1 The Birth of Science - MSRI

62 3. Other Hellenistic Scientific Theories
by centuries during which there had been no continuity in the transmission
of information. 61 Now we must ask ourselves how it came about that
Marinus and Ptolemy, who knew the method used by Eratosthenes and
had access to the same information about Syene, did not try to repeat the
simple measurement of the inclination of the sun. We might also ask why
Columbus did not repeat the measurement himself, instead of traveling
throughout Europe looking for information about the size of the earth in
libraries. Or yet why neither Galileo nor any of his contemporaries did
it. Clearly Eratosthenes’ method hides a further difficulty, which escapes
those who think it trivial. We will come back to this in Section 10.1.
3.3 Mechanics
We alluded in Section 1.5 to the main features of Aristotelian mechanics.
By contrast, the mechanics (literally, “science of machines”) we encounter
in the first Hellenistic treatise we possess on the subject, Archimedes’ On
the equilibrium of plane figures, already has the characteristic structure of a
scientific theory in our sense. That work deals with two closely connected
problems: the law of levers and the location of barycenters of plane fig- page 96
ures. 62
Archimedes’ interest in the theory of levers is clearly aimed at the study
of machines and in particular at the calculation of their mechanical advantage.
Unfortunately very little remains of contemporary theoretical writings
on this subject; Archimedes’ other treatises have perished. 63 But we
can reconstruct some features of third century B.C. mechanics by combining
information from three sources: the one surviving Archimedean book;
61 Studies at Alexandria had been tragically interrupted by the persecution unleashed by Euergetes
II in 145 B.C. (page 7). The Library survived, and became the main element of continuity
between the golden era and the revival of the imperial age. But the scarcity of intellectuals after the
persecution was such that the position of the head of the Library fell to a certain Cida “from the
corps of lancers” ( ), as we know from a papyrus (P. Oxy. 1241, II, 16). It is easy
to see how this situation led in the imperial age to that passive dependence on written authorities
that became even more acute later on and that is sometimes backdated to the golden period of
Alexandrian science, through the conflation of two profoundly different cultural climates.
62 Mach’s criticism that Archimedes deduced the law of levers from inadequate symmetry considerations
([Mach], I.3, I.5) reflects a lack of understanding of the function of the Archimedean
postulates. Mach considers only the first two postulates, whereas in deducing the law of the lever
Archimedes makes essential use of the sixth. This is emphasized by O. Toeplitz, W. Stein and E.
J. Dijksterhuis, who showed how much subtler the Archimedean analysis was than Mach’s (see,
for example, [Dijksterhuis: Archimedes], 291–295). Even as keen an intellect as Mach’s can fall into
the trap of assuming that the long time elapsed grants us an automatic and facile superiority over
Hellenistic scientists.
63 The one remaining piece is probably an excerpt from a longer work, Elements of mechanics
( ), which Archimedes himself seems to cite under this title (On floating
bodies, 25; ed. Mugler, vol.~III).
Revision: 1.13 Date: 2002/10/16 19:04:00