[Émilie du CHÂTELET]. Alexis-Claude CLAIRAUT... - Lot 21 - Conan Belleville Hôtel d'Ainay

Lot 21
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[Émilie du CHÂTELET]. Alexis-Claude CLAIRAUT... - Lot 21 - Conan Belleville Hôtel d'Ainay
[Émilie du CHÂTELET]. Alexis-Claude CLAIRAUT (1713-1765), mathematician. Autograph manuscript, also annotated by Jean-Jacques DORTOUS de MAIRAN, who has inscribed at the top: "minute de l'écrit ajouté à la feuille de la Rép. précédente par M. Clairaut". 1 p. ½ in-4. [Le Tremblay, 22 September 1738]. Reply to Emile du Châtelet on the march of the rays of light in the atmosphere, annotated by Dortous de Mairan who added a sketch in the margin. It follows the previous batch. "I have just taken away from Mr de Mairan this answer that he wanted to insert in the letter of Mr Dufay []. It is with great reason that you wish to draw him into the Newtonian doctrine []. As for me, I do not join my efforts to yours, because I do not consider him at all as an enemy of Mr. Newton, on the contrary, he accepts all that he has proven. As for the cycloid which was the subject of your dispute, without going into the physical cause of refraction, it seems to me, as it does to Mr. de Mairan, that it is not the shortest line in this case. I will remind you as much as I can of the property of the cicloid by which it is the line of the fastest descent. If a body descends along a cicloid AB, experiencing at each point M the impulses of gravity, that is, having at each instant a velocity proportional to the root of the height PM, this body arrives from A to B by the shortest possible time. Does it follow from this that every time a body travels through a cycle it will be in the shortest time? []. This does not happen in the case of the corpuscle of light that travels through the atmosphere, at least, I have no reason to suspect it. I also believe that M. Bernouilli only found the cicloid for solar energy in a hypothesis of a particular density of the atmosphere, which perhaps does not occur in nature [] ". Provenance : former collection of Baron de Trémont, sale of December 9, 1852 (n°437).
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