441 
. 1888-89.] Dr T. Muir on the Theory of Determinants. 
' 2 ± aa{ 
a (n ~ 2) 
' • * ft re-2 
2 + A (M ~ 1) A < ” ) 
— re— 1 re 
e 
+1 
re — 1 
RA W ’ 
re 
2±aoq' . 
. . . 
re-3 
y . a(»- 2 ) a( w_1 ) a( w ) 
^ ±A re-2 A re— 1 re 
\ 2 ± aeq' . 
(re -2) 
. . . a> i 
re -2 
BS±A^:?A« 
a 
s±A,'V- • • 
2 ± aoq' 
R2 ± A 2 "A 3 "'. . . . A ( ”> 
Hamm aequationum prima suppeditat, 
2±a < ::; , a ( : ) = ke±«« 1 ' 
• a 
in- 2 ) 
re — 2 
= RA ! 
re — 1, re 
re- 1, re > 
quae cum formula (4) § pr. convenit. Deinde aequationum 
(10) duas, tres, quatuor etc. primas inter se multiplicando, 
prodit formularum systema hoc : 
f 2 + A ( ” _ i ) A ( ' ,) = 
— re — 1 re 
E 2 + adj. . 
a (w_2) 
• ' a n - 2 » 
2 + A (w -;?A < ”- 1) A ( ” ) = 
R 2 2 ± aa-[. . 
^ — re— 2 re— 1 re 
re-3 5 
2 ± A/ A 2 " .... = 
“ Quas formulas amplectitur formula generalis, 
2 ±A ( *+}>A ( *+*\ . . . A ( ” ; = R ’*-*- 1 
"V ' (ft) 
Z±aa 1 ... . a k 
( xx . 5) 
Cauchy’s theorem 
2 ± AA,' .... A w = R” , 
which may he viewed as the ultimate case of this, Jacobi arrives at 
by expressing S±AA/. . . A ( f in terms of A, A 1? . . . , A n and 
their cofactors, substituting for the said cofactors their equivalents 
as just obtained, viz. 
dR 71 - 1 , cqR"- 1 , a 2 R M_1 , . . . . , a w R M_1 , 
and then using the identity 
A a + Ajcq + . . . + A n a n = R . 
Passing over the twelfth section, which relates to certain special 
