By Gerard G. Emch
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Additional resources for Algebraic Methods in Statistical Mechanics and Quantum Field Theory (Physics & Astronomical Monograph)
E. D. -L. Lagrange (1788), Méchanique analitique, 1st Edition, Veuve Desaint, Paris (1788) [after the reprint of the second revised edition of 1811/1815 with new title ‘‘Mécanique analytique’’ in two volumes, Veuve Courcier, Paris; reprinted by Gabay, Paris, 1997, from the fourth edition edited by J. Bertand and G. Darboux] by Gérard Maugin. Translator’s remarks are placed within square brackets in the main text. This is a verbatim translation without any ambition of literary prowess. P 10 [on the principle of composition of forces] ……… The second fundamental principle of statics is that of the composition of forces.
We shall expose this formula in its whole extent: we shall even try to present it in an even more general manner than done until now, and give of it new applications. As to the nature of the principle of virtual velocities, we must agree with the opinion that it is not sufficiently obvious by itself to be erected as a primary principle, but we can view it as the general expression of equilibrium, deduced from the previously mentioned two principles. …………. PP 223-224 [on d’Alembert’s dynamics and other principles of dynamics] ………….
Concerning the proofs of these principles in themselves, the scheme I have followed to grant them all the clarity and simplicity that they likely deserve, has always been to deduce them from the consideration of the motion alone [this indicates the marked preference of d’Alembert for kinematics over the notion of forces], viewed in the simplest and clearest manner. All that we perceive distinctly well in the motion of a body is that it traverses a certain space and it takes a certain time to achieve this.
Algebraic Methods in Statistical Mechanics and Quantum Field Theory (Physics & Astronomical Monograph) by Gerard G. Emch