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First editions of both the work outlining what is now known as d'Alembert's Principle, and its much lengthier companion volume, published a year later and rarely found together. The Traité de dynamique, "d'Alembert's magnum opus, was one of the first to give a unified view of mechanics. It started out from a minimum of principles, one of which came to be named after him" (Landmark Writings in Western Mathematics). The Principle states that the internal force of inertia must be equal and opposite to the forces that produce acceleration. "D'Alembert's Principle seems to have been recognized before him by A. Fontaine, and in some measure by Johann Bernoulli and I. Newton. D'Alembert gave it a clear mathematical form and made numerous applications of it. It enabled the laws of motion and the reasonings depending on them to be represented in the most general form, in analytical language" (Cajori, p. 242). The principle is based on the three laws of motion that d'Alembert presents earlier in this work, the law of inertia, the parallelogram of motion, and the law of equilibrium and the conservation of momentum; "he actually assumed the conservation of momentum and defined mass accordingly. This fact was what made his work a mathematical physics rather than simply mathematics' (DSB). This work was the foundation for Lagrange's classic book on analytical mechanics which codified the laws governing the motions of any systems of bodies. d'Alembert is also credited with laying to rest, in the Traité, the vis viva controversy by investigating its philosophical basis and dismissing its ontological reality. 'In this way d'Alembert was clearly a precursor of positivistic science'" (ibid.). In the companion volume, Traité de l'équilibre et du mouvement des fluides, d'Alembert uses his principle to describe fluid motion and mechanics. His treatment was an alternative to that already published by Daniel Bernoulli in his Hydrodynamica (1738), and d'Alembert often arrives at the same conclusion. Cajori, A History of Western Mathematics, p. 242; En Français dans le Texte 147; Landmark Writings in Western Mathematics pp. 159-167; Norman 31 and 33; Parkinson p. 159; Printing and the Mind of Man 195; Poggendorff I, col. 28; Roberts and Trent p. 7; Roller and Goodman I, p. 26; Trente livres de mathématiques qui ont changé le monde, pp. 193-201. Two works bound in a single vol., quarto (213 x 162 mm). With 4 folding engraved plates in first work, 10 folding plates in second work. Contemporary speckled calf, rebacked preserving parts of the original spine, spine with raised bands, decorated in gilt in compartments, red morocco label, blindstamp rule border to boards, marbled endpapers and edges. Early 19th-century book label of J. B. Tailhand to front pastedown, early signature to initial binder's blank, and early inscription to title page with an annotation below the imprint "c'est un tribut rendu aux connoissances et pas moins aux qualités du coeur de Monsieur." folded in. Binding firm with light rubbing, corners restored, darkening to rear cover, sporadic light browning and foxing, all folding plates without tears with a few plate numbers a little cropped, light damp staining in upper inner margin towards end of second work with terminal binder's blank and rear free endpaper loosening a little at head. Very good copies.
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