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ents or flowing Quantities 5 the Relation of which 
Fluents is always exprefs'd by fome Algebraical Equa- 
tion, either given or required. If this Equation be 
given, and the Relation of the Fluxions is required, 
it conftitutes the dir eft Method of Fluxions 5 but 
when the contrary, 'tis the inverfe Method of 
Fluxions . 
Sir lfaac y in his firft Problem, which takes in the 
direft Method of Fluxions, (hews how to find the 
Relation of the Fluxions in a very general Manner, 
and by a great Variety of Solutions. This way of 
refolving the Problem is peculiar to this Work. He 
likewife extends it to Equations involving feveral 
Fluents, which accommodates it to thofe Cafes, wherer 
in any complex or irrational Quantities may be found, 
or Quantities that are geometrically irreducible. 
Then he demonftrates the Principles of his Method, 
or the Precepts of Solution, from the Nature of 
Moments or vanifhing Quantities, and from the ob- 
vious Properties of Equations, which involve indeter- 
minate Quantities.. 
The Commentator much inlarges upon this whole 
Do&rine ; he enters into theReafon and Ufe of this 
Multiplicity of Solutions, and fhews it is a neceffary 
Refultfrom the different Forms the fame given Equa- 
tion may acquire.- But efpecially he takes the Au- 
thor's Demonftration into ftrift Examination, endea- 
vours farther to illuftrate and enforce its Evidence, and 
to clear it from all the Objections that either have or 
may be urged againft it. He even contends, that tho* 
the Moments and vanifhing Quantities of the Author, 
could be proved to be impoflible, as has been fug- 
gefted by fome Mathematicians, yet even, then they 
would 
