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

DETERMINANTS IN GENERAL (BOURGET, 1877) 6

67

BOURGET, J. (1877): DOLP, H. (1877):
TEIXEIRA, F. G. (1877): ZELEWSKI, A. (1877).
[Principes l616mentaires sur les determinants,... Journ. de Math.
E14m., i. pp. 5-11, 33-37, 193-194.]
[DIE DETERMINANTEN,... 2te Auflage, bearbeitet von WY. Soldan.
iv+94 pp. Darmstadt.]
[Nogoes elementares sobre a theoria dos determinantes. Jorn. de
Sci. Math. e Astron., i. pp. 138-141.]
[THEORY OF DETERMINANTS, with Applications. (In Polish.) x+
191 pp. Krakow.]
In regard to the first three of these no remark is necessary save
that the second edition of Dblp's booklet is an improvement on the
first, the changes including (pp. 18-19) a variant of Becker's proof
of 1871 regarding the interchange of rows and columns. The fourth
I have not seen.
STUDNICKA, F. J. (1877).
[Beitrag zur Determinanten-Theorie. Sitzungsb.... Ges. d. Wiss.
(Prag), pp. 120-125.]
The main object of the paper is to advocate the use of
(A11An~n-A1flAf1) + a22. a, an 11 -as a means of evaluating Ial1a22... an,. The application of it,
to obtain a result in continuants and another in skew determinants
had already been made (Brioschi, 1856: Trudi, 1862).
DOSTOR, G. (1877).
[ELE~MENTS DE LA THE'ORIE DEs DE~TERMINANTS, avec application
'a 1'alg~bre, la trigonom~trie et Ia geometrie analytique dans le
plan et dans l'espace, 'a l'usage des classes de mathelmatiques
speciales. xxxi+352 pp. Paris.]
Up till the appearance of Dostor's work no text-book in French
had been available for students save the translations of Brioschi