Mr. waring on the General 
9 6 
tioned quantities w, r, x, t, Sec ; and fimilarly let be 
either equal to, or a divifor of the fum of any number 
(7 ) of the remaining quantities ; and alfo let n be either 
equal to, or a divifor of the fum of any number (/) of 
the remaining quantities; then will n be either equal to, 
or a divifor of the fum of the (71— 7— a —g") remaining 
quantities : find the fum of all quantities of this fort 
1 .2. 3.-7 — 2 x 7—1 x T .2. 3.. a - 2 x a — 1 x 1 .2.3.. 0 — 2 x 
g — 1 x 1 .2.3.. 77 — T—a— g'— 2 X 7 T— 7— a— fl'— 1 x « 4 , which 
fum call c ; and fo on ; then will the above-mentioned 
fum Sec. + u r j 3 y$‘ Sec. + «-jS &c. + a'/SyJ* 
&c. + Sec. = =p(i.2.3..7r*-ax7r-ix/z-A+B-C + D- See.) 
where it will be + if 7r be an odd number, otherwife 
In this cafe, if a indices be m , b indices be r, c in- 
dices be s, d indices be t, Sec. then will the above-men- 
tioned fum = -=h 2 ' 5 — — 2 x - - — — A+B 
1,2. 3. .a x 1.2.3..^ X 1 .2* 3 »*c X 1.2.3. .</x 
7. Let <x, j 3 , y, J', f, 8cc. be the roots of the equation 
&Vl = o, and the refolution be x-aH/p-^b-yp 1 + C\/p^- i r 
d\/p‘ i .....+ hVp\..+ky p 1 " isy p ' 1 ... + Q\/p^.... +riyp^..., 
+ s \Zp n ~ A +t : yp a ~ i + vl/p ,M + U\/ p“~ l ; then will the dif- 
ferent values of x be refpeftively al/p x a+biyp z xod + 
ciyp i x trp+d-yp^ x a 4 .... +hiyp x x of... + kiyp^ x of + 
s</p’ 
!— 4 
XCC 
n — 4 
+tS/p" 
~3 
+ \/ p’ 
x of-'+uyp*- 1 
