the impulse of water, the maximum of effect takes place when the velocity of the wheel is one third of the velocity of the current. Mem. de l'Ac. 1704. We find several other very ingenious ideas in his -numerous writings; but he had commonly the defect of being obscure, which greatly injured his reputation. This fault he acknowledged himself. The celebrated Fontenelle, whom I had the honour of knowing in his latter years, and whose kindness to me I remember with gratitude, told me one day, that, as secretary to the Academy of Sciences, he once made an abstract of a paper of Parent's, who was astonished to find his ideas so clearly expressed in it, and thanked him in the following words: Domine, illuminasti tenebras meas. Father Malebranche very ingeniously described the obscurity of this geometrician: Mr. Parent,' said he, has a great deal of sense, but he wants the key to unlock it.' " Varignon enjoyed a very high reputation, for which he was indebted to his post of mathematical professor at the Mazarin college, and his faculty of expressing his ideas with perspicuity, though his style was loose, incorrect, and diffuse. He was thoroughly destitute of genius; and we do not find he resolved one of the grand problems of the day: but he was gifted with an excellent memory, read much, turned over again and again the works of inventors, generalized their methods, made their ideas his own, and some of his pupils took the treasures of his memory, either disguised or amplified, for discoveries. He published a treatise On general Mechanics, in. which he applies the principle of the parallelogram of forces forces to the laws of equilibrium with clearness and precision. The memoirs of the Academy of Sciences abound with calculations of his of every kind. Our chief obligation to him is for having illustrated several passages in the Principia: in the present day he would have commented on Euler and d'Alembert. Saurin wrote much less than Varignon, but his mind was far stronger, and approached nearer to the true genius of invention. By the few mathematical performances we have of his it is fair to presume, that he would have raised himself to the first rank, had he begun the study of geometry at an early period, and applied himself to a particular branch. In the memoirs of the Academy for 1709 he gave a very elegant general solution of the problem, in which it is required, among an infinite number of similar curves, described in the same vertical plane, having the same axis, and originating from the same point, to determine that, of which the arc, comprised between the point of origin and a straight or curved line of a given position, is passed through in the shortest time possible. He is the first, who fully elucidated the theory of tangents to the multiple points of curves. See Mem. de l'Ac. 1716, 1723, 1727. His knowledge, both theoretical and practical, in every part of clock and watch making was also very profound, as appears by the two papers he sent to the Academy of Sciences on this subject in 1720 and 1722. All these able men, and many others of an inferiour order, united in promoting the progress of the method of fluxions. A warfare, which had silently fermented for several years, and at length burst out with violence in A a 3 in 1711, respecting the claims to prior invention of this method, at first gave reason to apprehend, that the time, which should have been spent in it's improvement, would be wasted in controversy; but these very discussions themselves proved advantageous to the science. This dispute has made too much noise, and is even still an object in which curiosity is tou highly interested, for me to dispense with giving. an account of it. I shall endeavour, therefore, to discuss the question, and to elucidate it with more care, than has yet been done. CHAP. CHAP. V. An Examination of the Claims of Leibnitz and Newton to the Invention of the Analysis of Infinites. THE HE productions of genius being of an order infinitely superiour to all other objects of human ambition, we need not be surprised at the warmth, with which Leibnitz and Newton disputed the discovery of the new geometry. These two illustrious rivals, or rather Germany and England, contended in some respects for the empire of science. The first spark of this war was excited by Nicholas Facio de Duillier, a genevese retired to England; the same who afterward exhibited a strange instance of madness, by attempting publicly to resuscitate a dead body in St. Paul's church, but who was at that time in his sound senses, and enjoyed some reputation among geometricians. Urged on the one hand by the english, and on the other by personal resentment against Leibnitz, from whom he professed not to have received the marks of esteem he conceived to be his due, he thought proper to say, in a little tract on the curve of swiftest descent, and the solid of least resistance,' which appeared in 1699, that Newton was the first inventor of the new calculus; that he Isaid this for the sake of truth and his own conscience; and that he left to others the task of deterA a 4 mining mining what Leibnitz, the second inventor, had borrowed from the english geometrician. Leibnitz, justly feeling himself hurt by this priority of invention ascribed to Newton, and the consequence maliciously insinuated, answered with great moderation, that Facio no doubt spoke solely on his own authority; that he could not believe it was with Newton's approbation; that he would not enter into any dispute with that celebrated man, for whom he had the profoundest veneration, as he had shown on all occasions; that, when they had both coincided in some geometrical inventions, Newton himself had declared in his Principia, that neither had borrowed any thing from the other; that, when he published his differential calculus in 1684, he had been masterof it about eight years; that about the same, time, it was true, Newton had informed him, but without any explanation, of his knowing how to draw tangents by a general method, which was not impeded by irrational quantities; but that he could not judge whether this method were the differential calculus, since Huygens, who at that time was unacquainted with this calculus, equally affirmed himself to be in possession of a method, which had the same advantages; that the first work of an english writer, in which the differential calculus was explained in a positive manner, was the preface to Wallis's Algebra, not published till 1693; that, relying on all these circumstances, he appealed entirely to the testimony and candour of Newton, &c. The assertion of Facio, being altogether destitute of proof, was forgotten for several years. In 1708, |