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

AXISYMMETRIC DETERMINANTS (CAYLEY, 1853) 139
a_ a1 ao.1
a 0 afl- 1, 1 an 1 nle re'sultat de l''lirnination sera
a00 0.
a10 all... al,n.1
Instead of paraphrasing this by means of a more familiar
notation, as the editor of Crelle found it necessary to do, it will
be better to apply it to a simple case, namely, where the given
equations are
a3cc3 + a2x2 + aixc + a0 = 0
b3x3 + b 2X2 + bix + b0 = of
being careful to proceed in such a way as also to justify the,
rule.' Beginning, with
ao+alx+a X2+a X3 ao~a1ly'+a y2+ t3y
b0+ b~x+ b2cc2~+ b3X3 bo~ bly~ b2 y2 + b3y3 +(-)
which vanishes for all values of y, we change it into
Ia0bo + (i0bl y ~ a0b2 1y2 + a~b. 3
+ Ialb01 x + alblccy +.x)
then into
Ia0b, I + Ia0b9l (Y~+ ) + Ia0b.31(y2 + yX X2)
+ I(alb2 IXY + a~b3XY (y + X)
+ a2b3IXy2
and finally into
1 ~~~x X
a0b1 abJ
Ia0b2l a0b0l + Ialb9) a'lb31 j
I Ub31 alb3l a~b3
where- the elements of the square array- are those of Bezout's
condensed eliminant, as we have already f ound in a footnote
when dealing with Jacobi's paper of 1835.