Page:The Analyst; or, a Discourse Addressed to an Infidel Mathematician.djvu/35

Rh  x + o, tands for nothing, upon this Suppoition as there is no Increment of the Root, o there will be no Increment of the Power; and conequently there will be none except the firt, of all thoe Members of the Series contituting the Power of the Binomial; you will therefore never come at your Expreion of a Fluxion legitimately by uch Method. Hence you are driven into the fallacious way of proceeding to a certain Point on the Suppoition of an Increment, and then at once hifting your Suppoition to that of no Increment. There may eem great Skill in doing this at a certain Point or Period. Since if this econd Suppoition had been made before the common Diviion by o, all had vanihed at once, and you mut have got nothing by your Suppoition. Whereas by this Artifice of firt dividing, and then changing your Suppoition, you retain 1 and $$nx^{n-1}$$, notwithtanding all this addres to cover it, the fallacy is till the ame. For whether it be done ooner or later, when once the econd Suppoition or Aumption is made, in the ame intant the former  on