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

COMPOUND DETERMINANTS (HUNYADY, 1879) 205

HUNYADY, E. (1879).
[Der Satz von Desargues uiber perspectivische Dreiecke. Crelle's
Journ., lxxxix. pp. 79-81.]
Here Hunyady's object is to establish the identity in coordinate
geometry which is the equivalent of Desargues' theorem. To this
end he first shows, in regard to the array
x1 X. X3 X4 X5 X6
Y1 Y2 Y 4 Y5 YG?/
1 Z3 Z4 Z5, (;
that
IY1Xz I I Xz I xXI2 -
| YZ.15 Z2X X2 Y 5 x| l ^ ^
I yz f x 2y II I x xyyz6f x Ii
I yZ6 I I XX Y I 3y6 I
which is readily done by multiplying the determinant on the left
rowwise by
X1 Y1 zi
X4 y4 Z4
2 Y2 Z2
He then forms the array
X1 X2 X3 X4 X5 X6
Y Y2 Y3 Y4 Y5 Y6
Z1 Z Z3 Z Z5 Z6,
where lXY.Z3 1], I X4Y5Z6 I are the adjugates of ] xy2z [, | x4y5Z6
respectively, and applying to it the theorem just reached obtains
of course
I Z z2X5 X3YI I 1 XlYz5 i I X4Y2Z5 1
I Xl1,3 I I X4Y3ZG 1
Here, however, each element of the irst column on the right can, by
multiplying by I xIy2z3 1, be shown to have I xy2z3 \ for a factor,
and similarly each element of the second column to have I x4yz61
for a factor, the right-hand member thus becoming
I xly2z3 * I 5Z6I * X4y I I X136 I;