( * 9 ) 
which is againfl: the Suppofition, The fame is true of 
theEquation A ^ ^ 3 6cc* 
= o, for the fame Reafon; ' ’ ‘ ~ " 
C o Fv. The biquadratick + — Aa?* p y » - 
Ca? -|- D = o, will have two imaginary Roots, if 
two Roots of the Equation .3A;V* + xBa; 
— C = o be imaginary- or if two Roots of the Equa- 
tion Aa; 5 ^xBa ;2 + 3Ca; — 4D= obe ima- 
ginary. But two Roots of the Equation 3 A at ' 
+ 2BAr — C==o mull be imaginary, when two 
Roots of the Quadratick 6 x^ — *3AAr + Br=o or 
of the Quadratick 3 Aa^* -_4Ba'+3C = o are 
imaginary^ becaufe the Roots of thcfe quadratick Equa- 
tions are the Limits of the Roots of that Cubick, by 
the third Theorem - and for the fame reafon two Roots * 
of the Cubick Equation A x^ ^ zB x ^ -f. 3CA? 
4 D = o muft be imaginary, when the Roots of the 
quadratick ^ A x^ x -j- 3Cz=o,orof the qua- 
dratick — 3 Ca^’-(- 6 D= o are impollible 
Iherefore two Roots of the Biquadratick at+ — Aat * 
-j- Bat*—. Cat -j- D = o muft be imaginary when 
the Roots of any one of thefe three quadratick Equa- 
tions 6 x^ ^ 3 Aa- + B = o, 3 Aa’*^4 Ba- -f 
3C — o, Ba"* 3CA; + 6D = o become imagina- 
ry ; that is, when -L A* is lefs than B, 1 L B* lefs than 
« 9 
A C, or -~C ^ lefs than B D. 
0 
Cor. If. By proceeding in the fame manner, you 
may deduce from any Equation at” — Ax’*'~~'^ 
B A* ^ — Cx ^ 6cc. == o, as many quadratick 
Equations as there are Terms excepting the firft and 
laft whofe Roots muft be all real Quantities, if the 
^ ^ pro- 
