1 The Birth of Science - MSRI

3.2 Geodesy and Mathematical Geography 59
Chorography, whose purpose according to Polybius is to determine the
location of sites and the distances between them, 48 seems to be an intermediate
step between the techniques used in town planning and in mathematical
geography.
The difference between Hellenistic mathematical geography and the
purely descriptive geographical works of classical Greece, Rome, and the
Middle Ages is a good illustration of the difference between scientific and
prescientific societies.
We know Hellenistic mathematical geography through a single work,
Ptolemy’s Geography, but that is enough to show that it was as scientific
as today’s. 49 It is a typical scientific theory with correspondence rules,
whereby each spot on the surface of the earth corresponds in the model to
a point on a spherical surface, identified by two spherical coordinates: latitude
and longitude. Ptolemy is also familiar with cartography; he knows
several projections (including modified conic projections, whose mathematical
properties he uses) in order to represent the earth on plane charts,
preserving all the information present in a spherical representation.
Ptolemy’s work records the latitude and longitude of about eight thousand
places, from Ireland to Southeastern Asia.
Mathematical geography, too, arose early in the Hellenistic period. The
quantitative description of the whole known world becomes an acutely page 92
felt need following the sudden expansion of the Greek world due to Alexander’s
conquests. Already around 300 B.C., Dicaearchus, a student of
Aristotle, had taken the first step toward the creation of mathematical geography
by identifying a parallel of latitude, that is, by selecting a series
of locations all having the same latitude, from Gibraltar to Persia. 50
Eratosthenes drew the first scientific map of the known world, extending
from Gibraltar to India and from Somalia to the North polar circle. His
work already relied on the spherical coordinates we use. 51 A place’s latitude
— the Greek word was , which originally meant “inclination”
and later gave our “climate” — is easy to fix, say by measuring with a sundial
the angle the sun rays make with the vertical at noon, on the day of
the solstice. Another way is to obtain it from the ratio between the dura-
48
Cited in Strabo, Geography, X, iii, 5. It may be significant that at the beginning of his work
Strabo compares geographers to architects who plan buildings or cities (Geography, I, i, 13). There
is no direct documentation for topographical maps.
49
In fact, “modern” mathematical geography is none other than Ptolemy’s, recovered by Renaissance
scholars.
50
The attribution of the introduction of the first parallel to Dicaearchus is based on a passage of
Agathemerus (Geographiae informatio, Prooem., 5 = [Dicaearchus/Wehrli], fr. 110).
51
The spherical shape of the earth was known at least as early as Parmenides, in the first half of
the fifth century.
Revision: 1.13 Date: 2002/10/16 19:04:00