Studied since the time of Plato’s Academy, conic sections (sections of a cone: circles, ellipses, parabolas, hyperbolas) were brought to force during the Scientific Revolution to describe planetary paths and projectile trajectories. Apollonius of Perga (3rd century B.C.) was the first to treat conics rigorously, and his work was the basis of several of Newton’s later demonstrations in the Principia.
There are four categories of conic sections: circles, ellipses, parabolas, hyperbolas, as illustrated above. Note that circles are by definition parallel to the base; parabolas are parallel to one side or the other.