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with this method, it may be ufeful to give the 
fubft.ii o it here in our own language. 
The author prcvioufly demonftrates the two fol- 
lowing proportions. 
Prop. I. That when a quantity is equal to no- 
thing, and is compofed of many terms, fome’of which 
are real, and the other are terms multiplied by ^ — i, 
thefumof therealones is equal to nothing ; and the fum 
of thofe that are multiplied by ^ — t alfo equal to 
nothing. This is the 69th article of his introduction. 
Prop. II. That when an equation involves ima- 
ginary roots only, the unknown quantity may always 
be fuppofed equal to my-n'J — 1; m and n being 
real quantities. This is the 80th article of his in- 
troduction. 
Then to find the roots of fuch 2n equation as we 
are fpeaking of, for every unknown quantity 
(# fuppofe) in the equation, fubfiitute ?n-\-n — 1, 
and you will obtain a new equation involving real 
terms, and terms multiplied by 1 j the former 
of which by Prop. I. are always equal to nothing, and 
fo are the latter : make them fo therefore, and you have 
two equations, from which the two afiumed quanti- 
ties m and n may be difcovered ; and confeauently, 
fince the value of# is by the fecond propofition equal 
to 1, it is difcovered alfo. 
What I mean in the former part of this article may 
be explained by the following inftance; fuppofe the 
real roots difcovered by the rulers abovementioned to 
be a, b, — c, &c. then put x-=.a, x—b,x— — c, &c.. 
tranfpofe the terms to one fide, and you have x—a 
=£=o, # — b= o, xq-c=o, &c. multiply all thefe lafl 
Yoju. LX* ' & k equations 
