( ) 
red with their proper Integrals or with their proper 
Fluents or not ; to find the Relations of the Integrals or 
of the Fluents, freed from their Increments or from their 
Fluxions. The Dire&ion I have given for finding the So- 
lution in finite Terms is but tentative. And I muft con- 
fefs I know of no other Method that is general for all Ca- 
fes. Fori can find no certain Rule to judge in general, 
whether any propofed Equa ion, involving increments 
or involving Fluxions, can be refolved in finite Terms. 
For this Reafon we are obliged to feek the general solu- 
tion in infinite Seriefes ; which when they break off] or 
when they can any way be reduced to finite Terms, they 
then contain the Solutions which we always hope for. 
The Method of finding thefe Seriefes is explain’d in the 
eighth Proportion, and that is by means of a Series that 
is demonftrated in the leventh Proportion. And this I 
take to be the only genuine and general Solution of the 
inverfe Methods. For in this Solution you always have 
thofe indetermined Coefficients, which are neceffary to 
adapt the Equation that is found to the Conditions of the 
Problem propofed. For want of this Circumftance all 
.other Methods are imperfe<2; and particularly Sit/faac 
Newtons. Method of finding Seriefes by a Rularand Pa- 
rallelograms labours under this Difficulty, becaufe it 
brings no new Coefficients into the refulting Equation, 
which may afterwards be determined by the Conditions 
of the Problem. However becaufe this Method is very 
ingenious and very elegant, I thought it proper to ex- 
plain it in the following (viz. the 9th) Prop. The »o th. 
nth % and iztb Proportions conclude thefirft Part, and 
in them I treat of the manner of finding the Integral or 
the Fluent, having given the Expreffion of a particular 
Increment, or of a particular Fluxion of it ; without be- 
ing involved with the Integrals, or with the Fluents, or 
with any other Increments, or with any other Fluxions of 
it. 
