174 



LIMITS AND FLUXIONS 



y terminatcs in the curve AC ; " And, at any pro- 

 peseci Position BC, conceive y to become Constant," 

 while B " moves uniformly any Constant Time, ?//;/, 

 with the Velocity at B, over the Distance x or BD ; 

 for then vigili y in the Time mn uniformly generate 

 the Rectangle ij, which Rectangle is plainly the 

 Fluxion of ABC in this Position {per Definii.).'" 

 Then follows the illuminating scholium : " It has 

 been commonly objected to the Accuracy of Fluxions, 



that the Trapezium or curvi- 

 linear Space BC<^^D, not the 

 Rectangle xy^ is the Fluxion 

 geometrically exact. But, 

 ^ this Objection is built, I 

 apprehend, upon a false Idea 

 of the Thing. It supposes a 

 Fluxion a complete Part of 

 r a flowing Quantity, and an 

 Infinity of Fluxions to con- 

 stitute the flowing Quantity, 

 which are Mistakes {per Definition and Lemma) 

 . . . if i- be imagined ìnfinitely little, an Infinity of 

 Increments may constitute the Area ABC. But, in 

 Fluxions, our Reasoning is quite differenti a Pluxion 

 can no more be called a Part of the Fluent, than an 

 Efìfect a Part of the Cause. For Instance; from the 

 Fluxion given we know the Fluent, and vice versa, 

 just as when a Cause is known to produce a certain 

 Effect, we can infer the one from a Knowledge of 

 the other. " 



We shall find that later this reference to cause and 



B 



FiG. 8, 



