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

LESS COMMON SPECIAL FORMS (HERMITE, 1855) 465
that the first was obtained by multiplying the given determinant
columnwise by itself in the form
d1 dt d3 t4
C1 C2 C3 C4
-b1 -b2 -b3 -b4
-(1 - a- -a4
A generalisation by Brioschi (1855) has already been dealt with
under Skew Determinants.
ZEHFUSS, G. (1858).
[Uebungsaufgaben fiir Schtiler. Archiv d. Math. u. Phys., xxxi.
p. 246; or Nouv. Annales de Math., xviii. p. 171; (2) ii. pp.
60-61.]
The proposition offered for proof by Zehfuss is in modern
phraseology to the effect that the determinant of the difference of
the two square matrices
a. a..... a. b b.... b
a2 Ct2. a2 b1 b2.... b,,
a, aC,.... aG, bi b2.... b,
vanishes for all orders higher than the second. The proof given
by Gustave Harang in the Nouvelles Annales rests on the
operations
col1-col2, co12-colg,.....
When n= 2 we have
a,,-b1 ac-b2 = (a- (tO2(b1-b2).
a2-b. a2-b2
CAYLEY, A. (1859, March).
[On the double tangents of a plane curve. Philos. Transac. R.
Soc. (London), cxlix. pp. 193-212; or Collected Math. Papers,
iv. pp. 186-206.]
The theorem on which an important part of this investigation
rests is enunciated by its author as follows: If the 2n - 1 coltumns
M.D. II. 2 G