**DIGITAL APPROACHES IN ELIMINATING THE HIGHER ORDER SYSTEMATIC
EFFECTS IN PTOLEMY’S GEOGRAPHIA LONGITUDE AND LATITUDE DIFFERENCES**

A. Tsorlini, E. Livieratos

*Aristotle University of Thessaloniki, Faculty of Surveying
Engineering, Thessaloniki, Greece*

*atsorlin@topo.auth.gr*

In his celebrated *Geography, *Claudius Ptolemy describes geographic sites (i.e. towns,
mountain picks, river mouths, promontories and other) as points with given
coordinates of spherical longitude and latitude type. These geographic coordinates
are following the known Ptolemaic reference system of parallels and meridians,
the origin of which are respectively close to actual Equator and close to the
Canary Islands many degrees west of the today’s origin at Greenwich. It is also
known that though latitudes are rather well defined, considering the level of
measuring accuracy at Ptolemy’s times, the longitudes suffer severe
shortcomings which are due to the difficulties of measurement time, which
corresponds to the longitude. The longitude values given by Ptolemy are also
strongly dependent upon the distance from the Canaries eastwards. Previous
research showed the order of magnitude of the longitude and latitude
differences of Ptolemy’s values from the today’s counterparts both in broader
and local scale, but without diving into a systematic geodetic approach on the
issue. The problem is challenging and deserves a revisiting because of the
advances of digital computational and visualization technologies (informatics
and infographics) which are massively available today allowing new approaches
and techniques in studying this extraordinary document of our cartographic
heritage as it is the Ptolemy’s *Geographia.*
In the paper, part of a broader research carried out the last years by the
Cartography Group of our Faculty we focus our interest on Ptolemy’s coordinates
given in *Geography* for the area of
actual Greece, listed mainly in Book III, Chapter XII about Europe and Table X,
but also in some other associated Chapters and Tables about Greece. Storing digitally
the coordinates for the area of interest (almost 600 pairs of coordinates), and
snooping the data, which is a laborious process because it requires the
cross-checking with the relevant coordinated given in a number of Ptolemy’s *Geographia *editions (in our case there
are used five), the finally accepted list is formed which is compared with
their today’s values. The core of the study concerns a two-dimensional spatial
analysis of the field of differences, testing various transformation functions
in order to determine and eliminate the systematic error pattern inherent in
Ptolemy’s coordinates. The result, using new “reductive” methods in the
comparison analysis (e.g. the concepts of the unit sphere, of the common
projective support) with all affined illustrations of the associated test,
shows the pattern of coordinate differences free of systematic effects up to
the 2^{nd} order, testing also and some higher order effects in order
to get a better understanding of the whole process. Finally a field of various
classes of spatial deformations of isotropic and anisotropic character, are for
the first time tested and visualized.