478 
Proceedings of Royal Society of Edinburgh,. [july 18 , 
— a result which in modern notation would take the form 
u 
u x 
u 2 
% 
2 
U 
u x 
u 2 
v 4 
X 
x x 
x 2 
X 3 
+ 
X 
X 1 
x 2 
x 4 
y 
Vi 
y* 
Vs 
y 
y\ 
y 2 
y 4 
z 
*i 
% 
z, 
o 
z 
% 
Z 2 
id + uf + . . ux + u x x x + . . uy 4 - u l y l + . . uz + u x z x + . . 
ux 4 - urx-i + . . x 1 + x, 2 + . . xy + x,y, + . . xz + xa. + . . , 
O O (XVIII. 3 
uy + u l y l + . . xy+x 1 y 1 + .. y 2 + y 2 +.. yz + y x z x + .. 
uz + u x z x + . . xz + x x z x + . . yz + y x z x + . . z 2 + z 2 + . . 
It is thus clear that, in November 1811, Binet was well on the way 
towards a great generalisation. He even says that the three 
identities may he looked upon 
“ comme les trois premieres d’une suite de formules con- 
struites d’apres une meme loi facile a saisir.” 
He merely indicates, however, the mode of proof he would adopt 
for the results obtained, and refers to possible applications of them 
in investigations regarding the Method of Least Squares (Laplace, 
Connaissance des Terns , 1813) and the Centre of Gravity (Lagrange, 
Mem. de Berlin , 1783). The mode of proof need not he given 
here, as it turns up again in the far more important memoir in 
which the theorem in all its generality falls to be considered. 
DE PRASSE (1811). 
[Commentationes Mathematicse. Auctore Mauricio de Prasse. 120 pp. 
Lips., 1804, 1812. Pp. 89-102 ; Commentatio vii.* : Demon- 
stratio eliminations Cramerianse.] 
Of previous writings the one which De Prasse’s most resembles is 
Rothe’s. There is less of it, and it shows less freshness ; hut there 
is the same stiff formality of arrangement, and the same effort at 
rigour of demonstration. 
* Separate copies of the Demonstratio eliminationis Crameriance are also to 
be found, bearing the invitation title-page : 
Ad memoriam Kregelio-Sternbachianam in auditorio philosophorum die 
xviii Julii mdcccxi. h. ix celebrandam invitant ordinum Academics 
Lips. Decani seniores cceterique adsessores .... Demonstratio elimi- 
nationis Crameriance. 
It is these copies which fix the date. See Nature , xxxvii. pp. 246, 247. 
