Refolution of Algebraical 'Equations. 103 
lues ul/n, 1&/7T, ys / ny &c. and the fame may be affirm- 
ed of the quantities v'V, ir,. \/ r, See. and confequent— 
ly the quantity g/ n+ v 7 g will have nxn different values 
and in the fame manner the root x=\/n+s/f +v / c+-(/t+ 
may be proved to contain nxnxnxnx 8cc. — n n ~' roots, 
and confequently in this refolution, in equations of fupe- 
rior dimenfions, the number of independent coefficients 
In- 1) willbe very few in proportion to the number of 
dimenfions n n ~\ or (if we refpect its formula) Vi* -1 of 
the refulting equation. 
Let n — 3, and the equation refulting will rife to an. 
equation of nine dimenfions, which has the formula of 
a cubic; for let x = ^/n + \/(> — a one root, then will; 
~ . I .. + a zlz. fzl a be two other of the nine roots, 
and confequently the roots will be x 3 - a 3 xx 3 — b^xx i -c i ' 
= 0, which has the formula of a cubic:, and in general 
the above-mentioned equation of dimenfions will,, 
for the fame reafon, have the formula of an equations 
of 2 dimenfions.. 
Let the refolution be x — -l/n + v / f + sfa +-\/t + 8tc.. 
where c, r, fcc. denote the roots of an equation; 
x”~ I —px”~' l +qx’’~ l - 8cc. = 0 -of (n-i) dimenfions,. them 
will the refulting equation free from radicals,, whole 
root is x y rife to z”~' dimenfions ; but as every affirma- 
tive 
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