1 The Birth of Science - MSRI

238 10. Lost Science
there is no direct documentary evidence for its use. 13 But the placement
of the tropic at the center of a shadowless zone, as logically implied by
Cleomedes’ statement just discussed, seems to be a case where the literature
preserves an indirect trace of the method in question. The lack of
direct testimonia about experimental averaging is hardly surprising, since
the manuscript tradition preserved neither the works where the technique
might have been used (such as Herophilus’ research on heartbeats) nor the
theoretical treatise by Eratosthenes titled On means, which might perhaps
have cast some light on the issue. 14
Next, the determination of the tropic through multiple simultaneous observations
affords an accuracy that would be pointless if the distance to
Alexandria were then estimated using days of journey. Is it possible that
the distance was actually measured? Eratosthenes was the first person to
make a map of Egypt. The degree of precision with which he managed to page 296
measure the distance from Alexandria to the tropic — that is, to the southern
border of the kingdom — is equivalent to that with which the chart
was made.
A record of the work involved in this topographical survey can be found
in the sources. Martianus Capella writes that the distance measurements
on which Eratosthenes’ estimate of the size of the earth relied were furnished
by the royal surveyors (mensores regii), 15 and Strabo relays some
data from Eratosthenes’ map of Egypt. 16 We know that already in the
Pharaohs’ time a detailed measuring of the land () was made
annually throughout Egypt. Under the Ptolemies the measurements were
entrusted to technical staff and royal inspectors in every village; they were
then collected and coordinated by the toparchs for each topos (a subdivision
of the nome), and then further up by the nomarchs for each nome
(province). The reports finally reached Alexandria, were they were used
for the preparation of tax rolls. 17 By combining this tentacular bureaucratic
organization with the new methods of scientific geodesy, good maps of
Egypt would not have been out of reach.
13
See, for instance, [Grasshoff], p. 203, where it is mentioned that the first documented instances
of averaging of experimental results are due to ninth-century astronomers in Baghdad.
14
We know the title of this work from Pappus, Collectio, VII, 636, 24–25 (ed. Hultsch). The only
other information we have is what we can deduce from another passage of Pappus (Collectio, VII,
662, 15–18), where, apparently referring to the same work, the author states that Eratosthenes
treated geometric loci related to means and that such loci, because of their particular definition, did
not fall within the scope of Apollonius’ classification.
15
Martianus Capella, De nuptiis Mercurii et Philologiae, VI, 598.
16
Strabo, Geography, XVII, i, 2. However, these data got corrupted on their way to us; a partial
reconstruction can be found in [Rawlins: ESNM].
17
For the organization of the land register and measurements under the Ptolemies, see [Ros-
tovtzeff: SEHHW], vol. I, pp. 275–276.
Revision: 1.11 Date: 2003/01/06 02:20:46