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

'218 HISTORY OF THE THEORY OF DETERMINANTS

he merely draws attention to the fact that the denominator on
the left being
(a0~alz+a Z2+.... 1zn
(ao
there results
(to = (1+~1z+S 2zi~n~+. 2+ + c2+ * n),
whence Wronski's set of relations follows at once.
This, of course, is much preferable to Brioschi's procedure.
It has to be noted, however, that by taking a roundabout way
Brioschi came across the equations connecting the N's and
the ss.*
After all, it is this set of equations and the two other similar sets that
are worth knowing, namely,
Newton's, a~s,. + cas,.r + a2s.-2 +.. +,.-1i + rca, = 0.
Wronski's, a,.+ x,,la + +2a,.r2 + +N + $a0 = 0.
Briosehi's, =r + '1Sr-1 + 25-2+ r N,-1.1