Will Ladislaw's words, which so disillusion the young Dorothea, might also depress the modern interpreter of Newton's theology. Encountering the bulk of Newton's manuscript theology, it is tempting to sympathize with Dorothea's eventual response toThe Key to all Mythologies, and to want nothing of it. The assessment of John Conduitt, Newton's son-in-law and executor, that his ‘relief and amusement was going to some other study, as history, chronology, divinity, and chemistry’ has in the past provided an ample excuse for those (...) who have wished to take such a course, and to ignore Newton's biblical criticism. In the last three decades, however, Newton scholarship has come to terms with its hero's twilight activities, and reclassified them as being at least as important to him as the natural philosophy of thePrincipia, and intimately bound up with the thinking behind that philosophy. But although many modern scholars are now reluctant to see Newton as Stephen Hawking in breeches, historians of science have tended to concentrate on the implications for Newton's philosophy of his religious and alchemical writings, and in the process often have distorted their religious context. Historians of ideas have been beguiled by Newton's disciples, and by the esoteric texts from Newton's library, to ride hobbyhorses of their own which do not always illuminate Newton's reasons for writing theology. There is a danger of ‘knowing what is being done by the rest of the world’ before troubling with what Newton was up to when he worried about religion and theology, channelling his energies into treatise after treatise on the interpretation of prophecy. I want to suggest what some of Newton's concerns may have been, by looking at his ideas of religious duty and of the Church, and to liberate Newton from his disciples for long enough to consider some of his ideas about the relationships of prophetic and natural philosophical explorations of divinity. (shrink)

Johann Bernoulli in 1710 affirmed that Newton had not proved that conic sections, having a focus in the force centre, were necessary orbits for a body accelerated by an inverse square force. He also criticized Newton's mathematical procedures applied to central forces in Principia mathematica, since, in his opinion, they lacked generality and could be used only if one knew the solution in advance. The development of eighteenth-century dynamics was mainly due to Continental mathematicians who followed Bernoulli's approach rather than (...) Newton's. The ways of thinking of the British Newtonians have, therefore, been somewhat forgotten. This paper is an attempt to assess what Bernoulli was criticizing and what were the immediate reactions of the Newtonians. In particular, I will concentrate on two papers by John Keill, submitted to the Royal Society in 1708 and 1714, in which the results on central forces achieved by the British were summarized and their methods defended. (shrink)

Comment caractériser les méthodes de démonstration mathématique utilisées dans les Principia de Newton? Ni géométrie à l'antique ni véritable «calcul différentiel», le raisonnement s'appuie sur les figures, mais en supposant qu'elles bougent et se déforment. Les situations infinitésimales sont traitées comme stade ultime de configurations finies, grâce à certains procédés de représentation (témoins finis de l'infinitésimal). Le temps intervient sous deux modes différents dans ces procédés. Les exemples sont pris dans les lemmes de la section I (proportions ultimes) et dans (...) la démonstration de la proposition 48-49 du livre I (rectification de l’épicycloïde). (shrink)