1 The Birth of Science - MSRI

60 3. Other Hellenistic Scientific Theories
tion of day and night at the solstice. 52 Fixing longitude has always been
much harder, until the advent of chronometers and radio, and we don’t
know what method Eratosthenes might have employed. Possibly it was
the one mentioned by Ptolemy at the beginning of his work, whereby one
finds the difference in longitude between two places by determining the
difference in latitude and estimating the angle that the line between the
two makes with the meridian. 53 In the case of cities linked by a sea lane,
this information would have been known approximately to seafarers plying
the route.
Eratosthenes’ most famous result was the measurement of the earth’s
meridian. 54 Earlier numbers, reported by Aristotle with no mention of
the method by which they were obtained, 55 had been “estimates” rather page 93
than measurements. The admiration earned by Eratosthenes’ feat was so
widespread that Pliny, centuries later, could still hear its echoes. 56
Eratosthenes’ method, as given by Cleomedes (and as expounded in numerous
textbooks and works of scientific popularization), is the following.
It was known that Syene (today’s Aswan) is located almost exactly on
the tropic line: during the summer solstice, the sun passes almost exactly
overhead at noon. Therefore, if someone in Alexandria at the same time
measures with a sundial the angle made by the sun’s rays with the vertical,
he has the angle formed by the vertical lines through the two cities. If
he knows also the distance between them as the crow flies, he can deduce
the distance corresponding to one degree of great circle. The difficulty in
knowing in Alexandria when it was noon in Syene is overcome by assuming
that Syene is directly south of Alexandria, so that noon occurs
simultaneously in both places.
We will return to the technical details in Section 10.1. For now we make
only a methodological observation.
Today Eratosthenes’ method seems almost banal to many people who
can easily explain it with the help of a drawing. Yet it is inaccessible to
prescientific civilizations, and in all of antiquity not a single Latin author
succeeded in stating it coherently. The difficulty lies of course not in the
geometric reasoning, in itself very simple, but in understanding that by
reasoning about a drawing one can derive conclusions about the whole
52 Compare [Szabó, Maula], part II.
53 Ptolemy, Geography, I, ii, iii.
54 This was described by Eratosthenes in his On the measurement of the earth, which is lost; we
know about the method involved chiefly through Cleomedes, Caelestia, I, 7, 48–110 (ed. Todd). We
will come back to Cleomedes’ account in Section 10.1.
55 Aristotle, De caelo, II, 14, 298a. Probably the method involved comparing the elevation of stars
at different places.
56 Pliny, Natural history, II, 247–248.
Revision: 1.13 Date: 2002/10/16 19:04:00