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

DETERMINANTS IN GENERAL (CAYLEY, 1843)

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and
Rx + R'y+... S+S'y+.......
A + B~i +... /..
A'+ B' +...
These are denoted by KU, FU, [ U; and the closing sentence of
the introduction is, "The symbols K, F, 1 possess properties
which it is the object of this section to investigate."
KU, it will be observed, is what afterwards came to be called
the discrirninant of U; and FU, IU are the results of making
certain linear substitutions for the elements of the first row and
of the first column of the determinant
x y z....
a /3 y;] a.3 y....
~ a" a " o
~7..... 1...
It is this determinant, therefore, which is under investigation
and under comparison with U. That it is a bipartite function of
x, y, z,... and e a, %,... is manifest when we think of expanding
it according to binary products of the elements of the first row
and of the first column, the expression for it in the notation of
bipartites being thus seen to be
x y z....
-I /3Y... -I'y "... I....
- /y'...| - ay'... |-la3......
-|... | |... - a/... |....
Now the properties of this which are investigated by Cayley are
properties possessed by the more general bipartite
x y z.
Ca1 a2 a3...
b1 b2 b3....
C1 c2 C3....