From the Engineering point of view, the Maximum Principle is physically an important property met by solutions of elliptic partial differential equations (PDE for short) of second order governing diffusion-convectionreaction phenomena. This property is also called Positivity-Preserving Property in the literature. At the discrete level the Positivity-Preserving Property is required for any numerical scheme designed for solving such PDE. By means of algebraic arguments it is well-known that conventional finite volume schemes for second order elliptic PDE meet the discrete maximum principle. In this communication we expose a new technique based upon geometric arguments for proving that conventional finite volume schemes for diffusion-convection-reaction problems meet the discrete version of Maximum Principle. Notice that the above mentioned geometrical technique works for any space dimension.