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

1)76 HISTORY OF THE THEORY OF ]DETERMINANTS

and as it also means that
from which we have
a6 a4 a. a2 a, a3 a4 a. a2 al1
b6 b4 13 b b 1 b5 14 b3 2 b11
fAfAfAf2 A' ~~~~11
a5 a6 a3 a2 a a3 a a3 a2 a
b5 6 b3 b2 1 b b4 13 b2 1)1
f5f6f3f2f 1 f5f4f3f2f 1
it follows that in later notation
a~b Ic2d3e4f6 I+ a'bl'c2d3e4f5 = a
a0b' C2d3e5f6 I+ a'blc2d 3e4f3 = lab,
a~b' c2d4e5f6 I I a0b' C2d3e4f5 I abc,
with similar results when the alternants are of any other order.
JOACHIMSTHAL, F. (1856, Sept.).
[De aequationibus quarti et sexti gradus quae in theoria linearum
et superficierum secundi gradus occurrunt. Grelle's Journ.,
liii. pp. 149-172.]
The problem of finding the normals drawn from anl external
point (,, )to the surface
x 2 ~2 z2
being dependent on the solution of the sixth-degree equation
_ _ _ _ b )j2 + 2 =
(a+U2+ (b +u)2 +(C + )2