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

COMPOUND DETERMINANTS (BORCHARDT, 1880) 207
which, with the help of a previous identity (-D = P) becomes
the result desired."
BORCHARDT, C. W. (1880).
[Remarque relative au memoire de M. Sylvester sur les determinants composes. Crelle's Journ., lxxxix. pp. 82-85; or
Werke, pp. 494 et seqq.]
After restating Sylvester's theorem of the preceding year, Borchardt intimates that in consequence of correspondence with
Sylvester he had been requested by the latter to withdraw the
theorem for the present. He then conclusively shows that the
enunciation cannot be accepted as correct by taking the simplest
possible case, namely, where
n = 4, a =2, a = 1,
b=2, =1,
and where, therefore, the subject under discussion is the resolvability of
13 14 23 24
13 141 2324 4,
that is to say, of the central four-line minor of the second compound
of 1234. According to Sylvester this central four-line minor
must be equal to
1234 12 34
1234 12 34
and Borchardt formally proves that it is equal to
1234 1. 12 12
1234 121 34
34 341
12 34,
as indeed is manifest from Franke's theorem of 1862, which Borchardt
had established and had helped to make known.
* This is not Pasch's proof, which would have necessitated the introduction
of additional notation and auxiliary matter not otherwise of use in the present
connection.