Refolution of Algebraical Equations. 93 
term above-mentioned = o ; if it be equal to n or in, 
then will the term be 1 . 2 x ft x bklp or t . mhklp \ 
If two of the three indexes a, v be equal to each 
other, then divide the above-mentioned term by 1.2; 
if the three indexes be equal, i. e. divide it by 
1.2.3 : find all quantities of this kind where X+p+v ei- 
ther is equal to n or 2 n, and add all the term from thence 
derived, and call the fum of them a. 
The fum of the contents of every four of the va- 
lues or roots above-mentioned, which is the coefficient 
of the fourth term of the equation required, will be 
■atyp*xx@y$+xfiy 8 + See. ( 0 ) + albiyp"- x cifiy$ z + afiyf'+ 
apyfi + u*( 3 y$ + Sec. (0) + 8cc : let bklq\/p’ +l/ - + ’ + % x 
ctlft'-y’f + cP'frfo' + oPftyPtf + oPfty^ + offfiyS 1 * + cP0y ^ v + 
+ See. denote a general term ; this term will be 
= o, unlefs x+[A+v+% either — n or in or 3 n ; in which 
cafe the term will be either- 1.2. $nbklqp or- 1.2. q > nhklqp t 
or- 1. 2 .^nbklqp^; unlefs X+n—v+^n, when the above- 
mentioned term will be -(1.2.3 ft -ft*) hklqp *; in this 
cafe if x~v, and confequently p ~ £, then it will be - 
(1.2.3ft- 1.2ft 1 ) bklqp ; but if x~[i~v= f=y, then will 
the term be - (1.2.3ft- 3ft 1 ) hklqp. 
In all thefe cafes, if two of the indexes A, [x, v, | be 
equal, then rauft the term given above be divided by 
O 2 1.2, 
