TEXT-BOOKS OF MIDDLEOF CENTUR Y 193 



pass for an Axiom, he may consider it thus ; let 

 D be their ultimate Difference, therefore they 

 cannot approach nearer to equality, than by that 

 given Difference D, contrary to the Hypothesis ; 

 which Supposition is absurd in ali Cases except 

 when D is nothing." 



To find the fluxion of òx"y"\ he lets ox, oy be 

 moments, expands the powers of x-\-ox andjz + ^j, 

 and finds the increments. Then he divides **by 

 the indefinite Quantity 0." " But since the 

 (Velocity or) Fluxion is required wherewith that 

 Moment first arises, in this Case the Moments ox 

 and oj will also be just arising and therefore 

 nothing, and consequently will be nothing, and 

 therefore ali the Terms wherein it is found will be 

 nothing." The final result then foUows. In his 

 Preface Emerson claims that ** Velocity must be 

 looked upon as the proper efìficient Cause of the 

 Space described ; and the Space described the 

 adequate Effect of that Cause." . . . **No incre- 

 ment can be taken so small, but it is stili further 

 divisible ad infinitum ; and since the Velocity is 

 by Supposition continually variable, it is plain, 

 there can be no two Points of the Increment in 

 both of which the Velocity is accurately the same. 

 It is therefore most manifest, that the Velocity bere 

 enquired after is peculiar to one only indivisible 

 Point ; . . . that the Velocity in any given Point 

 of the Line described . . . has a certain, fixed. 

 determinate Value. . . . Here a metaphysical 

 Disputant may demand, how it comes to pass, that 



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