The second cartographic method of Ptolemy (ca. 100-ca. 178) attempts to reproduce an image of the oikumene (that is, the inhabited world) more closely resembling that of the terrestrial globe, giving the representation a spherical appearance that is almost totally lacking in the first method. While visually pleasing, this concession adds nothing as regards the measurability of geographic coordinates, a requirement already fully satisfied by the first cartographic method.
To obtain the desired effect, Ptolemy imagines that he is looking at the globe from a point located exactly at the center of the oikumene, not only with respect to longitudinal amplitude as in the first method, but also with respect to the latitudinal amplitude. The viewpoint thus shifts from the zenith of the Rhodes parallel to that of the parallel passing through Syene (modern Aswan), situated precisely on the Tropic of Cancer, at latitude 23°30’ north. Next, Ptolemy imagines a representational plane tangent to the point of intersection between the central meridian and the Syene parallel, and he proceeds to transfer the geographic coordinates onto it. As a result, the largest circle tangent to the representational plane and orthogonal to the central meridian—in other words, the ecliptic circle—appears as a horizontal straight line. Such a circle does indeed lie on a plane passing though the observer’s eye. For the same optical reasons, the central meridian will be seen as a vertical straight line.
Because he needs to ensure that distances are measurable, Ptolemy marks the equal intervals of 5 degrees on the horizontal line that define the map’s longitudinal amplitude to the right and left of the central meridian. With the same intervals, he then marks the latitudes of the main parallel circles on the central axis. These are the Equator, the so-called anti-Meroë parallel, and the Thule parallel. As the Equator intersects the ecliptic circle at 90 degrees from the central axis, it will be shown on the plane as an arc intersecting the horizontal line at either end. The other circles will appear as arcs concentric to the first. Their widths are defined by the measurement of the five-degree intervals, which varies with latitude. The center of the curvature of the parallel arcs appears on the central axis after tracing the chord of the equatorial semi-arc and the straight line orthogonal to the center of the chord. By joining the ends of the parallel arcs with two curved lines representing the 0 degree and 180 degrees meridians, Ptolemy obtains the space containing the map of the oikumene. As in Ptolemy’s first method, the map is designed as a “peel” transferred from the globe to the flat surface.