of Edinburgh, Session 1885-86. 
553 
time after the date of Gerhardt’s publication it escaped observation, 
Lejeune Dirichlet being the first to note its historical importance. 
It is true that during bis own lifetime, Leibnitz’s use of numbers in 
place of letters was made known to the world in the Acta Erudi- 
torum of Leipzig for the year 1700 {Responsio ad Dn. Nic. Fatii 
Duillerii imputationes, pp. 189-208) ; but the particular applica- 
tion of the new symbols which brings them into connection with 
determinants was not there given. 
CRAMER (1750). 
[Introduction a l’Analyse des Lignes Courbes alg^briques, par 
Gabriel Cramer, pp. 59, 60, 656-659. G4nbve, 1750.] 
The third chapter of Cramer’s famous treatise deals with the 
different orders (degrees) of curves, and one of the earliest theorems 
of the chapter is the well-known one that the equation of a curve 
of the %th degree is determinable when \n{n + 3) points of the curve 
are known. In illustration of this theorem he deals (p. 59) with 
the case of finding the equation of the curve of the second degree 
which passes through five given points. The equation is taken in 
the form 
A + Ih/ + Cx + Dyy -1- E xy + xx = 0 ; 
the five equations for the determination of A, B, C, D, E are 
written down ; and it is pointed out that all that is necessary is the 
solution of the set of five equations, and the substitution of the 
values of A, B, C, D, E thus found. “ Le calcul v4ritablement en 
seroit assez long,” he says; but in a footnote there is the remark 
that it is to algebra we must look for the means of shortening the 
process, and we are directed to the appendix for a convenient 
general rule which he had discovered for obtaining the solution of 
a set of equations of this kind. The following is the essential part 
of the passage in which the rule occurs : — 
“ Soient plusieurs inconnues z, y , x, v , &c., et autant d’equa- 
tions 
A 1 = 7Az + Y hf + X 1 ^ + V 1 ?; + &c. 
A 2 = Z% + Y 2 y + X 2 x + \ 2 v + &c. 
A 3 = Zh + Y 3 y + X 3 ^ + Y 3 v + &c. 
A 4 = ZH + Y ±y + X 4 ^ + V% + &c. 
&c, 
