The third cartographic method of Ptolemy (ca. 100-ca. 178) offered an illusionistic representation of the oikumene—that is, the then known part of the world—depicted as if it were viewed on the surface of a globe surrounded by an armillary sphere. According to Ptolemy, many had tried to produce a representation of this kind, but with unsatisfactory results. Having presumably observed an actual model, Ptolemy imagines a viewer looking at the total picture from a spot located at the center of the oikumene—that is, at the intersection between the plane passing through the central meridian and the plane passing through the parallel of Syene, modern-day Aswan. The meridian and the parallel divide the surface area of the oikumene exactly in half, vertically and horizontally.

Ptolemy constructs the model with a ratio of three to four between the radius of the terrestrial globe and the radius of the armillary sphere. He sets the observation distance so that the entire oikumene is visible in the space between the equinoctial armilla and the Tropic of Cancer. The front semi-circle of the ecliptic is conveniently the southern one, which, as it extends downward, does not overlap the oikumene. The observer’s eye is positioned in such a way that the central meridian and the Syene parallel appear as orthogonal straight lines, whereas all the other arcs appear as curves whose bends increase as one moves away from the center. Contrary to what the laws of optics would require, but consistently with the map’s practical purpose, the intervals between the meridian and the parallels are kept equal, highlighting the ingenious combination of the map’s flat representation of the oikumene and the perspective drawing of the armillary sphere.