1 
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+ 6 = o 
— - 3A^*— -bA^j/ — Aj;» 
-|- X B ^ -J- lij; 
— G 
And confequently 4 ^*— bA^’ + xB^— C mufl 
be the Produd of the three remaining Values of jf 
vin g its S ig n cha nged ; that is, it mufl be equal to 
— b — axe — a xd — a when e is fuppofed equal 
to it mufl be-— — b xc — bxd — b when 
e = b ; it mufl be — — cxb — d — c when 
e =z c and it mufl be — ^ — d x b ^d x c — d 
when c = d. Now it is manifefl that thefe Produds 
b — a X c — a X d ^ a , a — h x c ^b x d — b^ 
a — c X b — c X d — Ci a — d xb d x c — d 
mufl be affeded with the Signs +> — > +> — refpec- 
tively* the firfl being the Produd of three pofitive 
Quantities, the fecond the Produd of one negative and 
two pofitives, the third the Produd of two negatives 
and one pofitive, and the fourth the Produd of three 
negatives. Therefore fince by fubflituting a.b^Cyd 
for e in the Quantity 4^* — 3 A + x B^ — C, it 
becomes alternately a pofitive and a negative Quantity, 
it follows from the lafl Lemma that /?, b^ c, d inufl be 
the Limits of the Roots of the Equation 4^* — 
3 A^?^ + ^ — C =: o, or of the Equation 4^ ? — 
3Aa;* + xl^x — C = o, 
C o R. It follows from this Theorem, that if a' o' 
are the three Roots of the Equation 4 x ^ — 3 A.v * -d- 
xBx — C =0, they mufl be Limits betwixt /;, c^d 
the Roots of the Biquadratick + — AAr*-j- B;i?* — 
Cat + = o: For if a^b^c^d are Limits of the 
Roots 
