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

History of geometry. 1) It was characteristic of Eudemus’ style
to compare the results of several geometers who worked on the same prob-
lem.
47
2) The expression ëxhúrhken prõto~ is also typical for him. 3) Eude-
mus took care to specify whether a strict mathematical proof was given or
not.
48
4) In his
Physics, Eudemus mentions Democritus (fr. 54a–b); in one
place he even addresses him in the vocative (fr. 75). 5) Eratosthenes, to whom
the
Method was addressed, certainly used Eudemus’ writings, which reinforces
the possibility that Archimedes too was acquainted with the
History of Ge-
ometry. If my assertion is right, we can add Democritus to the list of the math-
ematicians named by Eudemus. An absence of his name from Proclus’
Cata-
logue, which appeared rather strange to many experts,
49
could be due to the
Neoplatonic editing of the
History of Geometry, which entailed considerable
reduction of this text.
45
Cat. 7b 27f., APo 69a 30f., 75b 37f., SE 171b 12f., b 34f.; Phys. 185a 14f.
46
II, 430.1f. = fr. 61c Lasserre. Cf. 68 B 155
DK.
47
Fr. 139–140, 146;
Schol. in Eucl. 654.3; Papp. Comm., 63; on the history of propor-
tions, see above, 173ff.
48
Cf. his remarks on Thales’ discoveries: fr. 135; Procl.
In Eucl. 157.10f., 250.20f.;
Heath.
History 1, 130f.
49
Tannery, P. Sur les fragments d’Eudème de Rhodes relatifs á l’histoire des mathéma-
tiques,
Mémoires I, 172; van Pesch, op. cit., 82; Heath. Elements 1, 36; van der
Waerden.
EW, 150.

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Chapter 5: The history of geometry
178
The wish to attribute to Eudemus the mention of all the significant math-
ematicians before Euclid is further justified by the fact that the other sources do
not tell us of any geometer of that period who do not appear in Eudemus, except
for Hippasus and Democritus.
50
Some of them, e.g., Mamercus, Neoclides,
Leon, Theudius, Athenaeus, and Hermotimus, are known only from Eudemus.
This seems to be a sufficient reason to attempt to connect with his
History of
Geometry even those names that, for various reasons, are omitted from the
Catalogue (if, indeed, we have independent and reliable evidence on them).
On the other hand, these very facts prompt us to examine the chronology of
the geometers
not mentioned by Eudemus. In Proclus we find several refer-
ences to a certain Amphinomus, taken from Geminus.
51
In one case Geminus
associates Amphinomus with Speusippus, opposing them to the mathema-
ticians of Menaechmus’ school (
In Eucl., 77.16f.); in the other, in contrast, he
writes about the mathematicians from the circle of Menaechmus and Amphi-
nomus (254.3f.). In all the references to Amphinomus, what is in question is
not specific mathematical discoveries, but methodological debates and prob-
lems of terminology.
52
Thus, Eudemus might have had good reasons to omit
Amphinomus in the
History of Geometry. After all, Speusippus and Xeno-
crates do not appear in this book either. There is, however, another possibility:
perhaps Amphinomus worked after Eudemus had finished his book. This
would make him a younger contemporary of Menaechmus, whose generation
is the last to appear in Eudemus. According to Geminus, Amphinomus held the
view that mathematics does not investigate the causes and that the originator of
this view was Aristotle (
In Eucl., 201.11). This seems to imply that Amphino-
mus lived after Aristotle. To be sure, Geminus (or his source) was not inter-
ested in chronology and could associate persons according to the similarity of
their views, regardless of when they lived. The total silence of the classical
sources on Amphinomus seems, rather, to indicate that he lived in the Hellen-
istic period.
53
One more reference in Proclus, likewise taken from Geminus, concerns a
certain Zenodotus, “who belonged to the succession of Oenopides, although he
was a pupil of Andron” (80.15f.). The mathematicians Zenodotus and Andron
50
Aristotle mentions several times Bryson’s attempt to square the circle (