BERKELEY'S ANALYST (1734) 81 



ing quantity, " " fluxion " ("the velocity with which 

 a flowing quantity increases or decreases "), " incre- 

 ment," " nascent increment " ("an increment just 

 beginning to exist from nothing . . . but not yet 

 arrived at any assignable magnitude how small so- 

 ever"), "evanescent increment" (similarly defined). 

 He then endeavours to prove the proposition : 

 "The Fluxions, or Velocities of flowing quantities 

 . . . are exactly in the first proportion of the 

 nascent increments, or in the last proportion of the 

 evanescent increments." He insists that "the first 

 ratio of the nascent increments must be the same, 

 whether the velocities be uniform or variable " ; 

 hence, "the nascent increments must be exactly 

 as the velocities with which they begin to be 

 generated." In further explanation, Jurin says that, 

 according to Newton, nascent increments are " less 

 than any finite magnitude," " their magnitude 

 cannot be assigned or determined," "the proportion 

 between them . . . being ali that is requisite in 

 his Method." In further explanation of the pro- 

 portion of evanescent increments he says, it " is 

 not their proportion before they vanish, " " nor is it 

 their proportion after they bave vanished," "but it 

 is their proportion at the instant that they vanish." 

 Jurin then states that Berkeley has " taken as 

 mudi pains as . . . any man living, except a late 

 Philosopher of our University, to make nonsense 

 of Sir Isaac Newton's principles; " There is no 

 occurrence in Newton's writings of "velocity with- 

 out motion," " motion without cxtcnsion," which 



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