In June, 1709, Newton intrusted the superintendence of a second edition of the PRINCIPIA to Roger Cotes, Plumian Professor of Astronomy at Cambridge. The first edition had been sold off for some time. Copies of the work had become very rare, and could only be obtained at several times their original cost. A great number of letters passed between the author and Mr. Cotes during the preparation of the edition, which finally appeared in May, 1713. It had many alterations and improvements, and was accompanied by an admirable Preface from the pen of Cotes. Our author's early Treatise, entitled, ANALYSIS PER EQUATIONES NUMERO TERMINORUM INFINITAS, as well as a small Tract, bearing the title of METHODUS DIFFERENTIALIS, was published, with his consent, in 1711. The former of these, and the Treatise De Quadratura Curvarum, translated into English, with a large commentary, appeared in 1745. His work, entitled ARTIS ANALYTICÆ SPECIMINA, VEL GEOMETRIA ANALYTICA, was first given to the world in the edition of Dr. Horsley, 1779. [Pg 48] It is a notable fact, in Newton's history, that he never voluntarily published any one of his purely mathematical writings. The cause of this unwillingness in some, and, in other instances, of his indifference, or, at least, want of solicitude to put forth his works may be confidently sought for in his repugnance to everything like contest or dispute. But, going deeper than this aversion, we find, underlying his whole character and running parallel with all his discoveries, that extraordinary humility which always preserved him in a position so relatively just to the behests of time and eternity, that the infinite value of truth, and the utter worthlessness of fame, were alike constantly present to him. Judging of his course, however, in its more temporary aspect, as bearing upon his immediate quiet, it seemed the most unfortunate. For an early publication, especially in the case of his Method of Fluxions, would have anticipated all rivalry, and secured him from the contentious claims of Leibnitz. Still each one will solve the problem of his existence in his own way, and, with a man like Newton, his own, as we conceive, could be no other than the best way. The conduct of Leibnitz in this affair is quite irreconcileable with the stature and strength of the man; giant-like, and doing nobly, in many ways, a giant's work, yet cringing himself into the dimensions and performances of a common calumniator. Opening in 1699, the discussion in question continued till the close of Leibnitz's life, in 1716. We give the summary of the case as contained in the Report of the Committee of the Royal Society, the deliberately weighed opinion of which has been adopted as an authoritative decision in all countries.