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

LESS COMMON SPECIAL FORMS (CAYLEY, 1858) 455
the product becomes
(y-/)('-/3') (8-/3)(y'-/3')
(a-y)(3'-y') (/3-y)(a'-y')
(a-3)(B/'-8') (/3-~)('-8')..
and there is obtained
1a a' aa' 1 a 3' a/3'
1 ' ' 1 /3 ' /3a' f (a- )( 3-)(a' -')(/3 ')12
1 oy yt 77' 1 y 8' y8 - (a — S)(3-y)(a '- )( 3'- ').
8' 86' 1 8 y' y7'
From this Cayley concludes (1) that T is not changed by the
transposition
a' 7)
and (2) that either form equals
(a-y)(/ - 6)(a'- ')(3'- 7') - (- )(/3- y)(a'- y')(/'- 6').
SARDI, C. (1864).
[Quistione 39. Giornale di Mat., p. 256, pp. 315-316.]
On the determinant T Sardi performs the operation which we
may indicate by
col4 - 3 col3 - 8' col2 + B36' coli,

thus obtaining

-~

1 a a (a-/)(a'1 /3 /3'
1 y 7' (y-/3)(y
1 6 6'
in which the cofactor of (a - )(a'-6') is
/3-7 /'-y'
(-y ' - y'
and the cofactor of (y - /)(y'- 8') is
3-a 13'-a'
6-a 8'-a'

-8')
- 8')