(39) 
NOTE ON HESSE'S GENERALIZATION OF PASCAL'S 
THEOREM. 
By Thomas Mum, LL.D. 
(Read September 16, 1914.) 
1. Having appended an additional column and an additional row, 
namely, 
a,,a2, a,j,0 and /3i,/6)2, /3„,0 
to the matrix of the determinant Hesse" denoted by [a, /3] the 
determinant of the matrix thus resulting ; and if the matrix of [a,/3] were 
similarly bordered by 
7i>y2> •••> yn>0,0 and c^.c^, c„,0,0 
the determinant of the resulting matrix he denoted by 
With the help of this notation a number of interesting identities were then 
established, and these he utilized for the purpose of proving an important 
extension of Pascal's theorem. 
2. The last of the identities reached by him was 
= [a,/3] [a,S] [a,^] 
M] [y.f] 
[e,i;] 
(Z) 
and, it being important for him to know whether the cofactor of | | on 
the left was equal to 0, he satisfied himself that it was so when n is 1, and 
merely added that the same mode of proof would not suffice when n>l. 
Something more definite than this being desirable, the present note takes 
the matter up at the point where Hesse left it. 
* Ahhandl. . . . hayer. Akad. d. Wiss., xi. (1872), pp. 177-192. 
