264 LTMITS AND FLUXIONS 



whole, in such dose agreement with those advanced 

 in the preceding reviews, that the query naturally 

 arises, whether Woodhouse is not the author of 

 those reviews. We have reached no final decision 

 on this point. 



In the preface Woodhouse passes in review the 

 difìferent methods of establishing the foundations of 

 the calculus. He criticises the use of motion in the 

 proof of the binomial and other related theorems. 

 '' It required no great sagacity to perceive, that a 

 principle of motion, introduced to regulate processes 

 purely algebraical, was a foreign principle." If the 

 binomial theorem and related theorems for the 

 development of a function be established by algebra, 

 independently of motion, then * * from the second 

 term of this expansion, the fluxion or differential of 

 a quantity may be immediately deduced, and in a 

 particular application, it appears to represent the 

 velocity of a body in a motion. The fluxionists 

 pursue a method totally the reverse ; they lay down 

 a principle of motion as the basis of their calculus, 

 thence deduce some of the first processes, and 

 establish the binomial theorem, by which it is said, 

 the extraction of roots may be effected. . . . The 

 project of extracting the square and cube roots of 

 algebraical quantities by a principle of motion, is 

 surely revolting to the common sense." 



** Of his own method. Newton left no satisfactory 

 explanation : those who attempted to explain it, 

 according to what they thought the notions of its 

 author, and . . . by reasoning which fairly may be 



