Note on Hesse s Generalization of Pascal's Theore^n. 
43 
that the said elements are minors of [aye?;,/3c46l, which is a determinant 
of the (?i4-4)th order. Further, a httle examination shows that they are 
the minors in that determinant which are complementary to the principal 
minors of the array 
0 0 0 0 
0 0 0 0 
0 0 0 0 
0 0 0 0. 
It is therefore interesting to inquire what would happen if we made 
the bordered determinant [aYer],(jci^6] a perfectly general determinant, 
substituting 
for the bordering columns, and 
for the bordering rows and the array of zeros. The left-hand side of the 
identity would then be 
and the four-line compound determinant on the right would be 
On inspection of these we readily perceive not only that the identity 
still holds, but that it may be viewed as simply an " extensional " of the 
truism 
The same "extensional" will be found arrived at by a different path in 
1881 on page 4 of vol. xxx. of the Transac. B. Soc. Edinburgh. 
Capetown, S.A. 
August 25, 1915. 
