237 

 Newtonian Idea of the Calculus. 



Arthur S. Hathaway. 



The history of the calculus shows that even a mathematical theory 

 cnuiiot escape the effects of environment. Sir Isaac Newton was for 

 many years the sole possessor of a knowledge of the calculus, and 

 used it with a power which few have been able to equal since his time; 

 yet he has had practically no intiuence on its present form of de- 

 velopment. This was due to Newton's dislike for controversy, so that 

 instead of contending for his ideas, he let them appear only in con- 

 cise and general form, or even not at all. With the exception of his 

 first two papers on optics, "all of his works were published only after 

 the most persistent solicitations of his friends, and against his own 

 wishes." The criticism which would have aroused an ambitious man to 

 a vigorous defense, had the opposite effect on his disposition. "I was 

 so persecuted." he wrote, "with discussions arising out of my theory of 

 light, that I blamed my own imprudence for parting with so substantial 

 a blessing as my quiet to run after a shadow." 



Newton was well versed in the method of fluxions, and the in- 

 verse method, that is in differentiation and integration, by the year 

 1(>G6. In 1G(!9 he circulated a manuscript on the subject among his 

 friends, but refused their solicitations to have it published, and it was 

 not until 1003 that it was communicated to the scientific world by 

 Wallis. in the .second volume of his works. During this interval of a 

 quarter of a century, Newton had changed his ideas in Important 

 respects, through extensive use of the calculus. He had developed his 

 Theory of Light, discovered the Binomial Theorem, determined the Law 

 of Gravitation, and the I'rinciples of Dynamics, and made important in- 

 vestigations in all departments of mathematical and physical science. 



Although the Prineipia, which appeared in 1G87, contained no direct 

 information on the calculus, yet its fundamental ideas and principles 

 were involved in every detail of the work. The development of the 

 Prineipia is due to the calculus, but NcAvton undertook the laborious 

 task of translating everything into the elementary geometrical methods 

 of the time and omitted many results which he had obtained by the 

 calculus, because he could not so interpret them. Many things have 

 been discovered since his time that were afterwards found in his papers 



