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

202 HISTORY OF THE THEORY OF DETERMINANTS

and the number of lines in the constructed minor
C,,a+C,a +.. +,,.
For example, if the generating determinant be
123456
123456,
and if the submitted minor of its third compound be such that each
of its elements contains two row-numbers and two column-numbers
chosen from 1, 2, 3, and one row-number and one column-number
chosen from 4, 5, 6, then the said submitted minor must be
1241 1251 126 134 135! 136 234 235 236
124 125 126 1341 11351 136 234, 235 236 I,
and according to Sylvester it is equal to
123456 2 123 I4 456
123456 123 456
Following on this illustration, or, rather, on the 'extensional'
of it, there is given an alternative mode of stating the theorem
together with full diagrammatic illustrations (pp. 56-65). The
paper concludes with an afterthought involving a further generalization in which oblong arrays take the place of determinants.
MUIR, T. (1879).
(See under this heading in chap. i.)
HUNYADY, E. (1879).
[A masodfoku feliiletek elmeletehez. Ertekesezek a math. tudomdnyok kore'bbl (Budapest), vii. 5 (36 pp.).]
[Beitrag zur Theorie der Flache zweiten Grades. Crelle's Journ.,
lxxxix. pp. 47-69.]
Hunyady's mode of discovery, as we have already seen, is the
familiar one of seeking out two or more expressions for one and the
same condition and then comparing the results. On this occasion
the condition is that connected with the existence of ten points on
a quadric surface. As the outcome of some research (pp. 47-48)
he brings together a series of related problems in geometry, and