"Toward the end of the year 1704, Newton gave to the World in one volume his Optics in english, an enumeration of lines of the third order, and a treatise on the quadrature of curves, both in latin. ...the treatise on quadratures, belongs to the new geometry. The particular object of this treatise is the resolution of differential formulæ of the first order, or of a single variable quantity; on which depends the precise, or at least the approximate, quadrature of curves. With great address Newton forms series, by means of which he refers the resolution of certain complicated formulæ to those of more simple ones; and these series, suffering an interruption in certain cases, then give the fluents in finite terms. The development of this theory affords a long chain of very elegant propositions, where among other curious problems we remark the method of resolving rational fractions, which was at that time difficult, particularly when the roots are equal. Such an important and happy beginning makes us regret, that the author has given only the first principles of the analysis of differential equations. It is true he teaches us to take the fluxions, of any given order, of an equation with any given number of variable quantities, which belongs to the differential calculus: but he does not inform us, how to solve the inverse problem; that is to say, he has pointed out no means of resolving differential equations, either immediately, or by the separation of the indeterminate quantities, or by the reduction into series, &c. This theory however had already made very considerable progress in Germany, Holland, and France, as may be concluded from the problems of the catenarian, isochronous, and elastic curves, and particularly by the solution which James Bernoulli had given of the isoperimetrical problem. Newton's opponents have argued from his treatise on quadratures, that, when this work appeared, the author was perfectly acquainted only with that branch of the inverse method of fluxions which relates to quadratures, and not with the resolution of differential equations. Newton almost entirely melted down the treatise of Quadratures into another entitled, the Method of Fluxions, and of Infinite Series. This contains only the simple elements of the geometry of infinite, that is to say, the methods of determining the tangents of curve lines, the common maxima and minima, the lengths of curves, the areas they include, some easy problems on the resolution of differential equations, &c. The author had it in contemplation several times to print this work, but he was always diverted from it by some reason or other, the chief of which was no doubt, that it could neither add to his fame, nor even contribute to the advancement of the higher geometry. In 1736, nine years after Newton's death, Dr. Pemberton gave it to the world in english. In 1740 it was translated into french, and a preface was prefixed to it, in which the merits of Leibnitz are depreciated so excessively, and in such a decided tone as might impose on some readers, if the writer of this preface Buffon] had not sufficiently blunted his own criticisms, by betraying how little knowledge of the subject he possessed."