P. HISTORY OF ' AATHEMATICAL - School of Mathematics

88 A HISTORY OF MATHEMATICAL NOTATIONS
tation being adopted, one has, if only one equation with one unknown
zis presented, z=~:. When there are two equations and two unknowns
z and y, one finds
and
Z
AIY2-A2Yl
.ZlY2_Z2Yl'
. ZlA2_Z2Al"
y= ZlY2-Z2Yl .
His method of solving simultaneous linear equations attracted the
attention of Bezout,' Vandermonde.s and Laplace. Bezout lets (ab')
stand for ab' - a'b; he similarly denotes a determinant of the third
order (ab'e"). An example of Vandermonde's symbols is seen in the
two equations
:~l+:~+~=O ,
~~ +:~+:=O,
in which the designation of coefficients by numerical superscripts and
subscripts resembles the device of Leibniz. Furthermore, Vandermonde
in 1772 adopts the novel notation
and
a If3 for aa..bB-ba..aP
alb
'
and finds
alf3 alf3
alb=-bla·
"Le symbole ++ sert ici de characMristique."
Laplace" expressed the resultant of three equations by (la. 2 b. 8 c),
those indices being placed to the left of a letter and above.
461. Early nineteenth eentury.-The first use of the term "determinant"
occurs in the following passage of K. F. Gauss: "Nume-
IE. Bezout, Theorie gbterale des ~quations alg~briques (Paris, 1779), p. 211,
214.
2 A. T. Vandermonde, Hisioire de l'acad. des scienc. Paris, annee 1772 (Paris,
1775), p. 516.
a P. S. Laplace, Hisioire de l'acad. des scienc. Paris, annee 1772 (2d partie),
p. 267, 294; (Euoree, Vol. VIII, p. 365-406.