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

22 HISTORY OF THE THEORY OF DETERMINANTS

The Second Section is said to concern "the notation and
properties of certain functions resolvable into a series of determinants," and it is at once seen that the functions in question
are obtainable from the use of n sets of n indices in the way in
which a determinant is obtainable from only two sets. Sylvester
spoke of them later (1851) as cornmmtants.*
CAUCHY, A. L. (1844).
[Memoire sur les arrangements que l'on peut former avec des
lettres donnees, et sur les permutations ou substitutions a
l'aide desquelles on passe d'un arrangement a un autre.
Exercices d'Analyse et de Phys. Math., iii. pp. 151-252;
or (Euvres completes, (2) xiii.]
The nature of the connection of this with the theory of determinants is evident from the title. Some of the elementary
portions of the memoir had in fact already appeared in Cauchy's
determinant papers of the years 1812, 1840, 1841, and have been
noted in our accounts of the latter. In these papers, as was
natural, only such isolated properties were given as might be of
immediate application to the main subject: here we have a
methodically arranged and lucidly written treatise. As, however,
in dealing with permutations the question of signature is not
taken up, there is no explicit reference to determinants: and all
that is therefore necessary is to direct attention to a storehouse
of information regarding a subject closely connected with them.
CAUCHY, A. L. (1844).
[Memoire sur quelques proprietes des resultantes a deux termes.
Exercices d'Analyse et de Phys. Math., iii. pp. 274-304; or
(Euvres completes, (2) xiii.]
By "resultantes a deux termes" are meant determinants of
the second order. The expression recalls "resultantes a deux
lettres," used by Binet in his memoir of November 1812; and as
* See Postscript to Cayley's paper "On the Theory of Permutants," Camb. and
Dub. Math. Journ., vii. pp. 40-51; or Collected Math. Papers, ii. pp. 16-26.