132 LTMITS AND FLUXIONS 



been used by bis antagonist ? " If bis argument 

 is sound, " it will bold against my expression, 

 tbat tbe figures inscribed and circumscribed do at 

 last coincide witb tbe curviHnear figure." Jurin 

 claims '*tbat if Mr. Robins's interpretation of tbe 

 first Lemma be admitted, Sir Isaac's demonstra- 

 tions, as tbey now stand, will not be accurate, nor 

 geometrically rigorous," for, " as tbey now stand, 

 tbe examples be bas given in tbe several Lemmata 

 of tbe first Section, are of sucb quantities and 

 ratio's only, as do actually arrive at tbeir respective 

 limits" (pp. (42) and (43)). '' Mr. Robins and I 

 bave been disputing some time, wbetber Sir Isaac 

 Newton used indivisibles. Tbat Gentleman main- 

 tains tbat be used tbem ; and grounds bis ebarge 

 upon tbe term infinitely little^ wbicb is sometimes to 

 be met witb in Sir Isaac Newton's writings : but be 

 does not explain tbe meaning of tbat term, wben 

 used eitber by Sir Isaac, or by tbe writers of indi- 

 visibles. I, on tbe contrary, distinctly explain 

 wbat I apprebend to be meant by it, botb wben 

 used by Sir Isaac Newton, and wben used by tbe 

 writers of indivisibles. ... I supposed tbe writers 

 upon indivisibles, by an infinitely little quantity, 

 to mean a quantity actually existing, fixed, deter- 

 minate, invariable, indivisible, less tban any finite 

 quantity wbatsoever " (p. {JZ)). Robins quotes 

 Pascal and Barrow as using tbe term indefinite in 

 place of infinite^ but tbe writers I quoted use infinite 

 and infinitely little. Tbere is difference of usage 

 among followers of Cavalieri. '' It is not denied, 



