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

PREFACE.

THE present work originated in certain notes, made about
twenty-five years ago, upon the properties of some of the
best-known higher plane curves; but upon attempting to revise
them for the press, it appeared to me impossible to discuss the
subject adequately without investigating the theory of the
singularities of algebraic curves. I have accordingly included
Plucker's equations, which determine the number and the species
of the simple singularities of any algebraic curve; and have also
considered all the compound singularities which a quartic curve
can possess.
This treatise is intended to be an elementary one on the
subject. I have therefore avoided investigations which would
require a knowledge of Modern Algebra, such as the theory of
the invariants, covariants and other concomitants of a ternary
quantic; and have assumed scarcely any further knowledge of
analysis on the part of the reader, than is to be found in most
of the ordinary text-books on the Differential Calculus and on
Analytical Geometry. I have also endeavoured to give special
prominence to geometrical methods, since the experience of
many years has convinced me that a judicious combination of
geometry and analysis is frequently capable of shortening and
simplifying, what would otherwise be a tedious and lengthy
investigation.