An elementary treatise on cubic and quartic curves, by A. B. Basset.

CHAPTER -I.
INTRODUCTION.
1. BEFORE commencing the study of plane curves, we shall
prove certain propositions connected with the Algebra of Quantics
which will be required in subsequent Chapters of this work.
A homogeneous function of any number of variables is called a
quantic. Quantics are called binary, ternary, quaternary, n-ary
according as they contain two, three, four or n variables; whilst
the degree of the quantic is denoted by the words quadric, cubic,
quartic, n-tic. Thus the general equation in Cartesian coordinates
of three straight lines through the origin is a binary cubic, whilst
the general equation of a conic in trilinear coordinates is a ternary
quadric.
The most general expression for a binary quantic is
aocw + ax'n-ly + a2x-2y2 +... an-_xyn-1 + ayn......(1),
which is usually written in the abridged form (a0, al,... a,,rx, y).
This form is generally the most convenient to employ in geometrical investigations; but in purely analytical ones it is usually
better to use the form
aoxn + nax"n-1y + n (n- ) a2'-2y2 +... nanlxyn- + any.. (2),
in which each term is multiplied by the coefficients of x in the
expansion of (1 + x)'. In this expression the coefficients are said
to be binomial, and the quantic is denoted by
(ao, a,, a2,... anx, y)n.
For quantics containing more than two variables a similar
notation is employed. Thus the expression
(ao, al,... a a.x l, X2,... x p)

B. C.

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