136 LIMITS AND FLUXIONS 



Quadratura Curvarum^ " Philalethes cannot remove 

 my objection by straining one or two of the words 

 to fit his sense " ; Newton meant there that vanish- 

 ing quantities should not he ''otherwise than finite 

 quantities" (p. 157). Moreover, " what kind of 

 nothings they must he, which with any propriety can 

 be said to pass into somethings, and for this reason 

 can be capable of bearing proportions, before they are 

 become anything, certainly requires explanation." 



A reply by Jurin in The Works of the Learned 

 for March, 1637, is kept within the very moderate 

 compass of io pages. The title of his contribution 

 is The Contents of Dr. Pemberton's Observations pub- 

 lished the last month. Nothing bere is of interest 

 in the interpretation of Newton. 



Dr. Pemberton's reply in the Aprii issue refers to 

 Jurin's phrase, *'they come nearer to equality than 

 to bave any assignable difference between them " : 

 *' My objection to the interpretation of Philalethes 

 [in the Minute Mathematician, p. 88] is, that these 

 words, which compose the third article of that inter- 

 pretation, in conjunction with the fourth article can 

 have no other signification, than that the quantities 

 come nearer to equality than to have any difference 

 between them before that point of time, wherein 

 they are supposed by the second article to become 

 equal ; ali which amounts to this inconsistency, 

 that there is a time, when the quantities have no 

 difference, and yet are not equal " (p. 306). Dr. 

 Pemberton again gives his endorsement of Robins's 

 interpretation of Newton. 



