BERNOULLI, (JOHANN). (+) NICOLAS (NIKOLAUS) BERNOULLI. - VIS-VIVA CONTROVERSY

Extrait D'une Lettre de M. Bernoulli, écrite de Basle 10. Janvier 1711, touchant la maniere de trouver les forces centrales dans des milieux resistans en raisons composée de leurs densites & des puissances quelques des vitesses du mobile. (+) Addition. (by Nicolas Bernoulli)

(Paris, L'Imprimerie Royale, 1714). 4to. Without wrappers. Extracted from "Mémoires de l'Academie des Sciences. Année 1711". Pp. 47-53 a. pp. 53-56 (Nicolas).

First appearance of an importent paper in mathematical physics. Bernoulli had shown that the principle of virtual velocities could be shown in analytical form. The principle can be derived from the energy principle and he applied this principle several times to mechanical systems of central forces. For these forces he applied the vis viva equation to the inverse two-body problem. For the corresponding problem of centrally accelerated motion in resisting medium he solved the differential equations and determined the central force in accordance with the Huygens formula(in the paper offered). - The Addenda by his his nephew, Nicolas Bernoulli, best known for the fundamental work "Ars Conjectandi" from 1713.

Order-nr.: 44748