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E shall now, as the conclusion of our history for

the reign of queen Anne, notice the literary and philosophical career of a few more of our countrymen ; who

, as we have seen, ranked very high among the learned, at this period, in the annals of Science. Sir Isaac Newton, with whom we concluded our last part of the History of Knowledge, towards the close of the year 1704, published, at the end of his Optics, his “ Enumeratio Linearum tertiæ Ordinis," and his treatise “De Quadratura Curvarum.” The first of these papers displays great ability, but is founded only on common algebra, and the doctrine of series, which the author had already brought to great perfection. The treatise “De Quadratura Curvarum contains the resolution of fluxional formulæ, with one variable quantity which leads to the quadrature of curves. By means of certain series he obtained the resolution of certain complicated formulæ, by referring them to such as are more simple; and these series being interrupted in particular cases give the fluent in finite terms. From this he deduced among other things the meb'



thod of resoiving rational fractions. In 1711 Newton pub. lished his “Method of Fluxions.” The object of this work is to determine, by simple algebra, the linear coefficients of an equation that satisfies as many conditions as there are co. efficients, and to construct a curve of the parabolic kind passing through any number of given points. The mathematical sciences were at this time indebted to foreigners as well as to Englishmen for a vast extension of their boundaries. Manfredi, professor of mathematics at Bologna. published a very learned work entitled “De Constructione Iguationum differentialium primi Gradus." He was author of other treatises, which did him high honour as a philosop'er and mathematician. Anthony Parent, a native of Paris, resolved about the same period the famous problem by which we obtain the ratio between the velocity of the power, and the weight, for finding the maximum effect of machines : and Joseph Saurin was celebrated for his theoretical and practical knowledge of watch-making, and was the first who elucidated ihe theory of

tangents to the multiple points of curves. While the sci. ence of analysis was thus rapidly advancing, the dispute between Newton and Leibnitz began to be agitated among the mathematicians of Europe. Ilitherto these illustrious rivals seemed to have been contented with sharing the honour of having invented the fiuxional calculus; but as soon as the priority of the discovery was attributed to Newton, the friends of Leibnitz came forward with eagerness in support of the claims of their master. In a small work on the curve of the swiftest descent, and the solid of the least resistance, de Duillier, an eminent mathematician of Genoa, attributed to Newton the invention of fluxions, and hinted that Leibnitz had borrowed his principles from the English philosopher. Exasperated at this insination, Leibnitz came forward in his own defence, and appealed to the adınissions of Newton in his Principia, that neither had borrowed from the other. Here the matter seeined to rest, till Dr. Keill, whom we shall have occasion shortly to refer to more at large, instigated by an attack upon Newton in the Leipsic Journal, repeated the same charge against Leibnitz. In 1711 he addressed a letter to sir Hans Sloane, secretary to the Royal Society, and ac


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