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

CONTINUANTS (MUIR, 1877)

4~17

8+ — b
r
b,
-c1 3+ —c2r b3
r
b3
-c c-+ j-cr b4
b4. - c 6+ r C4r b5
r
the two sets of operations necessary to establish it being
row1+ r roW2, rOW2+ r rrow3.
and
c012 -r coll, C013-r col2.
The case previously announced is that where
c1C = c2 3=....=1 and 8-r=/3.
Bauer's resnlt regarding the product of two continued-fractions
having been noted in reviewing his paper, the generalization of it
here obtained may also be shortly alluded to. Denoting by F the
continued-fraction
b,(b2- a)
/33
bll (b - a)
the author first shows, with the help of his theorem in continuants,
that
- (b - a) + (-C F-b1.
b2 + b3(bb - a)2 P + b2- b3 +- 2 F '+ bj
+ b3 - b4 +bn (bn - a))
/ + b, - a'

M.D. IHL