Chasles’ Theorem as a 3D Analogue of Pascal’s Theorem

The geometrical peculiarity of the line of mutual intersection of second-order surfaces and tetrahedron is considered, which is the essence of Chasles’ theorem. 3D models have been developed, which vividly illustrate different variants of the theorem. The method of building 3D models is given, which allows to use those in an educational course on the theoretical basics of geometrical modeling. A proof for one of the theorem variants is given. A conclusion has been made on the necessity to develop illustrative examples for all the variants of the theorem and its universal proof. The work has been performed using 3D computer modeling in AutoCAD package and SolidWorks.