BERKELEY'S ANALYST (1734) 75 



98. Berkeley justifies his use of the expression 

 '' increment of a rectangle " by quoting from Newton 

 (our § 1 7), " rectanguli incrementum aB -\-òA." 



'* You say ' you do not consider AB as lying at 

 either extremity of the moment, but as extended 

 to the middle of it ; as having acquired the one 

 half of the moment, and as being about to acquire 

 the other ; or, as having lost one half of it, and 

 being about to lose the other.' Now, in the name 

 of truth, I entreat you to teli what this moment 

 is, . . . Is it a finite quantity, or an infinitesimal, 

 or a mere limit, or nothing at ali ? . . . If you 

 take it in either of the two former senses, you con- 

 tradict Sir Isaac Newton. And, if you take it in 

 either of the latter, you contradict common sense ; 

 it being plain that what hath no magnitude, or is 

 no quantity, cannot be divided " (§ 30). 



"... You observe that the moment of the 

 rectangle determined by Sir Isaac Newton, and the 

 increment of the rectangle determined by me are 

 perfectly and exactly equal, supposing a and ò to 

 be diminished ad infiniiurn : and, for proof of this, 

 you refer to the first lemma of the first section of 

 the first hook of Sir Isaac's Principles. I answer 

 that if a and /; are real quantities, then ab is some- 

 thing, and consequently makes a real difference : 

 but if they are nothing, then the rectangles 

 whereof they are coefficients become nothing like- 

 wise : and consequently the monientuvi or ina-e- 

 mentuni, whether Sir Isaac's or mine, are in that 

 case nothing at ali. As for the above-mentioned 



