PEOCEEDINGS 
OF THE 
ROYAL SOCIETY OF EDINBURGH, 
VOL. XV. 1887 - 88 . 128 , 
The Theory of Determinants in the Historical Order 
of its Development. By Thomas Muir, M.A., LL.D. 
Part I. Determinants in General (1812-1827). 
(Continued from p. 518 of vol. xiv.) 
Up to this point a thorough understanding of the notation 
(“S) 
is the one essential. Taking the particular instance 
(«So) 
we first call to mind that it is an abbreviation for the determinant 
whose first row has for its last “terme ” the determinant 
^ 1.10 » 
— that is to say, an abbreviation for the system whose determinant 
we should nowadays write in the form 
^1.1 
^1.2 
^(2) 
. . 6*1.10 
(2) 
^*2.1 
'^2.2 
■ • ^2.10 _ 
^10.1 
6*102 • • 
' • “lO.lO 
The next point is to realise what determinants are denoted by 
i7ow the number 10 being of necessity a combinatorial, and, as 
the figure in brackets above it indicates, of the form 
n{n — 1) 
1.2 ’ 
VOL. XV. 19/2/89 
2i 
