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

2 HISTORY OF THE THEORY OF DETERMINANTS

one and the same unknown between the first equation and each
of the other equations of the set, then in treating in the same way
the set of n-1 equations thus derived, and so on until a single
equation Nx= D results. As negligible factors are not struck
out in the course of the work, the discovery of the law of
formation of the coefficients in the successive sets of equations
is made unnecessarily difficult, and N and D are obtained in
unwieldy forms. Thus, in the case of the six equations
a11 +b1+ 2.... + fix = sj
ax + b22 +... +f/26 = 82
the expression found for the last coefficient of x6 is, in later
notation,
aI Ib23d4e5f6( 1. I alb2cd4. I C1b03 2 tb2 'l..l8,
and for the term independent of x6
alb2c,34e586. ac. ab2c% i3. I c b,. (18,
with the result, of course, that
= alb2c3d4e5s6 1
6 I atb2C3d4e5f6 '
It will readily be agreed that this procedure, though fresh, is
not an improvement on others previously known.
CHELINI, D. (1840).
[Formazione e dimostrazione della formula che da i valori delle
incognite nelle equazioni di primo grado. Giornale Arcadico di Sci....., xxxv. pp. 3-12.]
The writings known to Chelini were Terquem's Manuel
d'Algebre, Bianchi's paper of 1839, and Molins' of the same
year. The paper, however, which his short and clearly written
exposition most readily calls to mind is Gergonne's of the year
1813. The "formazione" is essentially Bezout's, and the
"dimostrazione" essentially Laplace's.