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

CHAPTER III.

AXISYMMETRIC DETERMINANTS, FROM 1841 TO 1860.
UNDER the heading of axisymmetric determinants in our first
volume a reminder ought to have been given that the determinant
of the set of linear equations reached by Bezout in his so-called
abridged method for eliminating the unknown between two
equations of the same degree is axisymmetric, the first appearance
of this special form being consequently thrown back to the year
1764 (see p. 317 of Bezout's Recherches..). Further, it should
naturally thereafter have been recalled that the said axisymmetry
had been discussed by Jacobi in 1835 (see History, i. p. 214,
pp. 485-487) and by Cauchy in 1840 (see History, i. pp. 242-243).
CAYLEY, A. (1841, May).
[On a theorem in the geometry of position. Cambridge Math.
Journ., ii. pp. 267-271; or Collected Math. Papers, i. pp. 1-4.]
A general account has already been given of this interesting
paper-interesting as regards the subject, and interesting as being
the author's first 'prentice effort. All that remains to be noticed
here is what may be called Cayley's series of vanishing axisymmetric determinants. These we may write in the short form. ()1 (X)13 1
()21 * (x)23 1
()311 ()32. 1
1 1 1.,