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

398 HISTORY OF THE THEORY OF DETERMINANTS

and his problem is to obtain for any one of the said series an expression involving no others of the series except the first two, the
multipliers ul, u2,...., and the addends Tl, 7r3,.... Taking
the case of seven equations, he finds the result of solution to be
1.....ul /11+3o
U2 -1... -1 + rl
83 =. 1 U4 -1. *.. 1 5 — 1.. 1 6 - 1 r5.... 1 z7.
the determinant being next transformed so as to show the cofactors of 3/ and /3 as continuants-a process which might have
been extended to the cofactors of the 7r's.
BAUER, G. (1872).
[Von einem Kettenbruche Euler's und einem Theorem von Wallis.
Abhandl. d. k. bayer. Acad. d. Wiss. (Miinchen), II. Cl. xi. (2),
pp. 99-116.]
The continued-fraction referred to is
n + n + + I
m + + n+ l
m+2+
and the theorem is that announced by Wallis in connection with
the identity
4 12
- = 1 -- 32
7T - "S + - 52
2 +.
of Brouncker, namely, that the product of
12 12
a - 2(a-I 1) 32 and a+1+ 1- 32
(a+- 1) 2(a )+ 2(a~1)1) +