BERKELEY' S ANALYST (1734) 59 



the remaining difìference will be à^-\-bh. There- 

 fore the increment of the rectangle generateci by 

 the entire increments « and <^ is <3:B + ^A. Q.E.D. 

 But it is plain that the direct and true method to 

 obtain the moment or increment of the rectangle 

 AB, is to take the sides as increased by their whole 

 increments, and so multiply them together, A+<a: by 

 B + <^, the product whereof AB + ^B + ^^A + ^(^ is the 

 augmented rectangle ; whence, if we subduct AB 

 the remainder à^ -\- b i^ -\- ab will be the true incre- 

 ment of the rectangle, . . . and this holds uni- 

 versally by the quantities a and b be what they 

 will, big or little, finite or infinitesimal, increments, 

 moments, or velocities " (§ 9). . . . The point of 

 getting rid of ab cannot be obtained by legitimate 

 reasoning. " . . . 



'jj, "The points or mere limits of nascent lines 

 are undoubtedly equal, as having no more magnitude 

 one than another, a limit as such being no quantity. 

 If by a momentum you mean more than the very 

 initial limit, it must be either a finite quantity 

 or an infinitesimal. But ali finite quantities are 

 expressly excluded from the notion of a momentum. 

 Therefore the momentum must be an infinitesimal. 

 . . . Por aught I see, you can admit no quantity 

 as a medium between a finite quantity and nothing, 

 without admitting infinitesimals " (§ 11). 



78. Berkeley next premises the following lemma, 

 which figures prominently in the debates about 

 fluxions : 



" ' If, with a view to demonstrate any proposition, 



