ALEMBERT, Jean le Rond d'.

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Traité de dynamique, 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 credite

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