traité dynamique loix lequilibre mouvement von alembert jean rond (2 Ergebnisse)

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.

First edition. "A LANDMARK IN THE HISTORY OF DYNAMICS" (PMM) [BOUND WITH:] THE BIRTH OF SCIENTIFIC METEOROLOGY . First edition of one of the classics in the history of science, d'Alembert's formalization of the new science of mechanics. "The 'Treatise on Dynamics' was d'Alembert's first major book and it is a landmark in the history of mechanics. It reduces the laws of the motion of bodies to a law of equilibrium. Its statement that 'the internal forces of inertia must be equal and opposite to the forces that produce the acceleration' is still known as 'd'Alembert's principle'. This principle is applied to many phenomena and, in particular, to the theory of the motion of fluids. It has become useful in the practical solution of many technical and mechanical problems, and is as important for the motion of bodies as is the principle of virtual velocities for their equilibrium the latter formulated by Johann Bernoulli in 1717. It was left to Lagrange to combine both these principles and to construct mechanical equations applicable to the motions of any system of bodies" (Printing and the Mind of Man, 195). "In the first part of the treatise Alembert developed his own three laws of motion: inertia, the parallelogram of motion, and equilibrium; his third law assumed conservation of momentum and defined mass accordingly. The second part contains the first statement of what is now known as 'Alembert's principle' (Norman). "The Traité de dynamique, which has become the most famous of his scientific works, is significant in many ways. First, it is clear that d'Alembert recognized that a scientific revolution had occurred, and he thought that he was doing the job of formalizing the new science of mechanics The Traité also contained the first statement of what is known as d'Alembert's principle. D'Alembert was, furthermore, in the tradition that attempted to develop mechanics without using the notion of force. Finally, it was long afterward said (rather simplistically) that in this work he resolved the famous vis viva controversy (whether, in modern terms, it is momentum or kinetic energy that measures the 'quantity of motion'), a statement with just enough truth in it to be plausible" (DSB). The second work, in which d'Alembert laid the foundations of scientific meteorology, is an application of the methods set out in the Traité de dynamique. He rejected the conception of Edmund Halley that the general circulation of the atmosphere is significantly controlled by the distribution of solar heating, and instead explained the origin of winds by means of the gravitational effects of the sun and moon. "In 1747 d'Alembert published two more important works, one of which, the Réflexions sur la cause générale des Vents, won a prize from the Prussian Academy. In it appears the first general use of partial differential equations in mathematical physics. Euler later perfected the techniques of using these equations D'Alembert's treatise on winds was the only of his works honored by a prize and, ironically, was later shown to be based on insufficient assumptions. D'Alembert assumed that wind patterns were the result of tidal effects on the atmosphere, and he relegated the influence of heat to a minor role, one that caused only local variations from the general circulation. Still, as a work on atmospheric tides it was successful, and Lagrange continued to praise d'Alembert's efforts many years later" (DSB). "This was the first attempt to express the motions of the atmosphere in mathematical terms; a new fruitful trend in meteorology" (Persson). "The [Traité de dynamique] was published in 1743 by David, the great bookselling and printing house, presented to the Académie des Sciences on 22 June and given a favourable review by the commissioners P. L. Maupertuis and F. Nicole. It includes a letter to Count de Maurepas, a 26-page preface summarizing and commenting on the main general ideas, and finally the body of the text with all its trimmings (table of contents, plates, corrections, extract from the records of the Académie des Sciences, royal favour). "Contrary to the author's current custom, the book is clearly structured. Following the definitions and preliminary notions (pp. 12), the first Part is entitled 'General laws of motion and equilibrium of bodies' (pp. 348). It consists of three chapters, each of which is subdivided into articles numbered continuously. These chapters represent the three great principles on which dynamics is based: I. 'On the force of inertia' (arts. 2 20); II. 'On composite motion' (arts. 2126); III. 'On motion destroyed or changed by obstacles' (arts. 2749). This last chapter contains, in particular, the theory of equilibrium. "The second Part, which is much larger (pp. 49186), is entitled 'A general principle for finding the motion of many bodies that act on each other in an arbitrary way, with many applications of this principle'. It consists of four chapters of disparate length and status: I. 'Exposition of the principle' (art. 50); II. 'Properties of the centre of gravity of many bodies combined, deduced from the preceding principle' (arts. 5172); III. 'Problems illustrating the application of the preceding principle' (arts. 73153); IV. 'On the principle of conservation of live forces' (arts. 154175). What is today called 'D'Alembert's principle' constitutes the single article of Chapter I. The rest of the second Part consists of what the author calls 'applications' "'D'Alembert's principle' (Chapter I of Part II) plays a pivotal role in the book: Part I paves the way for it and Chapters IIIV of Part II consist of applications. Moreover, it is this principle that posterity has universally accepted as one of D'Alembert's main contributions to science" (Crépel, pp. 161-3). "It was not so much a principle as it was a rule for using the previously stated laws of motion. It can be summarized as follows: In any situation where an object is constrained from following its normal in.