The Visual Point and the Construction of the Geometric Order of the Oikoumene

Ptolemy's Geography is an ancient opus of cartographic theory with the “oikoumene” (inhabited world) as the object that is described using geometry as the basic method. Based on the “Hermes perspective” from Eratosthenes and the Euclidean optical tradition, Ptolemy constructed a geometrical “visual point”, by which different mathematical methods, such as Euclidean optical propositions, plane geometry theorems and flattening, were integrated, and a systematic geometric mapping method was proposed, the first in the history of Western geography. The employment of the “visual point” in Geography reflects Ptolemy's mathematical philosophy. Through the assumption of the visual point, the oikoumene can be observed and imitated quantitatively, and endowed with a geometric and imagistic order. By way of the world image thus represented, geography was incorporated into Ptolemy's larger world picture of mathematics. In this process, the “visual point” also acts as the “Archimedean fulcrum” for Ptolemy to creatively synthesize different mathematical methods and accomplish transformation from the spherical image to the plane map.