The discoveries of Johann Kepler and Bonaventura Cavalieri were the foundation upon which Sir Isaac Newton and Gottfried Wilhelm Leibnitz erected that wonderful edifice, the Infinitesimal Calculus.
Really, we first experience that particular causes have particular effects; then induce that causes similar to those have effects similar to these; finally, deduce that when a particular cause of the kind occurs it has a particular effect of the kind by synthetic deduction, and that when a particular effect of the kind occurs it has a particular cause of the kind by analytic deduction with a convertible premise, as when Newton from planetary motions, like terrestrial motions, analytically deduced a centripetal force to the sun like centripetal forces to the earth.
Probably there was as much foundation for this legend as for the more rationalistic explanation of William Newton (Display of Heraldry, p. 145), that the fleur-de-lis was the figure of a reed or flag in blossom, used instead of a sceptre at the proclamation of the Frankish kings.
In 1646 he is found in partnership with two other deprived clergymen, keeping a school at Newton Hall, in the parish of Llanvihangel-Aberbythych, Carmarthenshire.
He knew indeed that before Newton had announced the inverse law Hooke and Wren and himself had spoken of it and discussed it, and therefore justice demanded that, though none of them had given a demonstration of the law, Hooke especially should receive credit for having maintained it as a truth of which he was seeking the demonstration.
But, as Newton charmingly puts it (Diet.
On the 12th of February 1689, the day of the coronation of William and Mary, Newton intimated to the vicechancellor that he would soon receive an order to proclaim them at Cambridge.
In Newton Upper Falls, Echo Bridge (of the Boston Aqueduct) crosses the Charles near the falls in Hemlock Gorge Reservation of the Metropolitan Park system.
Xxiv., from which it was copied and reprinted in the Ada Eruditorum (1707), and also in the Memoirs of the Academy of Sciences at Paris; General Laws of Nature and Motion (1705), a work which is commended by Wolfius as illustrating and rendering easy the writings of Galileo and Huygens, and the Principia of Newton; An Institution of Fluxions, containing the First Principles, Operations, and Applications of that admirable Method, as invented by Sir Isaac Newton (1706).
Dr Bentley, the master of Trinity College, had for a long time urged Newton to give his consent to the republication of the Principia.