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

JACOBIANS (NEUMANN, 1868) 263
NEUMANN, C. (1868).
[Zur Theorie der Functionaldeterminanten. Math. Annalen, i.
pp. 208-209.]
This is merely an unexpected verification of Jacobi's 'fundamental
lemma' of 1844 (Hist., ii. pp. 230-234).
CLEBSCH, A. (1868).
[Ueber eine Eigenschaft von Functionaldeterminanten. Crelle's
Journ., lxix. pp. 355-358.]
[Note zu dem Aufsatze "Ueber eine Eigenschaft...." Crelle's
Journ., lxx. pp. 175-181.]
The property in question is to the effect that If uP, u2,?3u....
be n +1I homogeneous integral functions of the rt1 degree in the n
variables x1, x,,,...; v1, v2,..., v,,,l be the set of Jacobians
formed from the u's; and wl, w,..., w,,+ the set formed in like
manner from the v's; then
u U2= U3
Wi W2 W3
By way of proof it is shown that, whatever values the a's and b's
may have, the last row of the determinant
av,?V,. x a
a, b,
yax, aDy ODy2
ax, ax... ax, a b2,av- a?n+ avn, ~a
Dx3-1 Dx2 D
laayj, i~b,,Uh
can be made to vanish: that therefore
Eb,hu, -Ea,w, - Zahuh.Zbkwk = 0;
and that therefore, "by putting the coefficients of the products
akb, separately equal to zero," there results

UhW7 - Ukwh, = 0

as desired.