It is evident that by an extension of the method of deriving from any triangle its polar triangle, it is possible to derive from any figure whatever another figure, the properties of which may be deduced at once from those of the first. This may be done either by imagining a point to move along the original figure and considering the envelope of the great circle of which the moving point is the pole; or by imagining a great circle to envelope the figure and considering the locus of its pole. In both cases two figures will be obtained; but these will be antipodal, and will therefore have like properties. Since the point of intersection of two great circular arcs is the pole of the great circular arc which joins the poles of these two arcs, the two methods of derivation mentioned above will lead to the same derived figure. These methods of transformation of figures are evidently closely analogous to that of reciprocal polars.