220 Proceedings of Royal Society of Edinburgh. [sess. 
is the same as 
b 
V 
b" 
c 
c' 
c" 
a 
a' 
a" 
a 
a' 
a!' 
a 
c 
c' 
c u 
+ b 
a 
a ' 
a" 
+ c 
b 
V 
b" 
= 
b 
V 
b" 
1 
1 
1 
1 
1 
1 
1 
1 
1 
c 
d 
c" 
— a disguised special case of Vandermonde’s theorem (xh.), the four 
elements of one row being each unity. (xn. 11) 
The next point is, that since the expression denoted by M, viz., 
a'"(bd) - a(b’c") + a\b"d") - a'\b"'d) 
is in modern notation 
the identity 
is 
the 
same as 
V 
b" 
V" 
d 
d' 
d" 
1 
1 
1 
a' 
a" 
a'" 
V 
b" 
b'" 
d 
d ' 
d" 
a a / a " a' 
b V b" b" 
c d c" c'" 
1111 , 
S' = - (&'e"-&V)M 
b V b" 
c d c" 
1 1 1 
a a ' a" 
b V b" 
c c' c" 
V b" 
a a' a" 
b V b" 
c c f c" 
1 1 1 
V" 
d" 
1 , 
and therefore is, like its eight companions, a fresh case of the 
theorem regarding a minor of the adjugate.* (xx. 2) 
DRINKWATEK, J. E. (1831). 
[On Simple Elimination. Philosophical Magazine , x. pp. 24-28.] 
Up to this date, almost 140 years after the publication of Leib- 
nitz’s letter to De L’Hopital, no English mathematician’s name 
* Instead of following Minding’s lengthy process, a mathematician of the 
present time would of course observe that the coefficients of A, B, C, D are 
the principal minors of M, and using Cauchy’s theorem would at once reach 
the desired conclusion, viz. , that the determinant of them = M 3 . 
