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

8 HISTORY OF THE THEORY OF DETERMINANTS

BAEHR, G. F. W. (1861).
[Propriete des coefficients du bin6me et theoreme Sylvester sur les
determinants. Nouv. Annales de Math., xx. pp. 417420.]
The theorem in question is Sylvester's unimportant second lemma
of 1852, Oct. (Hist., ii. p. 77).
COINTE, I. L. A. LE (1861).
[Memoire sur les determinants crameriens ou resultants algebriques.
Annali di Mat., iv. pp. 233-245.]
This so-called memoir, lengthy and tiresomely precise, ends
only in a rule like Reiss' (1829) and Cantor's (1855) for telling the
sign of a permutation when the ordinal number of the permutation
is known.
PAINVIN, L. (1862).
[Memoire sur les tetraedres. Nouv. Annales de Math., (2) i. pp.
267-286, etc.]
The memoir opens with a preliminary theorem in determinants
(pp. 267-271) which, if stated in the form
{adjuglalnj}2 = adjug { Jan,2}
would justly be viewed as merely a case of a theorem of Cauchy's
of the year 1812 (Hist., i. p. 121). It must be noted, however,
that what Painvin establishes is something more important, namely,
the identity of the two determinants ' elementa element,' that
is to say, the identity of their matrices. (Cf. Hist., ii. p. 95.)
TRUDI, N. (1862).
[TEORIA DE' DETERMINANTI, e loro applicazioni. xii+268 pp.
Napoli.]
This is a text-book similar in scope to those of Brioschi and
Baltzer, but intended for less advanced readers. The explanations
are consequently fuller, the illustrations are more numerous, the
less simple theorems are broken up for gradual absorption, and to
deductions that are self-evident are given formal enunciations.