84 LIMTTS AND FLUXJONS 



says Jurin, is defined by Newton as ''nascent 

 increment, " its magnitude is " utterly unassignable." 

 Jurin continues : 



105. " You seem much at a loss to conceive how 

 a nascent increment, a quantity just beginning to 

 exist, but not yet arrived to any assignable 

 magnitude, can be divided or distinguished into 

 two equal parts. Now to me there appears no 

 more difficulty in conceiving this, than in appre- 

 hending how any finite quantity is divided or dis- 

 tinguished into halves. For nascent quantities may 

 bear ali imaginable proportions to one another, as 

 well as finite quantities." 



106. Near the dose Jurin enters upon the dis- 

 cussion of Berkeley's Lemma, given in the Analyst : 

 " If one supposition be made, and be afterwards 

 destroy'd by a contrary supposition, then everything 

 that followed from the first supposition, is destroyed 

 with it." Not so, says Jurin, when the supposition 

 and its contradiction are made at different times. 

 ''Let US imagine yourself and me to be debating 

 this matter, in an open field, ... a sudden violent 

 rain falls . . . we are ali wet to the skin . . . it 

 clears up . . . you endeavour to persuade me I 

 am not wet. The shower, you say, is vanished 

 and gone, and consequently your . . . wetness 

 . . . must bave vanished with it. " You say that 

 your explanation of the correctness of results as 

 due to a compensation of crrors, was intended by 

 you to apply, not to Newton, but to Marquis de 

 l'Hospital ; your statements werc such that not I 



