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

Ethics (981b 26f.).
217
Democritus (68 B 144) says nothing about leisure. The first to mention leisure was
Isocrates (
Bus. 21–23), followed by Plato (Crit. 110a). But leisure plays no role in
the
Laws (677a–683b), where Plato’s theory on the origin of culture is stated in great
detail, or in the
Epinomis (974d 3–977b 8).
218
See e.g. fr. 53 Rose =
Protr. fr. 8 Ross; Pol. 1329b 25f., where leisure is not men-
tioned.
219
Met. 981a 12 f., 981b 10 f.; EN 1139a 17f. See also Wehrli’s commentary on fr. 133.

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Chapter 5: The history of geometry
212
scheme, Eudemus emphasized the practical
origin of Egyptian geometry, since
even Thales, who borrowed this science from Egypt, still proved some things in
a more particular and some in a more general way (fr. 133).
The idea of the progressive growth of knowledge is older than both Aristotle
and Eudemus. Already Isocrates employs ëpídosi~ and ëpididónai as notions
designating qualitative development and advancement (
Paneg. 10, 103, 189).
The verbs from the same semantic group, such as aÿxánein, proagage$n, and
proércesqai, acquire a similar meaning with Isocrates.
220
These notions are
often found where he discusses the discovery and development of various téc-
nai, in particular the progress of rhetoric and the constant quest for novelties.
221
Aristotle employs the verb proagage$n when referring to the advancement of
mathematics by the Pythagoreans (
Met. 985b 23f.) and ëpídosi~ for express-
ing the idea of rapid progress in contemporary mathematics and in all the téc-
nai in general (EN 1098a 24–25). In Philodemus’ quotation from the Aca-
demic treatise, ëpídosi~ is used twice: first, with regard to all mathematical
sciences, and second, in connection with geometry. In Eudemus, ëpídosi~ ap-
pears only once, and conspicuously in the passage of the
Catalogue praising
Plato’s role in geometry, but aÿxánein, proagage$n, proércesqai occur in
this text unusually often.
222
One of the criteria of progress in mathematics, for Eudemus, was the degree
of generality of mathematical propositions.
223
Thales was the first to teach ge-
ometry “more generally” (
In Eucl., 65.10), Eudoxus augmented the number of
“general theorems” (67.4) by developing a new theory of proportions, and
Theudius gave to many partial propositions a more general character (67.15).
This also coincides with Aristotle’s notion of the development of sciences from
the particular to the general. Another notion shared by the Peripatetics was the
idea, going back to Plato, of the cyclical character of the historical process.
224
Humankind, being eternal, periodically goes through a number of regional ca-
tastrophes in which most arts and sciences perish, so that later generations are
compelled to discover everything (or nearly everything) anew.
225
Proclus refers
to Aristotle’s opinion on the periodical emergence of sciences before the very
beginning of the
Catalogue (64.8f.), which, in Wehrli’s edition, opens with the
220
See above, 77 n. 140.
221
See e.g.
Nic. 32, Antid. 81–83, 185, Paneg. 10.
222
ëpauxánein (66.16), aÿxánein (67.5), proagage$n (67.7, 67.22), proércesqai
(66.17). See Edelstein,
op. cit., 92; Thraede. Fortschritt, 141f., 154.
223
Lasserre.
Eudoxos, 161f.
224
See above, 109 n. 133.
225
Arist. fr. 13 Rose (= fr. 463 Gigon), fr. 53 (=
Protr. fr. 8 Ross = fr. 74.1 Gigon); Cael.
270b 16–24;
Mete. 339b 25–30; Met. 1074b 10–13; Pol. 1269a 5f., 1329b 25–33;
Theophr. fr. 184 FHSG; Dicaearch. fr. 24. Cf. oÿ gàr mónon pólei~ te kaì Éqnh,
fhsín, @rcà~ kaì télh lambánousin, !~ eı~ pantel4 l2qhn ëkpese$n, @llà
kaì dóxai kaì técnai kaì ëpist4mai toñto páscousin (Philop. In Arist. Mete.,
17.26f.). See Festugière.
 Révélation, 219f.; Palmer, op. cit., 192ff., 196 n. 26.

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5. Teleological progressivism
213
following words: “Since we have to examine the beginnings of arts and sci-
ences in the course of the present period …”.
226
Uncertain as we are whether
these words go back to Eudemus himself, the idea formulated here is quite ap-
propriate for an introduction to the
History of Geometry. In his Physics, Eude-
mus criticized the Pythagorean idea of recurrence of all phenomena and events
in exactly the same way (@riqmŒ, fr. 88), but this is obviously not what the Ar-
istotelian theory implies. Defending this theory, Theophrastus stated that the
discoverers of sciences had lived about a thousand years earlier (fr. 184.145f.
FHSG), which brings us back to the period immediately preceding the Trojan
War, the period with which the Greeks used to start the history of their cul-
ture.
227
There is no reason to suppose that Eudemus rejected the idea of the cyc-
lical development of sciences, especially since in all other cases the coinciding
or at least the proximity of the basic historical notions of the teacher and the
student are obvious.
Hence, it is Aristotle’s historico-philosophical notions of the development
of humankind in general and of arts and sciences in particular that formed the
conceptual basis of the
History of Geometry. That is what distinguished Eude-
mus’ history from the ordinary histories that, according to Aristotle, describe a
great number of events coinciding in time but having no connection with each
other (
Poet. 1459a 16–29).
228
Unlike them, Eudemus’ îstoría contains, in
compliance with Aristotle’s requirements, both @rc2 and télo~, and possesses
an intrinsic unity as a result. The events of this history, i.e., the discoveries of
Greek mathematicians, were connected by causal relationship, which Eudemus
never failed to emphasize, and demonstrated, in total, the general regularities in
the progressive growth of knowledge: from the simple to the complex, from the