( po ) 
propofed Equation has no imaginary Roots. The 
Quadratick deduced from the jhree firft Terms x” — 
will manifeftly have this Form, 
nxn — I xn — 'LXn — 3 6cc. x x^ ^ — n — i X 
^ ^ — 3 X // — 4 6Cc. xAAr-l-^^ — 'LXn — 3 
Xn — 4 X — 5* < 3 cc. X B = o, continuing the Fad- 
ors in each till yon have as many as there are Units in 
n — 2. Then dividing the Equation by all the Fad- 
ors — 2, n — 3 < 3 Cc. which are found in each Coef- 
ficient, the Equation will become nxn — ix;v* — 
n — iX2.Aa;-4-2xi xB= o,whofe Roots will be 
imaginary by Prop. i. when nxn — 1X2X4B exceeds 
■ n — I 
n — i|*x 4 A*, or when B exceeds A%fo that the 
2 
propofed Equation mufl: have fome imaginary Roots 
A * ^ as we demonftrated after 
when B exceeds 
2 n 
another Manner in the v^^^ Propolition. The Quadra- 
tick Equation deduced in the fame Manner from the 
three hrft Terms of the Equation A .v — 2 B.v”*"* 
+ 3 C 6cc. =r o, will have this Form n — 1 x 
n — X X « ^ 3 6cc. xAa;^ — n > — 2x?/ — 3 x 71 — 4 
6cc. x 2 B;v-|-^^ — 3 n — 4x;/ — 5'<5cc. X3C=: 
o 5 which by dividing by the Fadors common to all the 
Terms, is reduced to — i xn — 2 x A ^ — 2. x 
4B AT-|- 6 C = OjWhofe Roots muft be imaginary when 
2 71 — 2 , . 
— X X B is Icfs than A C : and therefore m 
in — I 
that cafe fome Roots of the propofed Equation muft be 
imaginary. 
Cor. III. In general, let D a: — E .v + 
F X be any three Terms of the Equation, at" — 
A X 
