A Discourse on the Theory of Fluxions. 53 
promised to present your readers with some new considera- 
tions of your priticighe, be pleased to pardon this digression. 
Bens. Bet. 
Art. IX.—A Discourse on the different views that have been: 
taken of the Theory of Fluxions; by Exizur Wricut. 
any of the vasdoubtedly Seated, on this 
account, Toes wake any considerable atigtionceppcrt in. this 
important branch. Although this science may assume @ 
more elevated rank by means of that sublimity, sehich arises 
from obscurity, and the ordinary mathematician may loo 
up to the adept in this department with a kind of enthusias- 
tic veneration, as having gained an enviable pre-eminence 
by — abstruse: elements; yet to the proficient him- 
self it is in a high degree satisfactory to lay the foundation 
of science in cee = evident principles, and to proceed on 
in the march of discovery in a path that inspires confidence. 
The a of a science shou rendered as plain as 
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 under 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 =, 
ton applied the calculus to quantities both geometrical and 
numerical, yet he chose to illustrate the theory by pene: 
cal ones; which by introducing the properties of motion, af- 
ford a very clear explanation. For —<— 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 
