BERKELEY'S ANALYST (1734) ^l 



consider the proportion or ratio of things implies 

 that such things have magnitude ; that such their 

 magnitudes may be measured " (§31). . . . 



83. " If it be said that fluxions may be expounded 

 or expressed by finite lines proportional to them ; 

 which finite lines, as they may be distinctly con- 

 ceived and known and reasoned upon, so they may 

 be substitutpd for the fluxions, ... I answer that 

 if, in order to arrive at chese finite Hnes proportional 

 to the fluxions, there be certain steps made use of 

 which are obscure and inconceivable, be those 

 finite lines themselves ever so clearly conceived, it 

 must nevertheless bc acknowledged that your pro- 

 ceeding is not clear nor your method scientific " 



(§ 34). 



Berkeley discusses this matter with reference to 

 a geometrie figure, and argues that "a point there- 

 fore is considered as a triangle, or a triangle is 

 supposed to be formed in a point. Which to con- 

 ceive seems quite impossible " (§ 34). . . . 



84. " And what are these fluxions ? The Veloci- 

 ties of evanescent increments. And what are these 

 same evanescent increments ? They are neither 

 finite quantities, nor quantities infinitely small, nor 

 yet nothing. May we not cali them the ghosts of 

 departed quantities ?"(§ 35). . . . 



" And if the first [fluxions] are incomprehensible, 

 what shall we say of the second and third fluxions, 

 etc.?"(§44). 



" To the end that you may more clearly com- 

 prehend the force and design of the foregoing 



