278 SIR ISAAC NEWTON. 



withholding the publication of his method, no sooner was 

 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 

 favour of Leibnitz.* 



But undeniable though it be that Newton made the great 

 steps of this progress, and made them without any anticipa- 

 tion or participation by others, it is equally certain that there 

 had been approaches in former times, by preceding philo- 

 sophers, to the same discoveries. Cavalleri, by his ' Geometry 

 of Indivisibles,' (1635,) Eoberval, by his 'Method of Tan- 

 gents,' (1637,) had both given solutions which Descartes 

 could not attempt; and it -is remarkable that Cavalleri 

 regarded curves as polygons, surfaces as composed of lines, 

 whilst Eoberval viewed geometrical quantities as generated 

 by motion ; so that the one approached to the differential 

 calculus, the other to fluxions : and Fermat, in the interval 

 between them, came still nearer the great discovery by his 

 determination of maxima and minima, and his drawing of 

 tangents. More recently Schooten had made public similar 

 methods invented by Hudde ; and what is material, treating 

 the subject algebraically, while those just now mentioned had 

 rather dealt with it geometrically.']' It is thus easy to per- 



* Leibnitz first published his method in 1684 ; but he had communicated 

 it to Newton in 1677, eleven years after the fluxional process had been 

 employed, and been described in writing by its author. 



t Cavalleri's ' Exercitationes Geometries'' in 1647, as his 'Geometria 

 Indivisibilis ' in 1635, showed how near he had come to the calculus. 

 Fermat, however, must be allowed to have made the nearest approach ; 

 insomuch that Laplace and Lagrange have botli regarded him as its in- 

 ventor. He proceeds upon the position that when a Co-ordinate is a 

 maximum or minimum, the equation, formed on increasing it by an 

 infinitely small quantity, gives a value in which that small quantity 

 vanishes. He thus finds the subtangent. But perhaps his most remark- 



