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

CHAPTER XIII.
BIGRADIENTS, FROM 1859 TO 1880.
HITHERTO the only bigradient considered had been that which
originates in the process of dialytic elimination: and although in
the period now reached bigradients of other origins make their
appearance, it is still Sylvester's that claims the greatest share of
attention. Note needs consequently to be taken that on account
of the existence of Bezout's eliminant, which of course is equivalent
in substance but which in form is axisymmetric, a difficulty of
classification arises, and that we adopt what seems the most generally
convenient course of not attempting to separate the two. Propositions, therefore, which concern the axisymmetric eliminant of two
binary quantics will be found as a rule under our present heading.
BRUNO, F. FAA DI (1859).
[THEORIE GENERALE DE L'ELIMINATION,... x+224 pp. Paris.]
In his section on the highest-common-divisor (pp. 47-52), Bruno,
denoting the rth Sturmian remainder of
aXn M+a amlx +...., b0x-1 + blx2 +...
by R,., finds for it the expression
I == m - r+1 n
1 =r - a-0 (o a.... (-2 a 1 a2 2,-r+t
* a *2r,-3 aC2,,+Z-2. a..... a a2r+-/l
ta0
a,._ ar+_1
b(, b1 b2.' ' b2,..- b2.+
2*, b2*. +-l
b bl.... b2,,_- b2r+_....... ' _* 6, b,.+1