To the first edition of Newton’s Optics, which appeared in 1704, there were added two mathematical treatises, entitled, _Tractatus duo de speciebus et magnitudine figurarum curvilinearum_, the one bearing the title of _Tractatus de Quadratura Curvarum_, and the other _Enumeratio linearum tertii ordinis_. The first contains an explanation of the doctrine of fluxions, and of its application to the quadrature of curves; and the second a classification of seventy-two curves of the third order, with an account of their properties. The reason for publishing these two tracts in his Optics (in the subsequent editions of which they are omitted) is thus stated in the advertisement:—“In a letter written to M. Leibnitz in the year 1679, and published by Dr. Wallis, I mentioned a method by which I had found some general theorems about squaring curvilinear figures on comparing them with the conic sections, or other the simplest figures with which they might be compared. And some years ago I lent out a manuscript containing such theorems; and having since met with some things copied out of it, I have on this occasion made it public, prefixing to it an introduction, and joining a scholium concerning that method. And I have joined with it another small tract concerning the curvilineal figures of the second kind, which was also written many years ago, and made known to some friends, who have solicited the making it public.” In the year 1707, Mr. Whiston published the algebraical lectures which Newton had, during nine years, delivered at Cambridge, under the title of _Arithmetica Universalis, sive de Compositione et Resolutione Arithmetica Liber_. We are not accurately informed how Mr. Whiston obtained possession of this work; but it is stated by one of the editors of the English edition, that “Mr. Whiston thinking it a pity that so noble and useful a work should be doomed to a college confinement, obtained leave to make it public.” It was soon afterward translated into English by Mr. Ralphson; and a second edition of it, with improvements by the author, was published at London in 1712, by Dr. Machin, secretary to the Royal Society. With the view of stimulating mathematicians to write annotations on this admirable work, the celebrated S’Gravesande published a tract, entitled, _Specimen Commentarii in Arithmeticam Universalem_; and Maclaurin’s Algebra seems to have been drawn up in consequence of this appeal. Among the mathematical works of Newton we must not omit to enumerate a small tract entitled, _Methodus Differentialis_, which was published with his consent in 1711. It consists of six propositions, which contain a method of drawing a parabolic curve through any given number of points, and which are useful for constructing tables by the interpolation of series, and for solving problems depending on the quadrature of curves.