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That Newton cannot be ranked in this respect with those extraordinary per- 

 sons is owing to the accidents which prevented him from entering upon 

 mathematical study before his eighteenth year; and then a much greater 

 marvel was wrought than even the Clairants and the Pascals displayed. 

 His earliest history is involved in some obscurity, and the most celebrated 

 of men has, in this particular, been compared to the most celebrated of 

 rivers (the Nile), as if the course of both in its feebler state had been con- 

 cealed from mortal eyes. We have it, however, well ascertained, that within 

 four years, between the ages of eighteen and twenty-two, he had begun to 

 study mathematical science, and had taken his place among its greatest mas- 

 ters; learnt for the first time the elements of geometry and analysis, and 

 discovered a calculus which entirely changed the face of the science, effect- 

 ing a complete revolution in that and in every branch of philosophy con- 

 nected with it. Before 1661, he had not read "Euclid;" in 1665, he had 

 committed to writing the method of fluxions. At twenty -five years of age, 

 he had discovered the law of gravitation, and laid the foundation of celestial 

 dynamics, the science created by him. Before ten years had elapsed, he 

 added to his discoveries that of the fundamental properties of light. So 

 brilliant a course of discovery in so short a time, changing and reconstruct- 

 ing analytical, astronomical, and optical science, almost defies belief. The 

 statement could only be deemed possible by an appeal to the incontestable 

 evidence that proves it strictly true. By a rare felicity these doctrines gained 

 the universal assent of mankind as soon as they were clearly understood ; 

 and their originality has never been seriously called in question. Some 

 doubts having been raised respecting his inventing the calculus doubts 

 raised in consequence of his so long withholding the publication of his 

 method no sooner was the inquiry instituted than the evidence produced 

 proved so decisive that all men in all countries acknowledged him to have 

 been, by several years, the earliest inventor, and Leibnitz, at the utmost, the 

 first publisher; the only questions raised being, first, whether or not he had 

 borrowed from Newton ; and next, whether, as second inventor, he could 

 have any merit at all, both which questions have long since been decided 

 in favor of Leibnitz. But undeniable though it be that Newton made the 

 great steps of this progress, and made them without any anticipation or 

 participation by others, it is equally certain that there had been approaches 

 in former times by preceding philosophers to the same discoveries. Caval- 

 Icri, by his Geometry of Indivisibles (1635), Roberval, by his method of 

 Tangents (1367), had both given solutions which Descartes could not 

 attempt ; and it is remarkable that Cavalleri regarded curves as polygons, 

 surfaces as composed of lines, while Roberval viewed geometrical quantities 

 as generated by motion ; so that the one approached to the differential calcu- 

 lus, the other to fluxions ; and Format, in the interval between them, comes 

 still nearer the great discovery by his determination of maxima and minima, 

 and his drawing of tangents. More recently Hudden had made public simi- 

 lar methods invented by Schoetin; and what is material, treating the sub- 

 ject algebraically, while those just now mentioned had rather dealt with it 

 geometrically. It is thus easy to perceive how near an approach had been 

 made to the calculus before the great event of its final discovery. There 

 had in like manner been approaches made to the law of gravitation, and the 

 dynamical system of the universe. Galileo's important propositions on 

 motion, especially on curvilinear motion, and Kepler's laws upon the ellipti- 

 cal form of the planetary orbits, the proportion of the areas to the times, 



