1888-89.] Dr T. Muir on the Theory of Determinants. 
765 
decrit, que je sache, que dans un seul onvrage elementaire frangais, 
peu repandu ( Manuel d'Algebre , p. 80, 2 e edition, 1836).” This 
indicates a sad contrast to the state of matters attested to by 
Gergonne,* showing that there is a fashion which changeth even 
in things mathematical. The new favourite, it also appears, was 
Bezout’s rule of 1764 ; for in passing this over, in order to give an 
account of the same author’s rule of later date, Terquem says in 
regard to it, “ Comme ce procede est decrit dans tous les ouvrages a 
l’usage des classes, nous ne nous y arreterons pas.” 
CAYLEY (1843). 
[Demonstration of Pascal’s Theorem. Cambridge Math. Journ., iv. 
pp. 18-20 ; or Collected Math. Payers, i. pp. 43-45.] 
At the outset of this paper two lemmas are given, the second of 
which stands as follows : — 
“ Lemma 2. Representing the determinants 
Vv 
*^ 2 > 
Vv 
X 8> 
Vv 
by the abbreviated notation 123, &c. ; the following equation 
is identically true : 
345. 126 - 346. 125 + 356 . 124 - 456 . 123 = 0. 
This is an immediate consequence of the equations 
% 
« 4 , 
X 6 
x v 
x v 
X Q 
* 
yv 
y# 
y 5 > 
y 6 
• 
• 
y*> 
y « 
2/5> 
y 6 
• 
• 
h. 
Z 5> 
Z 6 
*5> 
Z 6 
x v 
x 2 , 
*5> 
x 6 
x Y , 
x 2’ 
* 
Vv 
Vv 
Vv 
Vv 
y& 
y 6 
Vv> 
y» 
• 
• 
h> 
2 2> 
*5> 
Z 6 
z i> 
z 2'> 
• 
. 
. 
(xxiii. 13) 
* The passage in question, which we quoted under Cramer, is to he found in 
the Annales de Math., xx. p. 45. 
