ioo Mr, waring on the General 
i. a; if three, by 1.2.3,; if four, by 1.2. 3. 4; and 
laftly if two are equal to each other, and the two re- 
maining indexes equal to each other, but not to the for- 
mer two, then mult the term aforefaid be divided by 
I *-2. 1.2* 
Find the fum of all the poffible terms of this kind, 
which call E. 
In the fame manner from the preceding Lemma may 
be found the aggregates of the contents of every five, 
fix, feven, &c. roots or values multiplied into each o- 
ther, which call refpedlively c, r>, E, Sec ; then will the. 
equation required be x” *— np (au + bv + ct+ ds +Scc .) x^ 1 - 
AX ”~ 3 + BX K— 4 - CX”~‘- 5 + T>X n C - &C. -O. 
From the fame principles may be deduced the moft 
general reduction yet known of equations to others of 
inferior dimenfions, e. g. 
Let (X) x ”+ (a + a&p + b^/p 1 + c^p 1 + ... + + 
tx/fF*) ^“— + (b +a'z/p+ b'Z/f+... + sVf^ + t'Vf^ 1 ) 
+ (c + a"\/p + ti'^/p 1 + Sec.) x K ~ 3 -i-8ec. = o. let oc, ( 3 , <y, 
l', See. be the refpedtive roots of the equation z m - 1 =0,, 
then, from the principles before given, may be formed 
the different values of the equation X, which being- 
multiplied into each other from the propofitions before- 
mentioned of the Meditationes Algebraicae, may be de- 
duced an equation of nm dimenfions free from radicals, 
2 whofe 
