The author argues that as long as euclidean processing provides the basis for CAD, there will always be a limit to the level of reliability achievable in a system, i.e., a CAD system contains within it elements that inevitably lead to a system's inaccuracy, instability, and complexity because “a division operation is the root cause of all evil”. The author proposes a new geometric processing paradigm in which there is no need of performing a division operation, i.e., “Totally Four-Dimensional Homogeneous Paradigm”. He discusses the paradigm from the points of its theoretical foundations, geometric definitions, geometric computations and topological definitions.