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

290 HISTORY OF THE THEORY OF DETERMINANTS

their values would be positive: also that one would possibly have
expected the second determinant to be identical with the first fourline minor in the third.
BAUER, G. (1868).
[Von der Zerlegung der Discriminante des cubischen Gleichung,
welche die Hauptaxen einer Flache zweiter Ordnung bestimmen (sic), in eine Summe von Quadraten. Crelle's Journ.?
lxxi. pp. 40-45.]
Bauer, with his eye on Kummer (Hist., ii. p. 295), takes the discriminant of
a-x h g
Ih b-x f = 0, or, say, x3-Px2+Qx-R 0,
g f c-x
in the form of Bezout's axisymmetric eliminant
6Q-2P2 -9R+PQ
-9R+PQ 6RP-2Q2
and, partitioning it into four determinants, succeeds in evolving
Borchardt's, his own, and Kummer's expressions for it in terms of
13, 10 and 7 different squares respectively.
GERONO, E. (1870): WISSELINK, D. B. (1877).
fNote sur une application de la theorie des determinants. Nouv.
Annales de Math., (2) ix. pp. 392-398.]
[Merkwaardige eigenschappen van eenen determinant van den.
derden graad. Nieuw Archief v. Wisk., iii. pp. 84-89.]
These are simple expositions of the properties of the three-line
orthogonant, Wisselink following the lead of Gerono.
VELTMANN, W. (1871).
[Beitrage zur Theorie der Determinanten. Zeitschrift f. Math. u.
Phys., xvi. pp. 516-525.]
Veltmann's second contribution (pp. 523-525) concerns Cayley's.
construction of an orthogonal substitution. He dispenses with