1888 - 89 .] Dr T. Muir on the Theory of Determinants. 
767 
Aj A 2 
Bj B 2 
c, c 2 
B 3 B 4 . 
c 3 c 4 . 
A 3 A 4 A 5 Ag 
B 3 B 4 B 5 B 6 
C 3 c 4 C 5 Cg 
“Consider now the points 1, 2, 3, 4, 5, 6, tlie coordinates 
of these being respectively x v y lt z v , x 6 , y Q , z 6 . I 
represent, for shortness, the equation to the plane passing 
through the origin, and the points 1, 2, which may be called 
the plane 12, in the form 
x 12* + y 12, + z 12 2 = 0; 
consequently the symbols 1 2 Z , 1 2, , 1 2 2 denote respectively 
?/iZ 2 ~ y& , z i %2 ~ z 2 x i j X \V* ~ > an( i similarly for the planes 
13, &c. If now the intersections of 12 and 45, 23 and 56, 
34 and 61 lie in the same plane, we must have by lemma (1) 
the equation 
12, 
45, 
23, 
56 x 
12, 
45, 
23, 
56, 
12. 
45 2 
23. 
56 a 
. 
. 
23, 
5 6* 
34, 
61, 
23, 
56, 
34, 
61, 
23, 
56 a 
34 2 
61* 
Multiplying the two sides of this equation by the two sides 
respectively of the equation 
Xq x 1 x 2 
Ve V\ y-> • - ■ 
% «l 2, . • • 
. . . # 3 x 4 x 5 
• • • y 3 y± y§ 
• % S 4 Z 5 
= 612 . 345, 
