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Demonstratio constructionis editae in Actis Lips. 1724 M. Jul. pro describenda Trajectoria reciproca, quae inter omnes algebraicas possibiles sit simplicissima [Johann B.] (+) Esplanatio Notationum suarum [Daniel B.].
Leipzig, Grosse & Gleditsch, 1725. 4to. In: ""Acta Eruditorum Anno MDCCXXV"". The entire volume offered in contemporary full vellum. Hand written title on spine. A yellow label pasted on to top of spine. Two small stamps to title-page and free front end-paper. Library label to pasted down front free end-paper. As usual with various browning to leaves and plates. [Johann Bernoulli's paper:] Pp. 318-25"" [Daniel Bernoulli's paper:] Pp. 470-474. [Entire volume: (2), 54, (37) pp. + five engraved plates.].
First printing of two paper's by father and son: Johann and Daniel Bernoulli. Daniel Bernoulli paper is a solution to the Riccati-equation: ""Using the first of the two transformations in [The Riccati-equation], Bernoulli succeded in constructing solutions of ""an inifinite number"" of Riccati equations for those values of n for which a solution can be expressed in finite terms. Bernoulli published these solutions in Acta Eruditorum for 1725 [the present paper]. (Greenberg. The problem of the earth's shape from Newton to Clairaut. P. 573).The offered volume contains many other papers by influential contemporary mathematicians, philosophers and historians.
(BERNOULLI, JEAN (JOHANN) & BERNOULLI, DANIEL. - THE MECHANICS OF THE HEAVENS.
Reference : 42459
(1735)
Essai d'une nouvelle Physique celeste. Servant à expliquer les principaux Phenomenes du Ciel, & en particulier la cause physique de l'inclinaison des Orbites des Planetes par rapport au plan de l'Equateur du Soleil. Qui a partagé le Prix doub...
Paris, Imprimerie Royale, 1735. 4to. Fine recent marbled boards. Printed titlelabel on frontcover. (6),144 pp. and 1 double-page folded engraved plate. Johann B's paper: pp. (1-) 91. - Daniel B's papers: pp. (93-) 122 and pp. 123-144. A few marginal brownspots.
First edition of these prize winning papers by father (Jean) and son (Daniel). - Both papers deals with the cause of the inclination of the planetary orbits relative to the solar equator. - In Daniel's paper he put foreward the hypothesis of the existence of an atmosphere, resempling air, and rotating around the solar axis, resulting in an increasing inclination of the planetary orbits toward the equator of the sun. Daniel was the first importent Newtonian outside Great Britain. The problems faced here (by Daniel) are treated in Newtonian manner.The publication of these papers by father and son resulted in a controversy between the two, forcing Daniel to leave his fathers house. - Poggendorff I:161.
