![]() Republished in: Leonhardi Euleri Opera Omnia (Societatis Scientiarum Naturalium Helveticæ, Geneva, 1912), serie secunda, v. Euler, Mechanica sive motus scientia analytice exposita, 1736. This principle is first deduced in the earlier Mechanica L. 152.] Euler calls it the “principle of mechanics”. Euler, Mémoires de l’Académie des Sciences de Berlin 7, 169 (1751), republished in Ref. In all these papers, the equations follow from the same dynamic premise in Harmonie L. 152.], Euler derives equations for (modern terminology) analytical mechanics. ![]() Euler, Mémoires de l’Académie des Sciences de Ber(1748), republished in Ref.2, p. 81-108.], Euler derives three differential equations (one for each coordinate) to describe the motion of a (modern terminology) point mass in modern notation, this is the equation F → = m d 2 r → d t 2. Fleckenstein (Societatis Scientiarum Naturalium Helveticæ, Geneva, 1957), p. Euler, Mémoires de l’Académie des Sciences de Berlin 6, 185 (1750), republished in Leonhardi Euleri Opera Omnia, serie secunda, v. Euler, Mémoires de l’Académie des Sciences de Berlin 3, 93 (1747), republished in Commentationes Astronomicæ Leonhardi Euleri Opera Omnia (Societatis Scientiarum Naturalium Helveticæ, Geneva, 1960), serie secunda, v. The case study is Leonhard Euler's “principle of mechanics”: in the absence of a general dynamic, some premise has to play a dynamic role the paper is a search for the dynamic premise in the “principle of mechanics”. In this paper, a case study is used to investigate the foundations of the laws of motion. Tackling foundations questions “at large” risks to conflate approaches that are conceptually distinct, and to neglect mathematical calculations that not only clarify, but in many cases give meaning to ideas. ![]() ![]() However, the fashion among historians is the historiography of science: relations among scientists - as expressed in citations, similarity of methods and research, and their social interaction - are searched for, therefrom writing a description “at large” of the flux and transformation of ideas as necessary as it may be, the mere description of facts cannot account for those specific arguments that make an idea appealing to a particular individual, and for it being fruitful. But there is no conceptual analysis without an archive of facts, which sets a context that defines the background or arena where scientists and science dwell. Many (if not all) questions about the foundations of physics require conceptual analysis, i.e., discussion of the necessity of a concept in a given context of categories, of the meaning of concepts, of the way a problem is stated and its relation to available mathematical tools, etc. This is better done in case studies, by analyzing arguments rather than pertinence to general contexts 1 1 The history of physics provides elements for an analysis of the foundations of physics: it discloses arguments (whether logical or empirical), questions for whose solution some category is proposed, clarify concepts, showing the “whys and wherefores” and the “hows”. This paper is broadly speaking a search for the arguments on which the categories of dynamic are founded for instance: why is mechanics written in the language of mathematics? why are the laws expressed by differential equations? why are these second order in time? what is the physical meaning of the energy T - V (the meaning must be very important, because from it the equations are obtained)? The list is huge.
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