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

DETERMINANTS IN GENERAL (FARUSSAC, 1845)

35

The method of proof is that known as "mathematical induction."
The details of it need not be given, as they correspond closely
with what are to be found in Scherk's paper of the year 1825,
the main differences being that Ferussac uses no special determinant notation, and, while clear and simple, is not nearly so
lengthy nor so laboriously logical.
TERQUEM, 0. (1846).
[Notice sur l'elimination. gNouv. Anrales de Math., v. pp.
153-162.]
This is a continuation of Terquem's paper of the year 1842.
Just as the previous portion dealt with Cramer and Bezout, this
deals with Fontaine (des Bertins), Vandermonde, and Laplace,
explaining concisely and clearly their main contributions to the
subject.
The only portion of it calling for notice is that in which
attention is drawn to the curious fact that Laplace makes no
reference to Vandermonde's paper read to the Academy in the
preceding year. In regard to this Terquem's remark is" I est extremement probable que Laplace n'a pas pris connaissance
du memoire de son confrere: on sait, d'ailleurs, que les analystes
fran~ais lisent peu les ouvrages les uns des autres. Ceci nous explique
egalement comment la resolution de l'equation du onzieme degre a
deux termes, la plus importante decouverte de Vandermonde, soit
restee ignoree jusqu'a ce qu'elle ait attire l'attention de Lagrange,
apres la decouverte similaire de M. Gauss."
Not only, however, does this explanation not carry us far, but
the question arises whether the point sought to be explained is
really the point which stands most in need of explanation.
Vandermonde's paper was read at the very beginning of 1771
and Laplace's in 1772: yet in the History of the Academy for
the latter year Laplace's occupies pp. 267-376 and Vandermonde's
pp. 516-532, and neither refers to the other's work.
It may be noted here that, notwithstanding Terquem's knowledge of the early history of determinants and his manifest
desire to induce his readers to take up the subject, he does not
himself hold the new weapon with a very firm grasp. For