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

DETERMINANTS IN GENERAL (RUBINI, 1863-1867) 13

RUBINI, R. (1863-1867).
[Elementi di Algebra. 2' ediz. 381 pp. Napoli. 3a ediz.
iv+295 pp. 1866.]
[Complementi agli Elementi di Algebra. Napoli, 1863. 2a ediz.
viii+484+iv. pp. 1867.]
Rubini was a skilled expositor. The third edition of the 'Elementi,' a superior text-book, contains in two chapters (vii. pp. 217 -230, x. pp. 249-292) of nine lessons an excellent account of the
subject, occupying about twice the space given by Todhunter. In
the 'Complementi' there are an equally helpful lesson on elimination (xxxi. pp. 244-258), a second (xliii. pp. 337-343) on Jacobians
and Hessians, and other 'applications' less important.
ROUTH, E. J. (1864).
[Note on the invariants of the equation of the second degree.
Quart. Journ. of Math., vi. pp. 270-278.]
The carelessly worded statement (p. 273), that " the determinant
f n m 11
n g k 1
m k h 1
is the sum of the minors of all the terms of the determinant
f n in
n g k
m k h
seems to be the first approximation to a later formulated theorem
regarding the sum of the signed primary minors of any determinant.
BALTZER, R. (1864).
[Theorie und Anwendungen der Determinanten. 2te vermehrte
Auflage. vi+224 pp. Leipzig.]
The enlargement referred to in the title would have amounted
to about forty pages if the former size of page had been retained,