The value for the central parallel and an additive parameter can be changed in the equations for the Bonne Projection in such a way that an approximation to Waldseemüller’s projections results. The Sylvanus, Werner and Bonne projection in polar coordinates all contain an arbitrary parameter f > 0 such that r = + f. The image of the North Pole accordingly lies on the central meridian at a distance f below the center of the parallels. In the Bonne projection f is assigned in a way that the radii touch the meridian curves always on a given parallel. Sylvanus unknowingly uses a similar value to Bonne, f = 10, and if we assign f = 0 we arrive at Werner’s projection. These of modifications result in the possibility of an infinte series of projections of the Waldseemuller type. This can be visualized by just a few examples from my models of Werner's projection below.
Waldseemüller’s map can be approximated in this same way using values of f between 7-8.5. The actual projection of the 1507 map differs from that represented in the above equations in that it has bends in the meridians at the equator, and the meridians are shown as segmented circular arcs rather than as continually changing curves. This difference is however trivial in the overall look of the projection and the distortions that is produces in the continents of the New World. Using these models the modern coast of South America has been projected in the figure below alongside the same region from the Waldseemüller map.