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

BORDERED DETERMINANTS (PAIGE, 1880) 445
Multiplying his 'determinant borde '
a a... a5 X1 1 V
b1 b2 5.2 /2 r2
e e2... e5 5 5 5, or V say,
11 1... 15
mn.2.. ~ 5. ~ ~
by lalb2c3d4e514 in the form
A1 A9... A5
B B2... B.
E1 E2.. E..... 1
1.
and dividing by alb2c3d4e512, he obtains
V. a1b2c3d4e512, = 1...... i A VI. 1... Xt2 A 2 2... 1.5 M5 X '5
2lA E/B. E/ E
2mA EIEB.....
iEnA EnB... EnE...
where EIA = iA1 +12A2 +... + 5A5,
EmiB = mnBl + m2B2 +.. + inB5.
He then substitutes (Hist., ii. pp. 199-200) for this eight-line determinant the quasi-product
i A2... * 5 21A l/B.... 2E
M1 M2 *. * /o A ImB... imE
1 *2 * * V5 EnA EnB... InE