Refolution of Algebraical Equations. 97 
aVp x j 6+bVfx ft + cVf x(S l + dyy x ft... +£ ftf x 
|0\.. + x ft + sftf^x ft‘~ 4 + tyf^xft-j-v 
x (S ^ 1 + x ft - 1 ; 
a\/p x y + blf p 1 x y 1 + C\/ p 3 x y 3 + dft p* x y + ... + byp x x 
y x ...+kiyf - X yf....... + s</f = ^ X y* -4 + X y* -3 + 
x y* -J + x f - 1 ; 
x $+ hyp* y + c<yp x ^ + d.yy x$\..+bypxy... 
+kyj* x y +syp~* x <^- 4 +/c / /-~ x ^*- 3 + x 
y~ ! ; 
Sec. See. Sec. Sec. 
and confequently the fum of the values or roots, which 
is the coefficient of the fecond term of the equation 
fought, will be ayp xa + /3 + y + cT + Sec. ( 0 ) + byp 1 x 
cd + 0 + y 1 + 1 ? 2 + Sec. (0) + cyp 3 x a 3 + ft + y 3 + (J 3 + 8ec. (0) + . . . . 
+vy^xA =r +0^ + y " -2 + <?* - * + Sec. ( 0 ) + uftf^x 
cd-'+y-'+y-'+y - 1 + sec. o) = o. 
The fum of the products of every two of the values 
or roots, which is the coefficient of the third term of 
the equation fought, will be a 1 y p 1 xa(S + cty+(Sy+ a< 5 “ + 
( 3 $+y$ + Sec. (0) + abyp 3 x aft + fix 1 + ay 1 + yod + fiy 1 + yft + 
aS 1 +da I + Sec. (0), and in general all the terms will be 
o, unlefs axuxpx a/ 3* -1 + fixl l ~ l + ay * -1 +ya B-1 +/Sy B— 1 + 
Vol. LXIX. , O yfi 
