BERKELEY'S ANALYST (1734) 89 



Ways without stirring from that Point," Walton 

 replies that there is no difficulty in supposing two 

 points existing in a given place each having its own 

 velocity, but he never said that they can go 

 in different directions "without stirring from the 

 Point." Berkeley, in his remarks about the fourth 

 fluxion of a cube, did not observe ali the conditions 

 which he [Walton] had imposed. " He [Berkeley] 

 intreats me to explain whether Sir Isaac's Momentum 

 be a finite Quantity, or an Infinitesimal, or a mere 

 Limit. I teli him, that Sir Isaac's Momentum is a 

 finite quantity ; it is a Product contained under the 

 moving Quantity and its Velocity, or under the 

 moving Quantity and first Ratio of that Space 

 described by it in a given Particle of Time." Since 

 both these factors are finite, the product is finite 

 (p. 62). *'By Moments therefore he is not to 

 understand generated Increments of Fluents, but 

 certain finite Products or Quantities of very different 

 Nature from generated Increments, expressing only 

 the Motions with which those Increments begin or 

 cease to exist " (p. 63). 



Rejnarks 

 109. Berkeley's Analyst must be acknowledged 

 to be a very able production, which marks a turning- 

 point in the history of mathcmatical thought in 

 Great Britain. 



His contention that no geometrical quantity can 

 be exhausted by division ^ is in consonance with 



^ See our § 79. 



