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

DK, Dox., 364a 15f. and above, 244 n. 74).
103
The first line is represented by Eudoxus’ Fainómena and ¨Enoptron (fr. 1–120),
the second by Eudoxus’ and Callippus’ calendar schemes and parapegmata (astro-
nomical calendars with weather indications included) (fr. 129–269), the third by
Eudoxus’
On Velocities with Callippus’ modifications (fr. 121–126).
104
Oenopides (41 A 7, 13–14), Hippocrates (42 A 5; see Burkert.
L & S, 305, 314, 332),
Philolaus (44 A 16–17, 21). Archytas’ astronomy is, unfortunately, almost com-
pletely unknown (cf. Zhmud.
Wissenschaft, 219f.), yet we are familiar with his at-
tempts to apply mathematics to harmonics, mechanics, and, possibly, to optics (see
above, 129 n. 45, 173f., 216). As Eudoxus’ teacher, Archytas may have been directly
involved in the further geometrization of astronomy (see above, 97f., and below, 274
n. 202).
105
Oenopides (41 A 10), Hippocrates (42 A 5), Philolaus (44 A 18–20). In the parapeg-
mata, the first of which belongs to Meton, the connection between astronomical and

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Chapter 7: The history of astronomy
254
seemed to regard Oenopides as the first to develop the methodological prin-
ciples of mathematical astronomy (7.5). By relating the
beginnings of this
science to Thales and Anaximander, he might have proceeded from the as-
sumption that their discoveries laid the basis for further progress. The intrinsic
logic underlying any science’s development had already been formulated by
Eudemus’ teacher:
For in the case of all discoveries the results of previous labours that have been
handed down from others have been advanced bit by bit by those who have taken
them on, whereas the original discoveries generally make an advance that is small
at first, though much more useful than the development which later springs out
them. For it may be that in everything, as the saying is, ‘the first start is the main
part’: and for this reason also it is the most difficult; for in proportion as it is most
potent in its influence, so it is smallest in its compass and therefore most difficult
to see: whereas when this is once discovered, it is easier to add and develop the re-
mainder in connection with it. This is in fact what has happened in regard to rhe-
torical speeches and to practically all the other arts: for those who discovered the
beginnings of them advanced them in all only a little way, whereas the celebrities
of to-day are the heirs (so to speak) of a long succession of men who have ad-
vanced them bit by bit, and so have developed them to their present form.
106
Even denying Aristotle’s teleological approach, one has to admit: without
fundamental notions introduced in astronomy before the mid-fifth century, its
further geometrization would have been impossible. In the first place, I mean
the central position of the earth and its spherical shape, the notion of the
heavenly sphere divided into zones by the equator, the tropics and the arctic and
the antarctic circles, the independent movement and order of the planets, and
explanations of solar and lunar eclipses. Interestingly, nearly all these ideas
were in fact interpreted later as eûr2mata, so that Eudemus could hardly have
passed them by unnoticed.
107
It is at this early period that deductive geometry, toward which mathematical
astronomy was subsequently oriented, also took shape. The general form and
methods of presenting the material in Autolycus’ and Euclid’s treatises was ob-
viously modeled on mathematical
Elements. Astronomy is presented here as a
deductive theory that consistently demonstrates its theorems, proceeding from
a number of definitions and axioms. The influence of geometry is also betrayed
meteorological phenomena has a regular character; see Rehm A.