Ptolemy's maps of earth and the heavens: A new interpretation

Abstract

0°. Among Ptolemy's works are two whose mathematical bases historians of science have interpreted in very much the same way. The works are The Planispherium and the cartographic sections of The Geography, and in both cases the interpretation has been in terms of pointwise projection of a portion of the surface of the sphere onto a portion of the plane. In the case of The Planispherium the sphere is the celestial sphere and the mapping appears to be stereographic projection of the portion of the celestial sphere to the north of "the greatest always-invisible circle"1 on the interior of a circular part of the plane. For example, Neugebauer 1975 (857-858) writes "it [The Planispherium] deals with the representation of the celestial sphere . . . known today as stereographic projection", Toomer 1978 (219) writes "the whole necessary theory of stereographic projection is set out in Ptolemy's Planispherium,'" and Pedersen 1974 writes "In the Planispherium ... Ptolemy describes how the celestial sphere can be projected in a different way, namely by stereographic (central) projection from the southern pole of the heavens onto the plane of the equator." In the case of The Geography however the sphere is the terrestrial globe and, in addition to Marinus's much-criticized representation of its surface, Ptolemy gives three other representations of the inhabited portion of the earth (the oikoumene in the language of Greek geographers) onto plane regions of varying shapes. Here again, the best of the recent literature on the topic has set forth Ptolemy's representations in terms of pointwise maps or projections of the sphere into the plane. Some examples are the analyses of F. Hopfner in the appendices to Mžik & Hopfner 1938 and the summary in Neugebauer 1975 (879-890).