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

460 HISTORY OF THE THEORY OF DETERMINANTS

JANNI, V. (1876?).[Nota sullo sviluppo di un determinante. 7 pp. '?.]*
The main result established here,
is Zeipel's. It closely resembles one previously given (Baltzer), and
may be proved in exactly the same way, the effect of the first transformation being to show that. the left-hand member is equal to the
last of its own principal minors, namely,
mo~+11(m 2)..(m-~n-1)n-1
Attributed also to Janni is the simple recurrent tof which the
five-line instance is
I 121 22. u2 ~4-43A-2-4u,.+uo X~0
1 3~ 3 33 U
41 4, 43 U4
It is at once established by performing the operation
row5 - 4 row4 + 6 row3 - 4 row2 + row,.
BONOLIS, A. (1876).
[Sviluppi di alcuni determinanti. Giornale di Mat., xv. pp. 113-134.]
Bonolis' earlier results may be best viewed as slight generalizations of simple identities of Zeipel's, and be most easily evaluated
by being made dependent on the latter. Thus the determinant
(n)0 amd (3m) Ia?" - t (.. ) an-.
(,m ~ d)0 aCtl+d (rn+ d)jam+d't...(m + d,. &fl(z - 91
(rn+ 2d)oatm~2d (m~ 2d)i Ant+2dc-t....(rn + d, an - rt
(rn+ rd) oa""n2L (m~+ rd)ian (d. (r+ rd)?.a11d+ t
*This pamphlet It have not seen. Garbieri in 1878 says in regard to it (Bull.
di Bibliogr. e di Storia delle sci. mat., xi. pp. 257-318), " in 81 di 7 pagine, senza,
nota d'anno, ne' di luogo di stampa, ne' di stamperia."
t It appears in an unnecessarily complicated form in G~inther's text-book (p. 197),
the reference being to " Janni, Lezioni di algebra complementare, Napoli, 1876,
p. 23." It is taken over by Pascal (pp. 179-180) and by Leitzmann (p. 138). All
of them state it incorrectly.