i82 LIMITS AND FLUXIONS 



Treatise of Sir Isaac Newton's with a Commentary 

 by Mr. Colson, and several other Pieces were 

 published on this Subject. After I saw that so 

 much had been written upon it to so good Purpose ; 

 I was the rather induced to delay the Publication of 

 this Treatise, till I could finish my Design. . . . 

 The greatest Part of the first Book was printed in 

 1737 ; But it could not bave been so useful to the 

 Reader without the second. . . . In explaining the 

 Notion of a Fluxion, 1 bave foUowed Sir Isaac 

 Newton in the first Book ... ; nor do I think 

 that I bave departed from bis Sense in the second 

 Book ; and in both I bave endeavoured to avoid 

 several Expressions, which, though convenient, 

 might be liable to Exceptions, and, perhaps, occasion 

 Disputes. I bave always represented Fluxions of 

 ali Orders by finite Ouantities, the Supposition of 

 an infinitely little Magnitude being too bold a 

 Postulatum for such a Science as Geometry. But, 

 because the Method of Infinitesimals is much in 

 use, and is valued for its Conciseness, I thought it 

 was requisite to account explicitly for the Truth, 

 and perfect Accuracy, of the Conclusions that are 

 derived from it . . . " 



165. In the Introduction to bis Fluxions Maclaurin 

 says : "... When the certainty of any part of 

 geometry is brought into question, the most efìfectual 

 way to set the truth in a full light, and to prevent 

 disputes, is to deduce it from axioms or first prin- 

 ciples of unexceptionable evidence, by demonstra- 

 tions of the strictest kind, after the manner of the 



