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

438 HISTORY OF THE THEORY OF DETERMINANTS
which by reason of the first property can be shown equal to
a(,y,...,,,) - A(y,...,,)
lA(ay, ) -A(y,...,) cos a,
or
A(y,...,,,0) osA(,,y,,,0)
A(y,..,,) A(/,y,...,,)
and ultimately, "by repeating this sort of transformation," equal to
cos2a cos2? cos2y/... cos20.
If we use for a moment the present-day notation for continuants,
viz., where
K (aib b2 )
K2
\+ b,. a.. ),....
Schlafli's results are seen to be
K( /31 32, ) =.K(K13 x)3 + 1K( 0.)/34
K(I 1 *32 OK.. 1) = K(P2 P37 K-IIPK+ll 07 1) i03
i '1.... - K 3 1...K K11+2 / ),
K 1 ''.-2 _.:...*:: 0?,3+3-1 3'( + 1... 3n1)
K(1... I... I I 1.. IJ... I-
-K IP1~ ~ 04 OIL 1 / j33 On-2 3... /
K( i. 3~1).K(/ 3...1n-2)J {3313 1.1 1 )
K) A - A.- ( \Kf A - ^+1 1 K;. - Al1
K1(i I.. - 1) KI... Ij ) (- )a
Q =(-1)~/3^ /33.../3~,
the only change being the writing of /1, 2/,... for -cos2a,
-cos2",...