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

CHAPTER XIV.

CIRCULANTS, UP TO 1860.
So far as mathematical writers have as yet noted, a set of
equations of the type
a(X1 + a22 +.. + ax,, = l1
acxn + ajx2 +.. + a,_-lx = U2
a21x + aX2,... + a,,2X = U
a2X1 + a3X2. +... + axl,. n
had not made its appearance in mathematical work prior to the
year 1846: and it is almost absolutely certain that before that
year the determinant of such a set had never been considered.
It is not at all unlikely, however, that the expression
a3+ b3+c 3-3abc
which is the case of the determinant for n equal to 3 had more
than once turned up in other connections, and that its divisibility
by a + b + c had been noted: but of this, too, there is no record.
CATALAN, E. (1846).
[Recherches sur les determinants. Bull. de V'Acad. roy......
de Belgique, xiii. pp. 534-555.]
As has been already explained, about half of Catalan's paper is
occupied with an elementary exposition of known properties of
determinants and with the establishment of a fresh theorem of
M.D. II. 2c