7 6 Proceedings of Royal Society of Edinburgh. [sess. 
It will be observed that neither the word “ determinant ” nor 
the word “resultant” occurs: indeed, throughout the paper, 
instead of resultant he uses “ final derivative,” a term which prob- 
ably may be traced to Sylvester.* 
Cayley (1843). 
[Chapters in the analytical geometry of n dimensions. Cam- 
bridge Math. Journ ., iv. pp. 119-127 ; or Collected Math. 
Papers , i. pp. 55-62.] 
Of the four short chapters which compose this paper, the only 
one which concerns us is the first, although in the others deter- 
minants are constantly made use of. At the outset an important 
notation is introduced which afterwards came to be generally 
adopted. The passage in regard to it is : — 
“ Consider the series of terms — 
X 1 
x 2 
• 
X 
Ax 
^2 
. 
• 
■h-71 
Kx 
^2 
. . 
■ 
the number of quantities A , . . . , K being equal to 
q (q<n). Suppose q + l vertical rows selected, and the 
quantities contained in them formed into a determinant, 
this may be done in y— different ways. 
The system of determinants so obtained will be represented 
by the notation 
x 1 
x 2 
• 
V 
^2 
Kx 
k 2 
• 
■h-n 
* See Sylvester’s paper of 1840. 
