216 
Proceedings of Boyal Society of Edinburgh. [sess. 
world. For the present it will suffice to note in regard to them 
that although general determinants in Laplace’s notation occur 
(p. 351, &c.), the real interest of the papers arises from the fact 
that use is made in them of that special form which afterwards 
came to be associated with Jacobi’s name. His introductory words 
concerning it are as follows (pp. 348, 349) : — 
“ Yocemus porro A determinantem differentialium partial- 
ium sequentium : 
bu 
bu 
bu 
bu 
bx 9 
bx i 5 
b x 2 3 
bx n _ j 
bu x 
bu x 
bu Y 
0^! 
bx 3 
Wz ’ 
’ fo*- 1 
bu n -\ 
9w»-i 
du n _ 3 
bx 3 
bx x 3 
bx 2 ’ ° 
b% n -l 
Erit e.g. pro tribus functionibus u } u v u 2> tribusque variabil- 
ibus x, y, z : 
du bu x bu 2 du bu x du 2 0«q du 2 du 
^ bx' by ' bz dx ° dz by by ' dx bz 
bu 2 bu 0«q bu b u x bu 2 bu bu x bu 2 
bz % by' bx by' bz ’ bx bz bx ' by 3 
quam patet expressionem casu, quo u, u v u 2 sunt expressions 
lineares, in expressionem ipsius A supra exhibitam redire.” 
MINDING (1829). 
[Auflosung einiger Aufgaben der analytischen Geometrie vermit- 
telst des barycentrischen Calculs. Crellds Journal , y. pp. 
397-401.] 
Unlike Jacobi, Minding was unaware, apparently, of the ex- 
istence of a theory of determinants. The functions occur at every 
step of his investigation, yet he makes no use of their known 
properties to obtain his results. 
He deals with four problems in his memoir, the second two 
being the analogues, in space, of the first two. Nothing noteworthy 
