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

36 HISTORY OF THE THEORY OF DETERMINANTS

-example, in giving in this volume an account of a paper of
Grunert's in Crelle's Joumrnctl, viii. pp. 153-159, in which the
author says"Eutwickein wir nemlich x', y' Z', durch Elimination aus den
Gleichungen:
x =Ax' + By' + Cz',
y = A'x' + B'y' + C'z',
z - A'x' + B"y' + C'z',
so erhalten wir:
' (B'C" - B"C') x + (BC - BC") y + (BC' - B'C) z
wena wir
L =AB'C" - A'BC" + A"BC' - AB"'C' + A'BC A"B'C
setzen "
he paraphrases the passage as follows:
"Les equations donnent
-i x [B'C"] + y [B"C] + z [BC'1
oiles crochets repr'sentent des bino'mes altern~s;
[B'C"] = B'C"f - B f
et ainsi des autres: L est la rgsullante, de'nominateur commun."
'The simultaneous use of birt~me alterne' and resultante is far
from happy. *
* Two years later we find him, in referring to a paper of Cayley's where
the determinant
L T S~
T M R i
S R N~,ocenrs, calling it, as he did in 1845, a "Ifonction cram~rienne," and writing it
{L T S~
TM R i
8 R N
See Noutv. Annales de.Aiath., iv. (1845), p. 535; vii. (1848), p. 420.