This arose from the study by Felix Klein and Sophus Lie of a new theory of groups of substitutions; it was shown that there exists an invariant theory connected with every group of linear substitutions.
The invariant theory then existing was classified by them as appertaining to " finite continuous groups."
This expression of R shows that, as will afterwards appear, the resultant is a simultaneous invariant of the two forms.
Respectively: then the result arrived at above from the logarithmic expansion may be written (n)a(n x) = (n)x, exhibiting (n) $ as an invariant of the transformation given by the expressions of X1, X2, X3...
F(a ' a ' a, ...a) =r A F(ao, a1, a2,ï¿½ï¿½ï¿½an), 0 1 2 n the function F(ao, al, a2,...an) is then said to be an invariant of the quantic gud linear transformation.