What Principles you proceed upon; how ſound they may be; and how you apply them? It muſt be remembred that I am not concerned about the truth of your Theorems, but only about the way of coming at them; whether it be legitimate or illegitimate, clear or obſcure, ſcientific or tentative. To prevent all poſſibility of your miſtaking me, I beg leave to repeat and inſiſt, that I conſider the Geometrical Analyſt as a Logician, i. e. ſo far forth as he reaſons and argues; and his Mathematical Concluſions, not in themſelves, but in their Premifes; not as true or falſe, uſeful or inſignificant, but as derived from ſuch Principles, and by ſuch Inferences. And foraſmuch as it may perhaps ſeem an unaccountable Paradox, that Mathematicians ſhould deduce true Propoſitions from falſe Principles, be right in the Concluſion, and yet err in the Premiſes; I ſhall endeavour particularly to explain why this may come to paſs, and ſhew how Error may bring forth Truth, though it cannot bring forth Science.
