[4.1] Aristotle's arguments for the
spherical shape of the Earth are given in On the Heavens,
Book 2, Part 14 (350 BCE). A modern translation by J.L. Stokes may be
found online at MIT on the Internet
Classics Archive.
Aristotle argued that the Earth must necessarily be spherical
because the weight of all its parts setting towards the center would
naturally form a spherical shape. Today we would recognize the tendency
to settle towards the center to be a consequence of gravity (Aristotle
does not, of course, use that word).
He noted the curved outline of the shadow of the Earth on the Moon, and
the different heights of stars between orthern and southern regions, as
mentioned in the lecture, but he also put forth a rather odd argument
that one finds elephants in Africa ("Pillars of Hercules" is the Strait
of Gibraltar) and India, arguing for "continuity of parts", meaning they
are close together on the surface of a sphere (they are far apart across
the mediterranian, but closer going west from Africa). The idea being
the world conceived by Aristotle is small, but not so small that small
changes in place result in dramatic changes in the heights of constellations.
[4.2] The definition of a stade in
modern units has been very contentious. A very compelling case has been
made by Donald Engels (1985, American Journal of Philology,
106, 298, full
article on jstor.org) for 1 stade = 184.98 meters (based on 8 Roman
miles to 1 stade). Two numbers reappear in the literature:
148 meters/stade, which was a mis-calculation by d'Anville in 1759,
and 157.4 meters/stade given by A. Letronne in 1851 (published
posthumously). I used to quote the 157m/stade number in my notes, which
gives a circumference of the Earth much closer to that of the modern
value. Engels' arguments, however, are very persuasive that Eratosthenes
would have used the Attic stade based on the Stadium of Athens, which
gives the conversion of ~185m/stade that I quote in these notes.
[4.3] The only description of
Erathosthenes' method that survives from antiquity is from On the
Orbits of the Heavenly Bodies written by Cleomedes in the 1st or
4th century AD (also known by the first word of its Greek title as the
Meteora). We know little or nothing else about Cleomedes,
not even his date or place of birth. It is clear that the numbers 5000
stades and 1/50th of a circle have rounded off for convenience,
contributing to the inaccuracy of the final result.
However, while the derived circumference is off by ~15%, the actual
difference in latitude between Alexandria (31°13' N) and Syene/Aswan
(24°05' N) is 7°08', or about 0.0198 of the arc of a circle,
within 1% of the value 0.02 (1/50th) quoted by Cleomedes for
Eratosthenes. This is well within any measurement errors expected for
the time.
