Page:The Analyst; or, a Discourse Addressed to an Infidel Mathematician.djvu/55

Rh the other Side of the Equation: So it mut be allowed a very logical and jut Method of arguing, to conclude that if from Equals either nothing or equal Quantities are ubducted, they hall till remain equal. And this is a true Reaon why no Error is at lat produced by the rejecting of o. Which therefore mut not be acribed to the Doctrine of Differences, or Infiniteimals, or evanecent Quantities, or Momentums, or Fluxions.

XXVIII. Suppoe the Cae to be general, and that xn is equal to the Area ABC whence by the Method of Fluxions the Ordinate is found $$nx^{n-1}$$ which we admit for true, and hall inquire how it is arrived at. Now if we are content to come at the Concluion in a ummary way, by uppoing that the Ratio of the Fluxions of x and xn are found to be 1 and $$nx^{n-1}$$, and that the Ordinate of the Area is conidered as its Fluxion; we hall not o clearly ee our way, or perceive how the truth comes out, that Method as we have hewed before being  cure