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

DETERMINANTS IN GENERAL (CHELINI, 1840)

3

Attention must also be drawn to a certain neglect in regard
to the theorem about the effect of increasing each element of a
row (or column) of a determinant by a constant multiple of the
corresponding element of another row (or column). It is unquestionably curious that this very elementary property should
not have been formulated at a comparatively early date. The
writers whose work came nearest to it were Scherk (1825) and
Drinkwater (1831): indeed it is little short of marvellous that
the latter author should have written his eighth and ninth
propositions in the form
/(v+ w, x, y, Z,... ) (V y.. ) +. )+/ (w, x, Z,,... ),
f(mx, y, z, t,... )=.f(x, y, z, t,... ),
(see History, i. p. 199), and should not have added
f(v+imx, x, y, z,...) = f(v, x, y, z...).
Though not formulated, the property in question, however, may
actually have been used: and there is certainly evidence of such
use in the last year of the period, as may be seen on turning to
the closing lines of Jacobi's De functionibus alternantibus (see
History, i. pp. 341-342).