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

mathe¯mata. Geminus, in
whom this fragment from Posidonius is found,
60
seems to have shared his
views. In his
Introduction to Phaenomena, however, it is not Plato or Eudoxus
but the Pythagoreans whom he mentions in this connection, though the argu-
ments in favor of the regular circular movement that he assigns to them bear an
indelibly Platonic character.
61
Hence, by the early second century AD, the gen-
eral thesis that astronomy is directly dependent on the basic principles estab-
lished by philosophy has taken root in the Stoic, Peripatetic, and Platonic
example: even Aristotle, who teaches us the same in logic, derived his logical argu-
ments from mathematics (
Proleg. Phil., 59.23ff.). See Gutas. Paul the Persian, 274f.
56
On the other hand, the mathematician Diodorus of Alexandria, following Posidonius
in his definition of differences between mathematics and physics, believed that the
two sciences were closely linked and could not do without each other in scientific re-
search: diaferoúsa~ goñn taúta~ ën ta$~ zht2sesin ëpipeplécqai t3n êtéran
deoménhn t4~ êtéra~ (Achil. Isag., 30.20–29 Maass).
57
Eud. fr. 148. See above, 86f., 273f.
58
He insists that the astronomers must build their theories on the fundamental @rcaí
taken from Plato and reproaches all those who deviate from these principles (Theon.
Exp., 199.9–202.7). Kidd, op. cit., 11, suggests that Dercyllides’ position, especially
in
Exp., 200.4–12, may reflect Posidonius’ ideas, but the Platonist’s program seems
to be of a more general character. See the next footnote.
59
His entire astronomy is deduced from ‘physical’ principles (Theon.
Exp., 147.19ff.).
All irregularities in the planetary motions are apparent and katà sumbebhkó~, they
have to be explained by different astronomical hypotheses: fusikòn mèn kaì @nag-
ka$on, kaqáper tà @plan4
,
kaì tõn Állwn oÿraníwn Êkaston âpl4n kaì
mían kaq’ aûtò foràn ômalõ~ féresqai kaì eÿtáktw~ (150.21f.).
60
See above, 229 f.
61
Gemin.
Eisag. I, 19–21 (see above, 271 n. 193): it is hard to imagine the divine and
heavenly bodies moving quickly and slowly in alternation; their immortal nature
implies circular regular movement alone. Theon (
Exp., 150.12f.) attributes to Pytha-
goras almost the same idea.

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1. The decline of the historiography of science
291
schools, so that its historical corollary – Eudoxus fulfilled Plato’s methodologi-
cal requirements – seems only natural.
The new interest in exact sciences, notable in Posidonius, is present in
Geminus’ works as well. It has to be pointed out again that his introductions to
astronomy and mathematics are of a systematical character; they are neither di-
rectly related to the history of science, nor make any use of Eudemus’ works.
62
Apart from the reference to the Pythagoreans as
pro¯toi heuretai, his introduc-
tion to astronomy does not include even the briefest historical overview. The
problems treated in his introduction to mathematics correspond on the whole to
the scientific interests of Posidonius, whose works were among Geminus’ main
sources. This textbook acquainted the reader with the foundations of mathe-
matics, its methodology, and philosophical discussions around it, with particu-
lar emphasis on the classification and elucidation of mathematical notions. All
Geminus’ fragments that contain the mathematicians’ names show that he re-
ferred to them to illustrate his theoretical propositions.
63
The Hellenistic math-
ematicians Amphinomus, Menaechmus, Zenodotus, and Theodorus figure in
the context of methodological discussions of the notions of ‘element’, ‘theor-
em’ and ‘problem’.
64
Apollonius, Nicomedes, Hippias, and Perseus are men-
tioned in connection with the classification of curves.
65
Archimedes is cited
once as an illustration of the subject of mechanics and another time as an
example of the mathematicians who call all the axioms postulates.
66
Geminus
reproaches Apollonius for his attempts at demonstrating the axioms; his book
about unordered irrationals is far too complicated to serve as an introduction to
mathematics.
67
Quite often Geminus refers to the authority of philosophers, considering
their opinion no less than that of mathematicians.
68
Plato and Aristotle are
62
See above, 185f. – The idea of Geminus as a historian of mathematics seems to be in-
eradicable. Since Barocius, the translator of Proclus’ commentary to Euclid (1560),
listed among Proclus’ sources