THE IX-AND-CIECTJMSCEIBED POLYGON. 
233 
we have, up to 45, which is all that is required, — - 
X 
1 
II 
II 
1 
X 
14=a-ix 
\o—a~^ X 
23= 
24 = 
25 = 
34= 
35 = 
45 = 
A. 
A. 
A 
A 
A 
A 
A 
— 1 a(P 
-|-2 ahdP 
-f 1 a^ccP 
( ^ 
+ 1 a^d^ 
— 2 acdp' 
— 1 €?d? 
4-4 a^hd? 
+ 2 a^cP 
— 2 a^cd? 
f -1 
- 1 a^d^ 
— 2 hcd 
— 1 a(?d 
— 4 
— 2 a-bc<P 
~2 b^d 
+ 4 abed? 
4-5 c?<?d? 
— 3 a^(?d^ 
-8 a^b’^d? 
-i- 4 a^bed? 
-1 c® 
+ 4 It^cd 
+ 6 adc'^d 
+ 4 a^c^d 
“ 1 
-t-4 ftVc? 
— 8 ab“c<P 
— 4 ab(?d 
— 2 aVc? 
— 8 oPe^d? 
+ 2 6c^ 
+ 2 ac* 
+ 8 ab^dr 
+ 2 bc^ 
4-4 ab(?d 
— 2 ac* 
-fS a¥c^d 
-1- 8 a^Wd? 
-8 b^cd 
— 20 aVc‘d 
4-2 ac® 
4- 4 abc^ 
-1-12 a?b’^(rd'^ 
— 4 
— 8 abc^ 
-8 
— 4 edbe^d 
+ 1 6 b*cd 
-4 
— 4 aV 
+ 8 b^c^ 
1 
— 4 
-7 
+ 7 
-7 
— 5 
+ 9 
— 5 
-7 
0 
H-7 
Forming in like manner the determinants of the matrix 
( C, D, E, F, .. ), 
D, E, F, G, . 
E, F, G, H, 
and representing these by 123, 124, &c., \iz. — 
we have, up to 234, 
C, D, E 
D, E, F 
E, F, G 
&c., 
123 = a-> X 
124 = a-> X 
134 = <z-ix 
234 = 
' A 
' 4- 1 
-1-2 (dbcdP 
— 1 d?(?d^ 
— 2 abc*d 
-1 ac® 
r ^ 
— 4 a?bd* 
— 3 a?c^(P 
— 8 a?b‘^cd^ 
— 4 a'^bc^d? 
-2 aVrf’ 
-f 4 ab‘^c*d 
4-2 a6c® 
f ^ 
-f I a*cd* 
-f 4 aWd^ 
+ 8 a?bc'^d^ 
— 3 a?c*d'‘‘ 
+ 8 a^b^cd^ 
4-12 d^Vc^d? 
— 2 add 
' . '' 
— 1 add? 
— 4 adbed* 
— 4 aVrf* 
-4 a='6Vrf’ 
-6 d^bc^d"^ 
-2 aW 
-1 
-15 
H-28 
-21 
and fiurther, the determinants of the matrix 
c C, D, E, F, .. ), 
D, E, F, G 
E, F, G, H 
F, G, H, I 
in the present case, the single determinant 
1234= 
C, D, E, F , 
D, E, F, G 
E, F, G, H 
F, G, H, I 
2 K 
MDCCCLXI. 
