Proof and its study on double tangent and monge theorems

By means of projective geometry,the paper has proved the famous double tangent points and Monge theorems on two intersection quadric surface in descriptive geometry.Through study,the property is found out that planes cutting edgewise quadric curve and quadric intersections from the quadric surfaces become the harmonic division.The property is also found out that both quadric surfaces which have double tangent points have another quadric surface which cuts edgewise quadric curve from both known quadric surfaces.