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

Léodamas, 552f.), who never-
theless saw the ultimate source in Philip’s book
On Plato (cf. above, 89f.).
206
I shall treat this subject in a forthcoming paper “On two Menaechmi”. As a prelimi-
nary, it is worth pointing out that we find in Geminus quite a few other ‘doubles’.
1) The Theodorus attested by Geminus (Procl.
In Eucl., 118.7) is definitely not
Theodorus of Cyrene, but a Hellenistic mathematician; 2) the Oenopides to whose
‘succession’ Zenodotus belonged (ibid., 85.15f.) is not Oenopides of Chios, but
most likely a Stoic philosopher (see above, 179 n. 54, and below, 260 n. 134); 3) the
Hippias who found the quadratrix (ibid., 272.8f., 356.6f.) is not the famous Sophist
Hippias, but a Hellenistic mathematician (Knorr.
AT, 82f.).
207
See above, 98f.
208
Translation according to Grynaeus’ conjecture merikõn instead of the manuscript
ôrikõn.
209
Knorr.
AT, 142 n. 30, 371 n. 25.

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Chapter 5: The history of geometry
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5. Teleological progressivism
Generally, Eudemus paid attention not only to the results and the form of their
exposition, but also to the method of the proof and its correspondence to what
was customary in his own time. In the
Catalogue, the improvement of geo-
metrical methods is discussed in much detail. Thales’ method is characterized
as in some cases more empirical, and in others more general, i.e., scientific,
whereas Pythagoras is credited with transforming geometry into an abstract
science and including it in the canon of education of a free man. Owing to the
efforts of Leodamas, Archytas, and Theaetetus, geometry became “more scien-
tific and systematic”, Leon discovered the method of diorism, and Eudoxus
used the method of analysis, while Amyclas, Menaechmus, and Dinostratus
“made the whole of geometry even more perfect” (Éti telewtéran ëpoíhsan
t3n Ôlhn gewmetrían, 67.11). It is significant that the Catalogue starts with
the words about progressing “from the imperfect to the perfect” (@pò toñ
@teloñ~ eı~ tò téleion, 64.25) and ends with the notice that “those who com-
piled histories of geometry bring the perfecting (teleíwsi~) of geometry up to
this point” (68.4f.). Of course, no author who lived after Eudemus could have
the idea of the ‘completion’ of geometry at the end of the fourth century, i.e.,
before Euclid, Archimedes, and Apollonius. This confirms again that the begin-
ning of the
Catalogue, as well, goes back to Eudemus.
I have suggested above that, in his histories of the exact sciences, Eudemus
employed the professional approach – of course, to the extent that this was
possible for a Peripatetic philosopher. This does not contradict the fact that
Eudemus’ views on development in general, and on the development of science
in particular, rely on the Aristotelian doctrine that we call teleological progres-
sivism. According to this doctrine, everything in nature, society, and culture de-
velops from a primitive state to a perfect one,
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and for many things this state
of perfection was thought to have already been achieved or almost achieved.
Tragedy, for example, had already attained its perfection, society had found its
best and final state in the
polis, and philosophy, whose early ideas were as im-
mature as childish speech, would be soon completed.
211
Against this back-
ground, Eudemus’ idea that geometry had achieved or almost achieved perfec-
tion seems quite natural.
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To be sure, such progressivism (not necessarily a
teleological one) was characteristic not only of Aristotle, but of many other
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“There is evolution towards a state of excellence all over in the design of nature; the
goal is the end,