[ 3^5 3 
would be fufficient for all the purpofes of Fluxions, and 
he produces Inftances of a like Nature from other parts 
of Mathematicks. And tho' the Author, Sir Ifaac 
Newton , in his prefeiit Treatife, does not direftly men- 
tion fecond Fluxions, or thofe of higher Orders ; yet the 
ingenious Commentator thinks proper to extend his 
Inquiries to thefe Orders of Fluxions, demonftrates 
their Theory, gives Rules and Examples for deriving 
their Equations, proves their relative Nature, and even 
exhibits them to View by Geometrical Figures. This 
laft he does chiefly in what he calls the Geometrical 
and Mechanical Elements of Fluxions 3 and he con- 
trives a very general Method, by means of Curve- 
lines and their Tangents, to make Fluxions and Flu- 
ents the Objeds of Senfe and ocular Infpe&ion 5 and 
thereby he illuftrates and verifies- the received Methods 
of deriving their Equations in all Cafes. 
In the Authors fecond Problem, or the Relation, 
of the Fluxions being given to determine the Rela- 
tion of the Fluents, which includes the inverfe Me- 
thod of Fluxions, he begins with a particular Solu- 
tion of it. He calls this Solution particular, becaufe 
it extends only to fuch Cafes, wherein the. given 
Fluxional Equation either has been, might have 
been, derived from fome previous finite Algebraical 
Equation. Then he fhews how we may return di- 
re&ly to this Equation. But this is feldom the Cafe 
of fuch Fluxional Equations, whofe Fluents or Roots 
are propofed to be found. For they have commonly 
Terms either redundant or deficient, by which they 
cannot be brought under, this particular Solution. 
Therefore to anfwer this Cafe alfo, he gives us a ge- 
neral Solution, in which he extracts the Roots of any 
propofed 
