Conic Sections are the figures formed by the cutting of a cone by a plane; they are five in number, corresponding to the different positions of the cutting-plane. When the cutting-plane passes through the apex of the cone, and coincides with the axis, the section is a triangle. When the plane cuts the axis at right angles, the section is a circle. When the plane cutting the axis obliquely, and passing through both sides of the cone, the section is an ellipsis. When the plane cuts the axis in a line parallel to one side of the cone, the section is a parabola: and lastly, when the plane either does not cut the axis, or cutting it forms with it an angle less than that formed by the side with it, the section is an hyperbola. The term conic section is applied more peculiarly to the three last figures; and the doctrines of their several properties constitute one principal branch of geometry, of great importance in astronomy and many other sciences. See Geometry.