The theory of determinants in the historical order of development, by Sir Thomas Muir.

AXISYMMETRIC DETERMINANTS (CAYLEY, 1846, 1856).95
Similarly the result of 1856 is that if A., B,.. be negative
elements of the adjugate of

a h gy
A b f 11
gfc C
and a, 3, y be quite arbitrary, then
a h g iN-y',
/I b ~f Y$-ag-4
g f c ull_-P e

A H G
H BF /3
G FC y

BRIOSCHI, F. (1854).
[LA TEoRIOA DEi DETERMINANTI,. v. viii+116 pp. Pavia.]
Brioschi (~ 6), in defining after Gauss (Hist., i. pp. 64-65) the fornm
adjunct or adjugate to

to be the form

E a,.,xx, I' I' 2Y. ~.
8=1, 21.
EA,,se.& r=, 2,.n

where AP. is the cofactor of al,s in I a1n f, but where there is no connection between the x's and e's, writes the two as determinants of
the (n +1)th order, namely,
a1-I XI All A12... A,_,.11..12. a,
x2 A21 A22 A2,, $2 a21 6122... a2,,
x, A,1 A,2 Ann I e an, a. a,
the justification for which is seen on developing the determinants
in; terms of binary products of the x's and the C's respectively, and
using in the case of the first a result of Cauchy's regarding the
adjugate of the adjugate (Hist., i.. p. 110). The first of the two
identities, for the case of n equal to 3, was given by Sylvester in
1850 (Hist., ii. pp. 117-118). The second we should have drawi
attention to when reporting (Hist., ii. p. 153) Salmon's remark