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

CHAPTER I.
DETERMINANTS IN GENERAL, PRIOR TO 1841.
SINCE the publication of the first volume of this History, two
other writings have been discovered which concern the general
subject and belong to the period therein dealt with. The authors,
Bianchi and Chelini, being very imperfectly acquainted with the
relevant literature of the previous part of their own century,
could scarcely be expected to make any advance: and, as the
following notices will show, no advance was really made.
BIANCHI, G. (1839, January).
[Sopra l'analisi lineare per la risoluzione dei problemi di primo
grado. Mem. dellc Soc. ita. ldelle Sci., xxii. pp. 184-227.]
Bianchi's knowledge of previous work on simultaneous linear
equations must have been. slight-confined, probably, to an
acquaintance with Cramer's rule and with Cauchy's so-called
"symbolical" solution as given in the Comrs d'Analygse of 1821:
unless this were so, he would scarcely have referred to the
methods given in such text-books as Ruffini's Elementary
Algebra and Euler's Elements. One is thus prepared to find
little new in his conscientiously laboured monograph, consisting
of -an introduction of five pages, a section of twenty-seven pages
on the solution of a set of n equations with n unknowns, and a
section of twelve pages on n equations with fewer unknowns.
The main interest lies in the first fifteen pages (pp. 189-204)
of the earlier section, these being devoted to establishing the
validity of Cramer's rule. The procedure consists in eliminating
M.D. II. A