[ 4 © 7 3 
then E f, ~~ F n Is le fs than nE nmml xE—~F but greater 
than n-F n ~ J xE—«F. 
The Ruels are fometimes propofed in a Form 
fomewhat different from the ufual manner of deferibe- 
mg them, with a View to facilitate the Computa- 
tions both in the diredt and inverfe Method. Thus, 
when a Fradtion is propofed, and the Numerator and 
Denominator are refolved into any Fadlors, it is 
demonftrated, that the Fluxion of the Fradlion divided 
by the Fraction is equal to the Sum of the Quotients, 
when the Fluxion of each Fador of the Numerator 
is divided by the Fadfor itfelf, diminifhed by the Quo- 
tients that arife by dividing in like manner the Flu- 
xion of each Fadlor of the Denominator by the 
Fadlor. 
The Notation of Fluxions is deferibed in Chap. 2. 
with the Rules of the diredt Method, and the funda- 
mental Rules of the inverfe Method. The latter are 
comprehended in Seven Propofitions, Six of which 
relate to Fluents that are afTignable in finite Algebraic 
Terms, and the Seventh to fuch as are afligned by 
infinite Series. It is in this Place the Author treats 
of the Binomial and Multinomial Theorems (becaufe 
of their Ufe on this Occafton), and they are in- 
vefligated by the direct Method of Fluxions. The 
fame Method is applied for demonft rating other 
Theorems, by which an Ordinate of a Figure being 
given, and its Fluxions determined, any other Or- 
dinate and Area of the Figure may be computed. 
The moft ufeful Examples are deferibed in this Chap- 
ter, by computing the Series's that ferve for deter- 
mining the Arc from its Sine or Tangent, and the 
Ggg Lo- 
