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

CHAPTEIIn IV.

ALTERNANTS, FROM 1832 TO 1860.
NOTE ought to be taken of the fact that the first three papers
here to be dealt with, namely, the papers by Murphy (1832),
Binet (1837), and Haedenkamp (1841) belong to the previous
period. Nothing, however, appearing in the former chapter on
the subject requires modification on that account.
Further, as exaggerated statements regarding Vandermonde's
contributibn to the subject have been widely accepted, it seems
desirable to point out the exact foundation on which such statements rest. In a paper* read in November 1770 Vandermonde
says (p. 369), "Or a2b + b2c+ c2a-a 2c- b2a- c2b, qui egale
(cC-b)(a-c)(b-c) a pour carre a46 +...." This is the whole
matter.t
MURPHY, R. (1832, Nov.).
[On elimination between an indefinite number of unknown quantities. Transac. Cambridge Philos. Soc., v. pp. 65-76.]
Murphy's third example in illustration of his method is the
set of equations
1 + xi + x2 +....+ x = 0o
1 + 2x, + 22x2 +.... - + 2x = 0
1 + 3x1 + 32x2 +.... + 3xn = 0
1 + nx1 + 2X2 +....+ n, = 0
* VANDERIONDE, N. Memoire sur la resolution des equations. flmn. de l'Acad.
des Sci. (Paris), Annee 1771, pp. 365-416.
t See Nouv. Annales de Mlath., xix. p. 181 footnote.