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

410 HISTORY OF THE THEORY OF DETERMINANTS

This does not agree with Ginther's result, an awkward error appearing in the last column of both his determinants, and thus also in
his continued-fraction.*
GUNTHER, S. (1873).
[Beitrage zur Theorie der Kettenbriiche. Archiv d. Math. u. Phys.,
Iv. pp. 392-404.]
Only one of the sections of this paper-the third (pp. 397-401)
-is connected with continued-fraction determinants, the subject
dealt with being practically an extension of the result given in the
immediately preceding paper by the same writer. Instead of the
special persymmetric determinant which there forms the denominator of the fraction proposed for transformation, we have now a
perfectly general determinant; that is to say, the given fraction
now is
a2 a.3.... a1 a2 a3..
b2 b3.. bi b2 b3
C2 C3.......
The procedure followed is the same as before, a double application
of it, however, being necessary.
*With the correct values for U and V as here given, it is possible to take
a step farther. For it will be found that
a2 as 1 a1 a3 1
U = a3 a a2 a3, V = 3 a o a2 a3
a, a1 a,. a1 a2
and consequently that the continued-fraction is
- ao aoa2 a a a2 a3 1
a1 - al a2 aoa2 a, a2 a3
a, a ao a a as
ao a2 a1 a, 1
ao a2 a3
a a2
where the three-line determinants are the complementary minors of the
elements (4, 1), (4, 2) of the original determinant, and where the two-line determinants are the cofactors of the last elements in the three-line determinants,
and so on.