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

CONTINUANTS (BAUER, 1872) 399
is a2. The two things are linked together in the title because the
main feature of the paper is the establishment of a relation between
a continued-fraction of Euler's type and a continued-fraction of the
very different type which appears in Wallis' theorem. If we denote
by S the continued-fraction
n
- n - a,..+ +a
which includes Euler's, and by T the fraction
+n + aa
a1 a, n+ a2
al + I
a2 +.
*.+ n + aar
ar 1 + a
a - + 1
the relation in question is
n(S +) _
S+n - T,
or, as Bauer puts it,
n(P +Qr) _ T
Pr + fQr,
where
Qr= C 1.....
-n — a a2 1....
~. -f-a3............ a-n-r 1ar
and P, is n times the complementary minor of the element
in the place (1, 1) of Qr. In the latter form it is a relation
between continued-fraction determinants, and as such claims our
attention.
By way of proof Bauer increases each row by all the rows following