JURIN V. ROBINS AND PEMBERTON 119 



use of the words ** perpetually " and ** endlessly," 

 ''the last difference," are again discussed at length. 

 Jurin quotes from Robins a passage which appears 

 to show that " Mr. Robins is now of opinion, that 

 Sir Isaac's demonstration is appHcable to such 

 quantities, as at last become actually equal, as well 

 as to quantities, which only approach without Hmit 

 to the ratio of equaHty " (p. 6"]) ; therefore, the 

 lemma, ''by Mr. Robins's own confession, may be 

 taken in the sense 1 have always understood it in " 

 (p. 68). However, this is in direct conflict with 

 Robins's earlier assertions. In the discussion about 

 the inscribed rectangles, both Robins and Jurin 

 agree that if the * ' base of the curve " (our abscissa) 

 be continually subdivided as in Euclid I io or V 

 IO, it is manifest ''that such subdivision can never 

 be actually finished " (p. 78) ; but Newton proceeds 

 difìferently — he supposes a line to be described by a 

 moving point. Jurin thereupon repeats exactly the 

 argument in Zeno's " Dichotomy," though he does 

 not mention Zeno, to show that a point moving 

 across the page in, say, one hour passes over i / 2 

 of the distance, then over i / 4 of it, then over 

 1/8, i / 16, etc. , and insists that "ali the possible 

 subdivisions of the line " will be " actually finished " 

 and " brought to a period at the end of the 

 hour." This is given in support of bis previous 

 argument that the rectangles inscribed in a curve 

 may reach the limit. " If Mr. Robins will teli me, 

 that the imagination cannot pursue these parallelo- 

 grams to the very end of the hour, I may ask him, 



