194 LIMITS AND FLUXIONS 



aiiy Velocity which continues for no Time at ali, can 

 possibly describe any Space at ali ; or whether its 

 Effect be absolutely nothing, or an infinitely small 

 Ouantity, or what it is. Here then it is, that our 

 Reason is at a Stand, and the human Faculties are 

 quite confounded, lost, and bewildered. . . . Now 

 whether such subtile Questions will be ever de- 

 termined, or not, yet there is one Refuge for us, 

 viz. that it is nothing at ali to our Purpose what 

 they are : . . . The Method of Fluxions has 

 no Dependence on these mysterious Disquìsitions. 

 What I apprehend the Method of Fluxions to be 

 concerned in, is . . . what a . . . variable Velocity 

 can produce in the whole. And here 1 think no 

 Reason can be assigned, why a variable Cause 

 •should not produce a variable Effect, . . . though 

 we have no Ideas at ali of the perpetually arising 

 Increments, or their Magnitude in their nascent or 

 evanescent State, that have so much, and to so little 

 Purpose, confounded and puzzled the mathematical 

 World." 



Thomas Simpsoji, 1750 



172. Simpson's Ti-eatise of Fluxions of 1737 has 

 already been noticed (our § 156). His text of 

 1750, The Doctrine and Application of Fluxions, 

 London, is new, not only in the title, but to some 

 extent also in the mode of exposition. He says in 

 his Preface (1750) that he has used a tract entitled 

 An Explanation of Fluxions in a Short Essay on the 

 Theory, printed by W. Innys and written by one of 



