196 LIMITS AND FLUXIONS 



Moments, generateci in equal Farticles of Time, in 

 order to determine those Velocities ; which he after- 

 wards teaches us to expound by finite Magnitudes 

 of other Kinds : Without which (as is already hinted 

 above) we could have but very obscure Ideas of 

 higher Orders of Fluxions : For if Motion in (or at) 

 a Foint be so difficult to conceive, that Some have, 

 even, gone so far as to dispute the very Existence 

 of Motion, how much more perplexing must it be 

 to form a Conception, not only, of the Velocity of a 

 Motion, but also infinite Changes and Affections of 

 It, in one and the same Point, where ali the Orders 

 of Fluxions are to be considered. 



" Seeing the Notion of a Fluxion, according to 

 our Manner of defining It, supposes an Uniform 

 Motion, it may, perhaps, seem a Matter of Diffi- 

 culty, at first View, how the Fluxions of Quantities, 

 generated by Means of accelerated and retarded 

 Motions, can be rightly assigned ; since not any, 

 the least, Time can be taken during which the 

 generating Celerity continues the same : Here, 

 indeed, we cannot express the Fluxion by any 

 Increment or Space, actually generated in a given 

 Time (as in uniform Motion). But, then, we can 

 casily determine, what the contemporary Increment, 

 or generated Space would be^ if the Acceleration, or 

 Retardation, was to cease at the proposed Position 

 in which the Pluxion is to be found : Whence the 

 true Fluxion, itself, will be obtained, without the 

 Assistancc of infinitely small Quantities, or any 

 metaphysical Considerations. " 



