A Discourse on the Theory of Fluxions. 53 



promised to present your readers with some new considera- 

 tions of your principle, be pleased to pardon tiiis digression. 



Benj. Bell. 



Art. IX. — A Discourse on the different views that have been 

 taken of the Theory of Fluxions; by Elizur Wright. 



Whoever has made the smallest progress in the science 

 of fluxions, must perceive, that there are difficulties attend- 

 ing the explanation of its first principles, which have never 

 yet been fully removed. The learner in the outset has to 

 encounter apparent errors, or to consider them lost in the 

 incomprehensibility of infinity, or if with Sir Isaac Newton 

 he chooses to view fluxions as illustrated by the philosophi- 

 cal principal of motion, he is still surrounded with mystery. 

 Many of the less aspiring are undoubtedly deterred, on this 

 account, from making any considerable proficiency in this 

 important branch. Although this science may assume a 

 more elevated rank by means of that sublimity, which arises 

 from obscurity, and the ordinary mathematician may look 

 up to the adept in this department with a kind of enthusias- 

 tic veneration, as having gained an enviable pre-eminence 

 by mastering abstruse elements ; yet to the proficient him- 

 self it is in a high degree satisfactory to lay the foundation 

 of science in clear, self-evident principles, and to proceed on 

 in the march of discovery in a path that inspires confidence. 

 The elements of a science should be rendered as plain as 

 possible. An examination of the different views that have 

 been taken of the theory of fluxions, and a discrimination of 

 the parts designed to be elucidated, will contribute in no 

 small degree towards attaining this object. Sir Isaac New- 

 ton considered the doctrine of fluxions uhder the idea of 

 quantities, that arise into existence by one uninterrupted in- 

 crement according to the laws of continuity. Quantities, 

 according to this method, are augmented in a manner, that 

 does not admit of distinct separable parts. Although New- 

 ton applied the calculus to quantities both geometrical and 

 numerical, yet he chose to illustrate the theory by geometri- 

 cal ones ; which by introducing the properties of motion, af- 

 ford a very clear explanation. For according to the illustra- 

 tion of Vince, in his first section, §7. page 3. " Let the line 

 FK be described with an uniform velocity, and AZ with an 



