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

100 HISTORY OF THE THEORY OF DETERMINANTS

and infer that it is the equivalent of
a+b+c+...+h a+c+d+e a+b+d+f a+b+c+g
a+c+-d+e a+c+d+-e a+d a+c
a+b+d+f a+d a+b+b+f a+b
a+b+c+g a+c a+b a+b+c+g
In connection with unisignant determinants like these, it is
desirable to recall Sylvester's paper of 1855 and Borchardt's of
1859 (Hist., ii. pp. 456-9).
SIEBECK, F. H. (1862).
[Ueber die Determinante deren Elemente die Quadrate der sechzehn
Verbindungslinien der Eckpunkte zweier beliebigen Tetraeder
sind. Crelle's Journ., lxii. pp. 151-159.]
The determinant in question is brought forward as a companion
to Sylvester's of the year 1852, being, in fact, the complementary
minor of the zero element in the latter. It is shown that the ratio
of the one to the other is
2rp cos p,
where r, p are the radii of the spheres circumscribing the tetraedra
and j the angle of intersection of the said spheres. The interest
of the paper, like Sylvester's, is mainly geometrical.
FREUCHEN, P. (1863).
[To Determinanter af nte Grad. Math. Tidsskrift, v. p. 42.]
The two determinants are the cases of Ferrers' of the year 1855,
in which a1 = a2= a...
ROBERTS, M. (1864).
[Question 694. Nouv. Annales de Math., (2) iii. pp. 139-140.
Solutions by L. Ferrara, G. Torelli, in Giornale di Mat., ii.
pp. 95-96, p. 191: solutions by A. Smet-Jamar, M. Cornu,
H. Picquet, in Nouv. Annales de Math., (2) iii. pp. 395-399,
and by " Mirza-Nizam," in (2) iv. pp. 500-504.]
Roberts' result is essentially the same as Ferrers' second, but is
expressed more suggestively, namely,