The equations of a stereographical representation of the ellipsoid on a plane, tangent to it in one of its poles, are sought, through a projection from the opposite pole. The equations of such a map in finite terms, come out to be very simple and easy to compute. Then, a comparison is made with the usual conformal stereographical projection, and the conclusion is reached that the linear deformations are equal in the two types of representation. Finally, the angular deformations of the polar projection are computed which, for high latitudes, are almost neglegible.