9 a 
La 11 
Appendix to a Method of extending. 
,» M*'* t t Nz ’ 3 
3 z v 4 . i ^ v 
11 16 *** T 3'9 ” 
e 
Rs 17 
xvz ^ © Sz lS , <, q Tz 19 
— + ‘ 
Bz Czz D z 3 E% 4 
AH 1 — ^ j 
e ee e i er 
/-\ T 3 r* ii 1 f. 
^3 42 X f X4 ^ ^ 
_ x Z£1 — 44 x Q" IG I £1 ^ 
4l X > 48 x ^ + rr^ 
5 6 V*« ^ Wz 2 ' 
6 0^ .20 “ f, X * %x 
ii x E£-ii x ^!! + &c or 
6 3 X f 2J 6 6 X f 22 + OCC. OF 
f' 9 
Fa 5 Gz* 
+ 
Hz 7 Iz” 
6 7 J 
K»« 
.Oz' 3 Pz ,+ 
Wz 7 ‘ 6z w Xz“ 
f 2 ‘ 66 X > 2 
+ &c ; 
in which it is evident that 
the generating fractions of the coefficients of the feve- 
ral terms are derived from thofe that immediately pre- 
cede them by the continual addition of the number 3 
to both their numerators and denominators.. 
An example of the refoluMon of a cubick equation by means 
of the expreffion \/ 3 fe+z + \/ 3 \e -Isj +4.\/ } ex the feriei 
c. given in Art. 5 _ 
Czz 
T" 
r* 6 ' Lz'° ?Z 14 T 
ttH riT ^ — 1 TF* + 
Art. 9. Let it be required to refolve the equation 
x 3 -x=l by means of the laid expreffion. 
Here q is = r, and r — | ; and confequently q 3 is — 1, 
and — — and — = ’ and - = which is lefs- than 
27 2 7 ' 2 6 7 4 36' 
3 
Pj, or J —. Therefore this equation does not come under 
cardan’s rule, but maybe refolved by the expreffion 
given in Art. 5, provided that though lefs than q —r 
is greater than half L or than — \ which it is, becaufe 
2 7 7 54 . 7 7 
3 it 
