230 LIMirS AND FLUXIONS 



his ovvn, whose Foundation, it seems, depends on 

 Cyphers^ and Nought Powers full of conceited Ex- 

 pressions. . . . He expresses his Ultimators by 

 the Help of ar°, j°, ^s°, etc. , calls them peculiar Units, 

 and of different Values, ali of which is absurd. . . . 

 I pass over ... his using ;r**, jj/°, <c^, for the same 

 End as others use i-, y, è. " 



John Petvin^ I750 



20 1 . Ina Sketch of Universal Arithmetic^ ^ brought 

 out as a posthumous booklet,we encounter acuriosity. 

 Its philosophy of mathematics and of fluxions in 

 particular is set off by the following quotations : 



(Page 156) **I do not then consider it [mathe- 

 matica! quantity] as generated or produced, but as 

 that which is. Time and Motion produce nothing 

 of the Kind, and bave no Place bere. Nor do I 

 consider it as continuous, nor as consisting of very 

 small or infinitely little Parts, but as consisting of 

 Parts in general. These Parts therefore I con- 

 sider as discrete: And by x^ y, ^, etc, I under- 

 stand Multitude. The Ones or Monads, of which 

 X is many, I cali x \ . , . Nor do I consider ;r, y, z, 

 etc. , barely as many ; but as a certain many. So 

 that X, y, ,:■, etc, are Wholes ; x, y, f, etc, their 

 respective Parts. These Parts may be considered 

 again as Wholes, consisting of another Order of 



^ Letters concerning Mind. To which is added, a Sketch of Uni- 

 versal Arithmetic ; comp7-ehending the Differential Calculus, aììd the 

 Doctrine of l'iuxions. Hy the late Reverend Mr. John Petvin, A.M., 

 Vicar of Ilsington in Devon, London, 1750. 



