i66 LIMITS AND FLUXIONS 



are entirely New . . . Our common Definition of 

 Motion, trans latto corporis de loco in locum is 

 certainly imperfect, and 1 am inclined to think, 

 that Aristotle's old exploded Definition of Motion 

 will, some time or other, come into Vogue again. 

 Actus entis in potentia^ cpiatcnus in potcìitia est. 

 Motion is an Efifect, and every Effect has a coin- 

 staneous Existence with the Action by which it is 

 produced." 



The definitions with which Smith starts out are 

 not very reassuring. "The fluxion of a surface is 

 the Velocity of the generating Line." "The 

 velocity of a generating Line is the Sum of the 

 Velocities of ali the Points of that Line, whether 

 these Points move with equal, or unequal Veloci- 

 ties. " The rectangle xy * * flows or increases by the 

 flowing of both its contiguous Sides " together ; 

 but it "flows into Length " by the velocity ja-, and 

 **it flows into Breadth at the very same Instant 

 of Time" by the velocity xy. " Therefore the 

 Velocity with which it flows into Length and 

 Breadth is the Sum of the synchronic Velocities," 

 xy-\-yx. 



Nor is the second topic displayed with illumina- 

 tion. "A nascent Ouantity is a Quantity in the 

 Instant of its commencing to exist." Similar to 

 this is the definition of " evanescent Quantity," as 

 are also the definitions of first and last ratios. 

 Interesting is the following proof that if " two 

 Quantities begin and cease to exist in any finite 

 Time T, . . . they have a first and a last Ratio," 



