( 5*9 ) 
whofe Index is the Dimenlions of the propofed Equa- 
tion, fubtrad Unity, then divide each Remainder by 
twice the Correfpondent ‘Vncia, and fet the Fradi- 
ons which refult from this Divifion, above the mid- 
dle Terms of the given Equation. And under any 
of the middle Terms if its Square multiplyed by the 
Fradion {landing above it, be greater than the Red- 
angle under the immediately adjacent Terms, Minus 
the Redangle under the next adjacent Terms, Tins 
the Redangle under the Terms then next adjacent 
— &c. place the Sign ~f-, but if it be lefs, place 
the Sign — . And under the firft and lafl Term 
place -f*. And there will be at lead as many im- 
pofiible Roots, as there are Changes in the Series of 
the under-written Signs from -f- to — , or from — 
to +. Let it be required to determine the Num- 
ber of impoffible Roots in the Equation x^ — 
£ x 6 -|- 1 $ x s — 23 x 4 -f- i8a? s -J- i ox 2 — 
1 8 x + 1 4 = o. The Vncia of the middle Terms 
of the 7th Power of a Binomial are 7, 21, 35, 35^ 
21, 7, from which fubtrading Unity, and dividing 
each of the Remainders by twice the correfpondent 
20 
* Vncia , the Quotients will be — , 
r 4 
34 20 6 3 10 1 7 
or 
70 
10 
42 
14 
21 
3 S 
34 
70 
17 
3 ? 
, — • which Fradions place above the middle 
21 7 
Terms of the Equation, has xi 
+ 
B b b b 
* 
1.0 
2 1 
5 x 6 + 15 
+ 
2 3 x 4 -£■ 
