bernoulli ‘proposed the problem of the brachystochrone (the Bernoullis’ term - the curve of quickest descent joining two points), to which Galileo had given an incorrect solution: he solved it himself (the answer is the cycloid) in 1697. It is due to his work on this problem and that of finding the curve of given perimeter which will enclose the greatest area that he is considered one of the founders of the calculus of variations. He is also remembered for his work on the exponential calculus; on geodesics; on complex numbers; and his treatment of trigonometry as a branch of the calculus.’ (DSB). He also first enunciated the principle of virtual work and was the first to denote the accelerating effect of gravity by the sign g, thus arriving at the formula v square equals 2gh. Todhunter and Pearson note Bernoulli’s treatment of the cause of elasticity in his Discours sur les loix de la communication du movement (1727) and his theory of ‘captive aether.’ Timoshenko remarks on his formulation of the principle of virtual displacements in a letter to Varignon.” (Bibliotheca Mechanica).
4 volumes 4to (247 x 196 mm) . Fully complete: vol. I: pp.  [i] ii-xxiv, [1-2] 3-563 [1:blank], title in red and black, 25 engraved plates, including a portrait of Frederick III of Prussia engraved by G.F. Schmidt, a portrait of Bernoulli by Schmidt after J. Ruber, and 23 folding engraved plates numbered i-xxiii; vol. II: pp. , [1-3] 4-620, 17 folding engraved plates numbered xxiv-xl; vol. III: pp. , [1-3] 4-563 [1:blank], 36 folding engraved plates numbered xli-lxxvi; vol. IV: [1-5] 6-588, 15 folding engraved plates numbered lxxvii-xci. Provenance: with gilt red morocco ex-libris of Robert Honeyman to front paste down of each volume. A very fine and completley unrestored set, housed in four fine custom half red morocco cases.