1 The Birth of Science - MSRI

236 10. Lost Science
at most 2.4% below or 0.8% above the true value. Such remarkable accuracy
has often been seen with suspicion, especially because it is true
only to a coarse approximation that Syene and Alexandria lie on the same page 293
meridian and that Syene lies on the tropic. Moreover, whereas modern
measurements, first attempted by W. Snell in 1615, 1a involved triangulation
over distances of a hundred kilometers or so, 2 it is generally held that
the distance between Syene and Alexandria was estimated by counting
days of travel. The conclusion ordinarily accepted is that Eratosthenes did
get an excellent value, but only as the result of a very lucky cancellation
of errors. 3
The size of the degree is not the only distance measurement that Eratosthenes
is reported to have made. He in fact compiled a map of the whole
known world. One of the data transmitted by Strabo is the distance from
Alexandria to Rhodes, which Eratosthenes found to be 3750 stadia. 4 This
value, too, is generally regarded as the result of a rough estimate 5 that is
close to right by accident.
Do we know for sure that Eratosthenes assumed that Alexandria and
Syene lay on the same meridian and that Syene was on the tropic? The
primary source of this information, Cleomedes, actually wrote:
Eratosthenes’ method, being geometric, seems more difficult [than
the previously explained method of Posidonius]. What he says will
become clearer if we allow ourselves to make two assumptions. We
assume first that Alexandria and Syene are on the same meridian. 6
Cleomedes does not give a detailed account of the method — that would
be pointless, Eratosthenes’ work still being available — but a pedagogical
1a Snell — best known for the sine law of refraction, about which more on page 305 — explicitly
designed his measurement as an attempt to duplicate Eratosthenes’ feat. The work, carried out in
the Dutch flatlands and described in Snell’s Eratosthenes Batavus (1617), relied on his recovery of
ancient methods of triangulation and of spherical geometry, which culminated in the book Doctrina
triangolorum (Leiden, 1627). On p. 62 of the latter we find a tantalizing tidbit of terminological
information, noted in [Carnevale]: according to Snell, Hipparchus and Menelaus used the term
tripleuron for spherical triangles. Because we possess no ancient testimonium on Hipparchus in
connection with spherical geometry, this may mean that Snell had some source no longer extant.
(In the case of Menelaus the source may be Pappus.) Note that Hipparchus preceded Theodosius,
the author of the oldest extant work on spherical geometry.
2 After Snell’s and other attempts involving distances too small to be effective, in 1669 the French
Academy undertook two careful measurements of distances over 100 km, under Picard’s direction,
and so obtained the first reliable values for the degree of the meridian, namely 57064.5 and 57057
Paris fathoms (toises de Paris). Picard related this unit to a precisely defined pendulum, so we
know it quite exactly (1949 mm); this gives an error of about 0.1%. See [Picard].
3 See, for example, [Heath: HGM], vol. II, p. 107; compare [Neugebauer: HAMA], p. 653.
4 Strabo, Geography, II, v, 24.
5 See, for example, [Neugebauer: HAMA], p. 653.
6 Cleomedes, Caelestia, I, 7, 49–52 (ed. Todd).
Revision: 1.11 Date: 2003/01/06 02:20:46