158 MiJ : el lane a Curio fa . 



and otherwhere, have tended fo much to the 

 Advancement of Mathematicks) have Me- 

 thods not unlike to this of mine } and there- 

 fore I afcribe no more to my felf in this 

 Matter, than only that I found out thefe 

 Theorems, not knowing whether any Body 

 elfe had done fo before or no ; and reduced 

 them into fo eafie a Form, that the whole 

 Calculus relating to them, might be taken 

 in, as it were, at one View. 



But before I make an end of Writing, 

 I think it improper, if (having not had an 

 Opportunity fooner) I make fome little re- 

 ply to the Famous Mr. Leibnitz!* Animad- 

 verfions upon my Series for finding the Root 

 of an Infinite Equation. 



That Excellent Perfon thinks fthiSu Series 

 not to be General enough, as not reaching 

 the Cafes where & and y are multiplied in- 

 to one another } upon which account he 

 fubftkutes another Series in the room of it, 

 which he aflerts is infinitely more General. 

 But that which led him into this fmall Mi- 

 ftake, I guefs to be this, that he took the 

 Quantities b 0 &c. for given Quanti- 

 ties, whereas they were to be us'd indiffe- 

 rently, either fox given or indeterminate ones. 



But I fhall add"one Example to ihew that 

 my Series extends to all Cafes. Let the 

 Equation be nyzj—z} ssj^ . 



In our Theorem let dfxnjjtj b~o, c~ < — 1, 

 h—Oj fen, or rather let g—yy-, b~o 0 i-=io. 



Then in either Cafe will 1 + « — : 



yy 



y 



9 



n 



ft 



,4 



Two 



