118 A NOTATION OF THE POINTS AND LINES IN PASCAL’S THEOREM. [401 
For the ten-partite arrangement, any double triad such as ABI .DKL gives 15 
intersections; 10x15 = 150; and any pair of double triads such as ABI. DKL and 
AEH.GKO gives 36 intersections; 45 x36 = 1620; and these are 
10 x . 
6g 
60 g 
1 
9 m 
90 m 
15 
- 150 
6p 
270 p 
4 h 
180 h 
8 r 
360 r 
45 x ■< 
81 
360 t 
8z 
360 z 
l2 w 
90 w 
36 
1620 
1770. 
For the six-partite arrangement any pentad such as ABHJN gives 45 intersections; 
6x45 = 270; and any two pentads 
such as 
ABHJN and AEGMI give 100 inter- 
sections; 15 x 100 = 1500 ; and these 
are 
(30 h 
180 h 
6 X 
(15 m 
90 m 
45 
270 
f 4 9 
60 g 
\8p 
270 p 
24 r 
360 r 
15 x \ 
24 t 
360 t 
24 z 
360 z 
6 w 
90 w 
100 
1500 
1770. 
I analyse the intersections of 
a Pascalian line, say AE, by the remaining 59 
Pascalian lines as follows: 
Observe that AE belongs to the triad AEH, the complementary triad whereof is 
GKO ; it also belongs to the pentad AEIMG. 
We thus obtain, corresponding to AE, 
the arrangement 
H H H 
B N J 
F L D 
H A 
H E 
IMG 
K G 0