IV. A general Method for exhibiting the Va- 
lue of a?i Algebraic Expreflion involving 
Jeveral Radical Quantities in an Infinite 
Series-. Wherein Sir Ifaac Newton \r The- 
orem for involving a Binomial, with an- 
other of the fame Author , relating to the 
Roots of Equations , are demonfir ated. By 
T. Simpfon I. R. S. 
Read Jan. jo. A MONG all the great improvements, 
which the art of computation hath 
in thefe laft ages received, the method of feries may- 
be juftly one of the mod conflderable j fince not only 
the dodtrine of chances and annuites, with fome 
other branches of the mathematics, depend almoft 
intirely thereon, but even the bufmefs of fluents, of 
fuch extenflve ufe, would, without its aid and con- 
currence, be quite at a hand in a multitude of cafes, 
as is well known to mathematicians. 
It is for this reafon, that the celebrated binomial 
theorem, for converting radical quantities into feries’s, 
is ranked, by many, among the principal difcoveries 
of its illuftrious author ; feeing, by means thereof, a 
vaft number of fluents are found, that would other- 
wife be impracticable : nor is there any cafe, however 
complex, to which it may not be extended. 
It is true, when two or more compound radical 
quantities are involved together, the operation, by 
having two or more feries’s to multiply into one 
another, 
