( H* ) » 
the Fluents given ; and the other (hewing how to find the 
Fluents freed from Fluxions, having given the Relations 
of the Fluxions, whether compounded with their Fluents 
or otherwife. The Principles of this Method may all be 
drawn dire&ly as a Corollary from the Principles of the 
Method of Increments. For Sir Ifaac Newton having de- 
pionftrated (Phil. Nat. Princ. Math. Sell. i. and in the 
Beginning of his Treatife De Quadratura Curvarum) that 
the fluxions of Quantities are proportional to their naf- 
cent or evanafeent Increments, if in any Propofition rela- 
ting to Increments, you make the Increments to vanilh 
and to become equal to nothing, and for their Proportion 
put the Fluxions, you will have a Propofition that will 
be true in the Method of Fluxions. This is but a Corol- 
lary to Sir Ifaac Newtons Demonftration of the Fluxions 
being proportional to the nafcent Increments. For this 
reafon, to make the Method of Fluxions to be underftood 
more throughly, I thought it proper to treat of thefe two 
Methods together, and I have handled them promifeu- 
oufly as if they were but one Method. Some people, be- 
cause that the Fluxions are proportional to the nafeenc 
Increments of Quantities, have thought that by the Me- 
shod of Fluxions Sir Ifaac Newton has introduced into Ma- 
thematicks rbeConfideration of infinitely HttleQuantities; 
as if there were any fuch thing as a real Quantity infinite- 
ly little. But in this they are miftaken, for Sir ifaac 
does only confider the firft or laft Ratio’s of Quantities, 
when they begin to be, or when they vanilh, not after they 
are become fomething, or juft before they vanilh ; but in 
the very moment when they do lo In this cafe Quantities 
are not confider’d as infinitely little ; but they are really 
nothing at the time that Sir Ifaac takes the Proportions 
of their Fluxions ; and the Truth of this Method is 
demonftrated from the Principles of the Method of In- 
«rements, in the fame manner as the Ancients demonftra* 
ted 
