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

AXISYMMETRIC DETERMINANTS (SALMON, 1859) 153
it is readily seen that, in the special case where = 2 and where
therefore I is the discriminant of the quantic, the evectant is.
expressible as an axisymmetric determinant, namely, that obtained by 'bordering' the discriminant by the contragredient
variables; for example, taking the ternary quadric
x y z
a h g x
h b f y
gf c z
we have for the evectant of its discriminant
a h g
h bf
g f c.
In recalling this fact at the beginning of his Fifteenth Lesson
and a further fact regarding the form of the evectant of a.
discriminant which vanishes, Salmon digresses for a moment to
put on record (~155) an implicated property of axisymmetric
determinants, namely, that if the cofactor of the element in
the place (1, 1) of an axisymmetric determinant vanishes, the.
determinant is expressible as 'a perfect square,' his meaning
being, the square of a linear function of the elements of the
first row.
It is not uninteresting to observe here that this unpretentious
but important manual of Salmon's and the very useful Theoorie
Ge'nerate de 'Elitzination of Faa di Bruno above and elsewhere:
referred to appeared almost simultaneously in the year 1859,
and that the one was dedicated to Cayley and Sylvester and
the other to Cayley.