78 LIMITS AND FLUXIONS 



multiplied by something ; and, if so, . . . when ab 

 is nothing, whether Ab-\-V>a be not also nothing ? 

 ì.e. whether the momentum of AB be not nothing? 

 Let him then be asked, what his momentums are 

 good for, when they are thus brought to nothing ? 

 . . . I wish he were asked to explain the differ- 

 ence between a magnitude infinitely small and a 

 magnitude infinitely diminished. . . . Let him be 

 farther asked, how he dares to explain the method 

 of Fluxions, by the Ratio of magni tudes infinitely 

 diminished, when Sir Issac Newton hath expressly 

 excluded ali consideration of quantities infinitely 

 small? If this able vindicator should say that 

 quantities infinitely diminished are nothing at ali, 

 and consequently that, according to him, the first 

 and last Ratio's are proportions between nothings, 

 let him be desired to make sense of this. . . . If 

 he should say the ultimate proportions are the 

 Ratio's of mere limits, then let him be asked how 

 the limits of lines can be proportioned or divided ? " 



Walton's Second Reply to Berkeley 



lOi. In a second reply ^ to Berkeley, Walton 

 States that in the Appendix to the Defence^ Berkeley 

 "has composed a Catechism which he recommends 

 to my Scholars " and which Walton quotes. I am 

 first to be asked, " Whether I can conceive Velocity 

 without Motion, or Motion without Extension. . . . 



^ J. Walton, Catechism of the Author of the Minute Philosopher 

 FuUy answer'd. Printed at Dublin. Reprinted at London, and sold 

 by J. Roberts, 1735. It is a pamphlet of 30 pages. 



