( I ) 
propos’d, as the Fluxions are, taking the Root fought 
for the only flowing Quantity, its Fluxion for Unity, 
and after every Operation dividing the Produd fuccef^ 
fively by the Numbers i, z, 3, 4, Hence I fooii 
found that this Method might eaflly and naturally be 
drawn from CVr. 2. Prop.y. of, my Methodus Incrmento- 
rum^ and that it was capable of a further degree of Ge- 
nerality; it being Applicable, not only to Equations- of 
the common Form, {yi%, fuch as confifl; of Terms where- 
in the Powers of the Root fought are pofitive and inte- 
gral, without any Radical Sign) but alfo to all Expref- 
lions in general, wherein any thing is propoled as given 
which by any known Method might be computed; if 
vice versa, the Root were confider’d as given : fuch as are 
all Radical Expreflions of Binomials, Trinomials, or of 
any other Nomial, which may be computed by the Root 
given, at lead by Logarithms, whatever be the Index -: 
of the Power of that Nomial ; as likewile Expreflions of 
Logarithms, of Arches by the Sines or Tangents, of 
Areas of Curves by the Ahfciffds or any other Fluents, 
or Roots of FlUxional Equations, d‘c. 
For the i^kc of this great Generality, it may not be 
improper to fhew how this Method is derived from the 
forefaid Corollary. Therefore jss and a: being two flowing • 
Quantities ( vvhofe Relation to one another may be ex- 
preft by any Equation whatfoever) by this Corollary, 
while z. by flowing uniformly becomes z-\-Vj x will 
OC OC' X 
become x -| r v —7- v ^ — -- -|- drc. • 
"L . z X. i«2«3^' 
XV 'xV^ . 
or ^ A 1 J- for ^ putting i. 
I I Xz I .z.j 
Hence if y be the Root of any ExprcfTion formed of • 
y Jind -known Quantities, and fuppofed equal to nothing, 
and , 
