Refolution of Algebraical Equations. 95 
mentioned quantities ; then will the fum above-men- 
tioned = + 1.2 3. 4. ..7T-2.7T-I x n\ where it will be + , 
if 71 be an odd number; otherwife 
In this cafe, if a indices be m , b indices be r, c in- 
dices be s, J indices be t, See. then will the above-men- 
tioned fum = =f 
1.2 3.4...^— 2 X ’T— I 
1.2.3..^ X 1.2.3..^ X 1:2.3. .cx 1 .2.$..dx & C. 
xn, 
Let n be either equal to, or a divifor of the fum of 
any number £ (iefs than 7 r) of the above-mentioned quan- 
tities m , r, s, /, &c. and confequently either equal to, or 
a divifor of the fum of the (tt— g) remaining quantities: 
find the fum of all poffible quantities of this kind 
1.2. 3. .£>—2 x (>— 1 x 1.2. 3 . .tit— 2 x 71 — 0-1 x 7z 2 , which 
fum call a. 
Let n be either equal to, or a divifor of the fum of 
any number ( a ) of the above-mentioned quantities m y , 
r, s y ty &c; and alfo equal to, or a divifor of the fum 
of any number (p) of the remaining quantities, and. 
confequently it will be either equal to, or a divifor of, 
the fum of the (7 remaining quantities; then, 
find the fum of all poffible quantities of this fort 
I » 2 , 3 • • (J 2 X (J~~" X X I« 2. ““2 x ^ ~~ I X X • 2 * 3 • . 7 T - ^ ~~~ (J 2 ■ 
x 7r-^> —a- i X« 3 , which fum call b. 
In the fame manner let n be either equal to, or a di- 
vifor of the fum of any number (r) of the above-men- 
tioned:. 
