JURIN V. ROBINS AND PEMBERTON 113 



of his objections against this doctrine [of fluxions], 

 found it necessary to represent the idea of fluxions 

 as inseparably connected with the doctrine of 

 prime and ultimate ratios, intermixing this plain 

 and simple description of fluxions with the terms 

 used in that other doctrine, to which the idea of 

 fluxions has no relation : and at the same time 

 by confounding this latter doctrine with the 

 method of Leibniz and the foreigners, has proved 

 himself totally unskill'd in both. These two 

 methods of Sir Isaac Newton are so absolutely 

 distinct, that their author had formed his idea of 

 fluxions before his other method was invented, and 

 that method is no otherwise made use of in the 

 doctrine of fluxions, than for demonstrating the 

 proportion between different fluxions. For, in Sir 

 Isaac Newton's words [see our §§ 29, 36], as the 

 fluxions of quantities are nearly proportional to 

 the contemporaneous increments generated in very 

 small portions of time, so they are exactly in the 

 first ratio of the augmenta nascentia of their fluents. 

 With regard to this passage the writer of the 

 Analyst has made a two-fold mistake. First, he 

 charges Sir Isaac Newton, as saying these fluxions 

 are very nearly as the increments of the flowing 

 quantity generated in the least equal particles of 

 time. Again, he always represents these augmenta 

 nascentia, not as finite indeterminate quantities, the 

 nearest limit of whose continually varying pro- 

 portions are here called their first ratio, but as 

 quantities just starting out from non-existence, and 



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