PREFACE 
This introduction to the classical theory of invariants of 
algebraic forms is divided into three parts of approximately 
equal length. 
Part I treats of linear transformations both from the stand 
point of a change of the two points of reference or the triangle 
of reference used in the definition of the homogeneous coor 
dinates of points in a line or plane, and also from the stand 
point of projective geometry. Examples are given of invariants 
of forms / of low degrees in two or three variables, and the 
vanishing of an invariant of / is shown to give a geometrical 
property of the locus /=0, which, on the one hand, is inde 
pendent of the points of reference or triangle of reference, 
and, on the other hand, is unchanged by projection. Certain 
covariants such as Jacobians and Hessians are discussed and 
their algebraic and geometrical interpretations given; in 
particular, the use of the Hessian in the solution of a cubic 
equation and in the discussion of the points of inflexion of 
a plane cubic curve. In brief, beginning with ample illustra 
tions from plane analytics, the reader is led by easy stages 
to the standpoint of linear transformations, their invariants 
and interpretations, employed in analytic projective geometry 
and modern algebra. 
Part II treats of the algebraic properties of invariants 
and covariants, chiefly of binary forms; homogeneity, weight, 
annihilators, seminvariant leaders of covariants, law of reciproc 
ity, fundamental systems, properties as functions of the roots, 
and production by means of differential operators. Any 
quartic equation is solved by reducing it to a canonical form 
by means of the Hessian (§33). Irrational invariants are 
illustrated by a carefully selected set of exercises (§35). 
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