266 LIMITS AND FLUXIONS 



227. As another objection to limits, or prime 

 and ultimate ratios, Woodhouse declares that * ' the 

 method is not perspicuous, inasmuch as it considers 

 quantities in the state, in which they cease to be 

 quantities." 



Moreover, "the definition of a limit, is neither 

 simple nor concise" (p. xvii). ' ' The name of Berkeley 

 has occurred more than once in the preceding pages : 

 and I cannot quit this part of my subject without 

 commending the Analyst and the subsequent pieces, 

 as formlng the most satisfactory controversial dis- 

 cussion in pure science, that ever yet appeared : into 

 what perfection of perspicuity and of logicai pre- 

 cision, the doctrine of fluxions may be advanced, is 

 no subject of consideration : But, view the doctrine 

 as Berkeley found it, and its defects in metaphysics 

 and logie are clearjy made out. If, for the purpose 

 of habituating the mind to just reasoning ... I 

 were to recommend a book, it should be the Analyst.'' 

 "The most diffuse and celebrated antagonists of 

 Berkeley, are Maclaurin and Robins, men of great 

 knowledge and sagacity : but the prolixity of their 

 reasonings confirms the notion, that the method they 

 defend is an incommodious one. " 



" Landen, I believe, first considered and proposed 

 to treat the fluxionary calculus merely as a branch of 

 Algebra : After him, M. Lagrange, a name ever to 

 be celebrated, in the Berlin Acts for 1772, laid 

 down its analytical principles ; and subsequently in 

 his Théoric des fo7ictio)is mialytiques^ 1796, he has 

 resumed the subject : in this treatise, the author 



