La decouverte par le Dr. E. A. Fellmann de l'exemplaire des Principia Mathematica de Newton ayant appartenu a Leibniz et contenant des notes marginales manuscrites (datant vraisemblablement de 1689), apporte un temoignage direct de la premiere reaction de Leibniz devant l'oeuvre du savant anglais. La presente edition met le document original entre les mains du lecteur, en l'accompagnant des notes et commentaires objectifs indispensables (en allemand et en francais). Le rapport de Leibniz a Newton a souvent ete envisage dans le (...) cadre de la facheuse querelle de priorite dans l'invention du calcul differentiel et integral. Or Leibniz, prenant connaissance des Principia, n'y voit pas un traite purement mathematique: refusant d'enteriner la scission entre la mecanique et les lois de la pensee, il se soucie avant tout d'etablir une fondation metaphysique pour la dynamique. Les Marginalia ont l'originalite de nous presenter, non pas un Leibniz adversaire ou rival, mais un Leibniz lecteur de Newton, dispose a tirer le meilleur parti d'un systeme qui aurait pu, a bien des egards, lui sembler etranger, comme le confirmera la systemisation ulterieure du concept de vis visa. (shrink)

The conventional view of the prehistory of Newton's synthesis in the Principia of his predecessors' work in planetary theory and terrestrial gravitation is still not seriously changed from that which Newton himself chose to impose on his contemporaries at the end of his life. In his own words:‘… the same year ‘1666’ I began to think of gravity extending to ye orb of the Moon & having found out how to estimate the force wth wch [a] globe revolving within a (...) sphere presses the surface of the sphere from Keplers rule of the periodical times of the Planets being in a sesquialterate proportion of their distances from the centers of their Orbs, & having deduced that the forces wch keep the Planets in their orbs must [be] reciprocally as the squares of their distances from the centers about wch they revolve: & thereby compared the force requisite to keep the Moon in her Orb with the force of gravity at the surface of the earth, & found them answer pretty nearly …’. (shrink)

By a simple revision of Newton's diagram for Proposition 6 of the third edition of the Principia, one can see directly how the mathematics of uniform circular motion have been employed to solve the Kepler problem of elliptical planetary motion in Proposition 11. Newton strove initially to build his dynamics on the linear kinematics of Galileo; and, in this utilization of uniformly accelerated linear motion to solve more complicated problems, he can be seen as revolutionary. But he could not escape (...) completely from the coils of celestial circularity, and in his utilization of uniform circular motion to solve problems of elliptical motion, he can be seen as reactionary. The key to understanding Newton's mature dynamics resides in the discussion of the alternate dynamics ratio, as presented here in section six. (shrink)

Historians of seventeenth-century science have frequently asserted that Kepler's laws of planetary motion were largely ignored between the time of their first publication and the publication of Newton's Principia . In fact, however, they were more widely known and accepted than has been generally recognized.Kepler's ideas were, indeed, rather slow in establishing themselves, and until about 1630 there are few references to them in the literature of the time. But from then onwards, interest in them increased fairly rapidly. In particular, (...) the principle of elliptical orbits had been accepted by most of the leading astronomers in France before 1645 and in England by about 1655. It also received quite strong support in Holland.The second law had a more chequered history. It was enunciated in its exact form by a few writers and was used in practice by some others without being explicitly formulated, but the majority, especially after 1645, preferred one or another of several variant forms which were easier to use but only approximately correct. The third law attracted less interest than the others, chiefly perhaps because it had no satisfactory theoretical basis, but it was correctly stated by at least six writers during the period under review.Between about 1630 and 1650 Kepler's Epitome Astronomiae Copernicanae was probably the most widely read work on theoretical astronomy in northern and western Europe, while his Rudolphine Tables, which were based upon the first two laws, were regarded by the majority of astronomers as the most accurate planetary tables available.Kepler's work certainly did not receive all the recognition it deserved, but the extent to which it was neglected has been much exaggerated. (shrink)

Diese Schrift gehört zu den wichtigen Dokumenten der Naturphilosophie von Leibniz und seiner Zeit und stellt das einschlägige Dokument für die Synthese der Lehre von den einfachen Substanzen und derjenigen von den lebendigen Kräften dar.