1888-89.] Dr T. Muir on the Theory of Determinants. 233 
IX = 
IX = 
0r 
dT 
0r 
a — v i + 
® a i,i 
3 + . . 
da 2> i 
• • s — 
° a n,\ 
ar 
0r 
dT 
'^ 1 + 
3 v 2 + . . 
(j(X 2,2 
. . + ~ 1 
0 a w, 2 
0r 
0r 
0 r 
3 V x + 
V a l,n 
3 ^2 + • • 
° a 2,n 
. . + o — « 
^ a n,n 
(vi. 6) 
JACOBI (1835). 
[De eliminatione variabilis e duabus aequationibus algebraicis. 
Crelle's Journal , xv. pp. 101-124.] 
In a memoir having for its subject Bezout’s method of eliminating 
x from the equations 
a n x n + a^x 71 ' 1 + .... + a x x + a 0 = 0 
b n x n + b^x 71 ' 1 + .... +5 1 x + 5 0 = OJ 
determinants are certain to occur explicitly or implicitly ; and, the 
author being Jacobi, one is not surprised to find them introduced 
near the outset and employed thenceforward. It is of course only 
a special form of them which appears, viz., that afterwards distin- 
guished by the term jpersymmetric ; consequently, for the present 
the main contents of the memoir do not concern us. Note has to be 
made, however, of two points — (1) that while Jacobi does not discard 
his former notation 21 ± a r „ a r „ . . . a r „ , he introduces and uses 
another, viz., 
• • • 5 'I'm 
S 0’ S 15 S 2’ * * * ? S m 
(2) that a page is devoted *to a fuller statement of the above- 
mentioned theorems regarding the adjugate determinant and a minor 
of the adjugate. The final sentence of this statement is all that 
need be reproduced. It is 
“ Sint igitur r/y\ . . . . , r (w-1) atque s,s',s", , s (w-1 
numeri omnes 0, 1, 2, ... , n - 1, quocunque ordine scripti; 
erit 
(vn. 8) 
