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

CHAPTER XII.

BIGRADIENTS, UP TO 1860.
As we have already pointed out (History, i. p. 487), bigradients
were first brought to light by Sylvester in 1840 in the paper
in which he made known his so-called "dialytic" method of
eliminating the unknown from two equations of the same or
different degrees. Shortly afterwards Richelot and Cauchy
recalled attention to Euler's and Bezout's method of 1764, as
giving substantially the same result as Sylvester's, the fact
being that the determinant obtained by Sylvester differs from
that obtainable in the other case merely by being its conjugate.
The details of these papers and of others related to them have
already been given.
CAYLEY, A. (1844).
[Note sur deux formules donnees par MM. Eisenstein et Hesse.
Crelle's Journ., xxix. pp. 54-57; or Collected Math. Papers,
i. pp. 113-116.]
Although Eisenstein's property * of the discriminant
a2d2- 3b2c2 + 4aCc3 + 4b3d - 6abcd, or A say,
of the binary cubic ax3 + 3bx2y + 3cxy2+ dy3,-namely, the property that
A2D2 - 3B2C2 + 4AC3 + 4B3D - 6A BCD
(a22 - 32c2 + 4 + + 4d - 6abcd)3
' Crelle's Journ., xxvii. pp. 105-106, 319-321.