The theory of determinants in the historical order of development, by Sir Thomas Muir.

424 HISTORY OF THE THEORY OF DETERMINANTS
where Rp is the persymmetric recurrent
a.....
a2 a, ao
a3 a2 a...... o........
a,, a,1-2 a9, an4.-3
I ai-i a,,-2 an-... 1 an- a,,-2
Then, putting for x in this in succession x., x2,.., xn, he has ai
set of equations from which he finds
/ 0P+l P+2 /+J4-I
0 1 2 n-1 \
X^1X2x~ ~ X~ a3
and.'.
x x 1x2x;.. * x*x2
- 1Z0 1Z'9 nll 1 2 * * * n 2
I 1 2 3 ' n*
= ( -)p'p l -p-i 0 1.
I X2 X ' n \I
] lX23~ 2 X;- I
= +1 + 1 f
-'(-) xo) + _lX) + * * * Plf'(l)f.
It thus follows that if x1 be the arithmetically smallest root,
li (-aORip) (-) -1[
(-ao) Xlir -a -- ao = - - I
Reurin..f-e t( 1)
Returning then to the first deied set of equations, Fiirstenau next
eliminates x3, x4,... and obtains a quadratic from which may be
found the two smallest roots x, x2, and from which in particular it
is seen that

x x2 = lir (aoR) - /R,p