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

18 HISTORY OF THE THEORY OF DETERMINANTS

As a matter of fact, however, a close examination shows that
the functions whose properties are investigated are not strictly
determinants, but belong to a class afterwards named bipartites
by Cayley himself. It is true that it is the determinant notation
which is employed in specifying the functions, but this is due to
the fact that the bipartite under discussion is of a very special
type, and so happens to be expressible as a determinant.
The function U from which he considers his three determinants
to be "derived " is
x(at+ +....)
+ y(a'+3+ +... )
+..... ~ ~ ~ ~
there being n lines and n terms in each line. This at a somewhat later date (1855) he would have denoted by
a' /3.....
and called a bipartite. A still later notation is
a /....
a' /3'.. y
from which each term of the final expansion is very readily
obtained by multiplying an element, 3' say, of the square array by
the two elements (y, 7j) which lie in the same row and column
with it but outside the array. The three determinants which
are viewed as "derivational functions " of this function U are
a /....
a' /3'. ~ ~
Ax + A'y +... Bx+B'y+.......
_ R + Si, + a /3
R' +S'+l.... a i a' 3'....R... ++.........,