By Gérard A. Maugin
Conceived as a chain of roughly independent essays, the current e-book seriously exposes the preliminary advancements of continuum thermo-mechanics in a publish Newtonian interval extending from the artistic works of the Bernoullis to the 1st international struggle, i.e., approximately in the course of first the “Age of cause” and subsequent the “Birth of the fashionable world”. The emphasis is rightly put on the unique contributions from the “Continental” scientists (the Bernoulli kinfolk, Euler, d’Alembert, Lagrange, Cauchy, Piola, Duhamel, Neumann, Clebsch, Kirchhoff, Helmholtz, Saint-Venant, Boussinesq, the Cosserat brothers, Caratheodory) in pageant with their British friends (Green, Kelvin, Stokes, Maxwell, Rayleigh, Love,..). It underlines the most breakthroughs in addition to the secondary ones. It highlights the position of scientists who left crucial prints during this historical past of medical rules. The publication indicates how the bold advancements that blossomed within the 20th century (and perused in a prior booklet of the writer within the related Springer sequence: “Continuum Mechanics throughout the 20th Century”, Springer 2013) came across wealthy compost within the optimistic foundational achievements of the eighteenth and 19th centuries. The pre-WWI scenario is easily summarized by way of a radical research of treatises (Appell, Hellinger) released at the moment. English translations through the writer of most crucial texts in French or German are given to the advantage of the readers.
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Extra info for Continuum Mechanics Through the Eighteenth and Nineteenth Centuries: Historical Perspectives from John Bernoulli (1727) to Ernst Hellinger (1914)
1) is replaced by a linear relationship (a linear vector relation in the language of Gibbs 3 The reader will be interested in Truesdell’s vision of Cauchy’s elaboration of the concept of stress in his Essay ‘‘The creation and unfolding of the concept of stress’’ in pp. 184–238 in Truesdell  (this was underlined by J. Casey, private communication). However, in contrast to the present study that emphasizes the story of the concept of stress from and after Cauchy, Truesdell deals with the conceptual stages that led to Cauchy’s notion of stress, with works by brilliant predecessors such as Stevins, Galileo Galilei, the Bernoullis, d’Alembert, Euler, Young, and Fresnel.
132]) and using no argument of geometry. He is even proud of the fact that no figures illustrate his exposition (although a few illustrations may have been welcomed). Lagrange in fact introduced a privileged tool for the ‘‘algebraïzation’’ of Mechanics. The second important point is that Lagrange, after some previous works by Clairaut  and Maupertuis  but above all with his introduction of generalized coordinates, really inaugurates an era where the recognition of invariance in mathematical physics has become fundamental.
In what follows I shall call motion of a body [here he means a point] the velocity of this same body considered on account of its direction, and call quantity of motion, in the ordinary sense, the product of mass by velocity. General problem. — Let a system of bodies be disposed in any manner with respect to one another, and let us suppose that we impose to each of these bodies a particular motion that it cannot follow because of the action exerted by other bodies: find out the motion that each body will take.