Unknown features of the mutual intersection of tetrahedron and quadric (Chasles’ theorem)

The geometric features of the line of mutual intersection of second-order surfaces and a tetrahedron, which are the essence of the historical Michel Chasles' theorem, are considered in the article. 3D models are developed and presented, which clearly illustrate various versions of the theorem. A method for constructing 3D models is presented, which allows using those in an educational course on the theoretical foundations of geometric modeling. A proof for one of the theorem variants is given. For one of these variants, conclusions that differ from those of Chasles have been obtained. A general conclusion is made about the need to develop a universal proof of the theorem. The work is carried out by computer 3D modeling in the AutoCAD package using AutoLisp programming, as well as in the SolidWorks package.