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

104 HISTORY OF THE THEORY OF DETERMINANTS
which occupies the corresponding place in Q; then the determinant of the grand array is equal to PqQ".
SIMERKA, W. (1858).
[Bestimmte Gleichungen des ersten Grades mit n Unbekannten
gelist mittels der Permutationslehre. Sitzungsb... Acad.
d. Wiss. (Wien), xxxiii. pp. 277-281.]
The contents of this simply-written paper are quite in accord
with the title. The author writes as if nothing had ever
previously been done on the subject. The common denominator
of the value of the x's in
aCrlx + a,r2X +..+ at rn,, = gn =
r=l
he denotes by 3(a1 a... an).
CASORATI, F. (1858, September).
[Intorno ad alcuni punti della teoria dei minimi quadrati.
Annali di Mat., i. pp. 329-343.]
The title here refers only to the latter half of the paper, the
other half being concerned with an auxiliary series of theorems
on the product-determinant. The first of these theorems is
avowedly old, being that which concerns the so-called product C
of two non-quadrate arrays
all a12 a13... aln, b1 b12 b13 *. b.l.
aC2 a22 a23.. a2., b21 22 bs2... b 2
aml am.2 am3. am,,, bml b m2 b3 *.. bzn
where n > m. The second, though not so spoken of, is only
new in form, and concerns any primary minor of C. Unfortunately, Casorati does not observe that any primary minor of C
is a determinant formed exactly like C after omitting a row
from the first array and a row from the second, and that
therefore his second theorem is unnecessary. Further, his mode
of procedure leads him to an expression for a multiple of the
minor, namely, for