Euler gave a formulation of the basic laws of mechanics where the requirements are in harmony. Usually, there is a difference between the syntactic structure and the logical structure of statements and statements composed of different (elementary) statements. The equivalence between the laws for rest and motion is demonstrated by (i) the equivalence of the syntactic and logical structure of these basic statements and (ii) by the same analytical form of the equation of motion (compare Sect. Lettres à une princesse d’Allemagne sur divers sujets de physique & de philosophie. L’autre proposition porte qu’un corps étant une fois en mouvement, conservera toujours éternellement ce mouvement avec la même direction et la même vîtesse, ou bien sera porté d’un mouvement uniforme suivant une ligne droite, à moins qu’il ne soit troublé par quelque cause externe ou étrangere.Ĭ’est en ces deux propositions que consiste le fondement de toute la science du Mouvement, qu’on nomme la Méchanique.” Euler. “Or on énonce communément ce principe par deux propositions, dont l’une porte, qu’un corps étant une fois en repos demeure éternellement en repos, à moins qu’il ne soit mis en mouvement par quelque cause externe ou étrangere. Euler maintained this procedure in correlating the “impenetrability of bodies and the liberty of spirits” Euler. Obviously, Euler presupposed the whole set of Descartes’ substances to define the subject of mechanics. ![]() So lange aber die Körper von einander entfernt, so verhindert keiner, dass die Uebrigen nicht in ihrem Zustande, verharren könnten.” Euler. Wenn wir also in der Welt nichts als Körper betrachten, so ist klar, dass ein jeder Körper so lange in seinem Zustande verbleiben muss, als sich von aussen keine Ursache ereignet, welche vermögend ist, in demselben eine Veränderung zu wirken. “Hier werden diejenigen Veränderungen mit Fleiss ausgeschlossen, welche unmittelbar von Gott oder einem Geiste hervorgebracht werden. Euler excluded those changes in the motion of bodies which are caused by spirits or by God. This process is experimental and the keywords may be updated as the learning algorithm improves.įollowing Descartes, the properties of bodies and the specific relation between bodies are explicitly distinguished from the properties of spirits by Euler. These keywords were added by machine and not by the authors. ![]() The comparison of Euler’s Mechanics (1736) and Du Châtelet’s Institutions (1740) does not only promote a deeper understanding of their legacy and importance in the eighteenth century science, but discloses additionally an interesting parallelism to the history of physics between 19, the hour of birth of the quantum mechanics and the theory of relativity Keywords Du Châtelet attempted to synthesize Newtonian and Leibnizian principles. Euler initiated a program for mechanics that ends up in an almost complete substitution of the geometrical methods by analysis and extremal principles. Both scholars were searching for a solution beyond the competing schools. ![]() The focal point of the present contribution is the analysis of the scientific programs of Euler and Du Châtelet that appeared in this context. ![]() The challenge and the goal were to clarify the relations between these three competing paradigms of mechanics. In the first half of the eighteenth century, the development of analytical mechanics was dominated by the reception and interpretation of the legacy of Descartes, Newton and Leibniz culminating in controversial debates on the fundamental principles endorsed by the adherents of different schools.
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