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

DETERMINANTS IN GENERAL (SCHLOMILCH, 1856) 93

SCHLOMILCH, 0. (1856).
[Brioschi's Theorie der Determinante und ihre hauptsachlichsten
Anwendungen. Zeitschrift f. Math. u. Phys., I. Literaturzeitung, pp. 80-87.]
After a faithful account of Schellbach's translation of Brioschi's
text-book, Schlomilch inveighs against the adoption of "die
miserable englische Terminologie," instancing Unterdeterminante,
Determinante mit recipro7ken Elementen, and Hessian, for the
last of which he proposes to substitute " Inflexionsdeterminante."
RUBINI, R. (1857, May).
[Applicazione della teorica dei determinanti. Annali de Sci.
nat. efis., viii. pp. 179-200.]
This resembles Chio's paper of 1853, having the same fundamental theorem, but different illustrative examples. In the mere
enunciation of the theorem Rubini is the more successful. Taking
the vn-line determinant whose element in the place r,s is acrs brS,
and denoting by A the determinant of the a's, and by Ar a
determinant obtainable from A on substituting for r columns of
a's the corresponding r columns of b's, he writes the expansion in
the form
A+ A1+ A+.... + EA,_+A,.
BELLAVITIS, G. (1857, June).
[Sposizione elementare della teorica dei determinante. iMemorie... Istituto Veneto,... vii. pp. 67-144.]
Notwithstanding its place of publication, this writing of
Bellavitis' is exactly what its title implies; and as a text-book
it could scarcely have failed to be useful, so simple and clear
is it in style. It consists of two chapters, one on determinants
in general (pp. 3-3()), and one on special forms (pp. 30-72): a
note of six pages on permutations appears as an appendix.
To Bellavitis we owe the modification of Laplace's notation
which is now in common use. The passage introducing it is: