The models show the penetration of two right circular cones, where four different cases arise. In all these models one cone can be pulled out, in order to show quite clear the curve of intersection.""

In the left model all straight lines of the surface of one cone intersect the second cone; one obtains two distinct space curves as intersection.""

In the second model the cones are situated such as each cone has straight lines of the surface that do not intersect the surface of the other cone. In this case the intersection is a closed space curve without double points.""

In the right model both cones have two common tangent planes; the curve of intersection splits up into two ellipses.

Circular cylinders are surfaces of the second order. If two surfaces of the second order intersect, generally an intersection curve of the fourth order is generated. This can have a maximum of one double point. If two double points occur, the curve collapses into two (flat) curves of the second order.