Leonid Zhmud The Origin of the History of Science in Classical Antiquity

Geography, since it
could belong to book II as well.
4
It is obvious in any case that, in a scientific
treatise on geography, Eratosthenes could not consistently select the material
on the same principles as Eudemus did in the
History of Astronomy. While
Eudemus focused his attention on the major discoveries exemplifying the pro-
gress of science, Eratosthenes combined this method with the doxographical
one, which allowed him to mention all the opinions relevant to a given problem
and to criticize those he disagreed with.
Unlike Eratosthenes’ historical introduction to
Geography, his dialogue
Platonicus derives directly from the material of Eudemus’ History of Geometry
(3.1). It does not seem, however, to develop Eudemus’ work in either content or
form. Selecting from the whole of the previous history of geometry the single
problem of doubling the cube (interesting for him since he took part in solving
it), Eratosthenes invents a fictitious story for it, based on the Academic legend
of Plato as the architect of science. Eratosthenes is unlikely to have done any re-
search in the sources: the solutions of Archytas, Eudoxus, and Menaechmus he
quotes are already found in Eudemus. Neither in the
Platonicus, where the sub-
ject imposed certain limitations on him, nor in his letter to the king Ptolemy III
does Eratosthenes mention any of the other solutions, that of Philo of Byzan-
tium for example, which, in principle, he could have known.
5
Platonicus pres-
ents the history of mathematics in the dramatic form of a popular philosophical
dialogue with mathematical content, in which its main hero, Plato, is the
4
Berger,
op. cit., 142f.
5
Knorr.
TS, 144f.

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Chapter 8: Historiography of science after Eudemus: a brief outline
280
mouthpiece of its author’s ideas. In spite of the popularity
Platonicus enjoyed
in Antiquity,
6
the genre itself does not seem to have had any direct followers,
though it may have exercised a certain influence on the mathematical anthol-
ogies of late Antiquity, which contained the solutions of such famous problems
as those of squaring the circle, doubling the cube, etc. In fact,
Platonicus, but
for its dialogical form, could be regarded as the earliest known example of such
an anthology. Yet even here Eratosthenes must have followed the histori-
ographical tradition of the Lyceum, represented, for example, by Aristotle’s
work on a still more famous scientific problem – that of the Nile’s floods.
7
Unlike the mathematics of the Imperial age, whose self-awareness increas-
ingly depended on its awareness of its distant past, the exact sciences of the
Hellenistic epoch had little reason to turn to the pre-Euclidean period. This lack
of historical sensibility can partly be accounted for by the very style of math-
ematical and astronomical treatises formed and generally adopted by the fourth
century: formal and utterly impersonal,
8
it left no place for historiographical
references or outlines. The surviving works by Euclid and Autolycus include
no names; the same is true of the Aristotelian
Mechanics and Aristarchus of
Samos’
On the Sizes of the Sun and the Moon and on Distances to Them. The
mathematical treatises of the second half of the third century often opened with
a brief introduction written in the form of a letter to a fellow scientist. In the in-
dividual introductions to the books of his
Conics, Apollonius cites several
names of his contemporaries and predecessors,
9
failing, however, to mention
Menaechmus and Aristeas the Elder, who laid the foundations of the theory of
conic sections. Archimedes’ introductions to his works, though more detailed,
treat his predecessors (Democritus, Eudoxus, Aristarchus) in the context of
analysis focused on individual problems – an approach typical of scientific lit-
erature up to the present day, not of historiography. The introduction to the
work by Diocles, a contemporary of Apollonius, also deals with a particular
problem: the author suggests using conic sections to solve the two tasks formu-
lated by Pythion of Thasos in his letter to Conon of Samos and by Zenodorus
during his visit to Diocles himself.
10
In Hypsicles’