II. An introductory memoir upon quantics

The subject of Quantics is defined as the entire subject of rational and integral functions, and of the equations and loci to which these give rise, but the memoir relates principally to the functions called quantics; a quantic being in fact a rational and integral function, homogeneous in regard to a set of facients (x ,y ..), or more generally homogeneous in regard to each of several such sets separately. A quantic of the degreesm ,m' .. in the sets (x ,y ..) (x' ,y' ..) &c. is represented by a notation such as (*)(x ,y ..)m (x' ,y' ..)m' ..), where the mark * is considered as indicative of the absolute generality of the quantic.