A curve (named from the Latin, curvus, meaning crooked), is a line which may be cut by a straight line in more points than one; a line in which no three consecutive points lie in the same direction. The doctrine of curves and of the figures and solids generated from curves constitutes what is called the higher geometry, and forms one of the most interesting and important branches of mathematical science. Curve lines are distinguished into algebraical or geometrical and transcendental or mechanical. The varieties of curves are innumerable; that is, they have different degrees of bending or curvature. The curves most generally referred to, besides the circle, are the ellipse, the parabola, and the hyperbola, to which may be added the cycloid. Research Curve