296 A SHORT HISTORY OF SCIENCE 



pernicus, Newton might never have published it but for the for- 

 tunate urgency of a faithful disciple, Edmund Halley. 



NEWTON'S MATHEMATICS : FLUXIONS. Newton's services to 

 mathematics itself were not less original and momentous than 

 to celestial mechanics. 



His extraordinary abilities . . . enabled him within a few years to per- 

 fect the more elementary . . . processes, and to distinctly advance 

 every branch of mathematical science then studied, as well as to create 

 several new subjects. There is hardly a branch of modern mathe- 

 matics which cannot be traced back to him and of which he did not 

 revolutionize the treatment. 



In pure geometry Newton did not establish any new methods, 

 but no modern writer has ever shown the same power in using those 

 of classical geometry, and he solved many problems in it which had 

 previously baffled all attempts. In algebra and the theory of equa- 

 tions he introduced the system of literal indices, established the bi- 

 nomial theorem . . ., and created no inconsiderable part of the theory 

 of equations. ... He always by choice, avoided using trigonometry 

 in his analysis, ... In analytical geometry he introduced the 

 modern classification of curves into algebraical and transcendental; 

 and established many of the fundamental properties of asymptotes, 

 multiple points and isolated loops. He illustrated these by an ex- 

 haustive discussion of cubic curves. Ball. 



Newton's greatest mathematical achievement was of course the 

 invention of the fluxional or infinitesimal calculus. In his Treatise 

 of the Method of Fluxions and Infinite Series he says : 



1. Having observed that most of our modern Geometricians 

 neglecting the synthetical Method of the Ancients, have applied 

 themselves chiefly to the analytical Art, and by the Help of it have 

 overcome so many and so great Difficulties, that all the Speculations 

 of Geometry seem to be exhausted, except the Quadrature of Curves, 

 and some other things of a like Nature which are not yet brought to 

 Perfection : To this End I thought it not amiss, for the sake of young 



to acquire and maintain it : it would perhaps increase my acquaintance, the thing 

 which I study chiefly to decline." Again in 1675 he writes "I was so persecuted 

 with discussions arising out of my theory of light, that I blamed my own impru- 

 dence for parting with so substantial a blessing as my quiet, to run after a shadow." 



