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

particular. It seems that we owe to Porphyry the present form of the
Catalogue,
i.e., a very abridged and tendentiously revised version of the
History of Ge-
ometry. Following Eudemus’ chronological exposition, he compiled a short
outline of geometry from Thales to the immediate forerunners of Euclid and
used it as a historical introduction to his commentary on the
Elements. It is con-
spicuous that, as soon as Porphyry leaves Eudemus’ text and turns to Euclid, he
begins to lack reliable historical data. The absence of any followers of Eude-
mus’ in the Hellenistic period made it very problematic for Porphyry to figure
out even a rough date for Euclid: he had to rely on casual remarks of Archi-
medes and Eratosthenes and on historical anecdotes (68.10). What a contrast
with Eudemus’ chronologies, which are accurate almost to a decade!
The last circumstance proves that Eratosthenes’
Platonicus was historical
only to the degree that it relied on Eudemus’ work. The chosen genre did not
allow Eratosthenes to continue the
History of Geometry; nor is it known
whether he wanted to continue it. The fragment concerning the history of the
discovery of means, which Iamblichus probably borrowed from Porphyry,
94
can scarcely derive from Eratosthenes. Although Eratosthenes found the last
four means and, therefore, must have known of the first six, there is no evi-
dence that he described the history of their discovery in the
Platonicus or in
other works.
95
In this case, Porphyry must have relied directly on Eudemus’
book.
It would be a mistake, however, to think that the final version of the
Cata-
logue is due to Porphyry. Specifically, the passage that ascribes to Pythagoras
the discovery of irrationality and of the five regular solids (65.15f.) can prob-
ably be attributed to Proclus. At any rate, we do not find this information in the
parallel passage in Iamblichus (
De comm. math. sc., 70.1f.) nor in his other
works on the Pythagoreans. Meanwhile, Pan-Pythagoreanism is much more
characteristic of Iamblichus than of Proclus, and if he had known this tradition,
93
Porphyry could have derived additional information from the same work as Philo-
demus (3.1), which would explain certain similarities between the
Catalogue and
column Y. It is noteworthy that Porphyry knew Hermodorus’ book
On Plato: he
cited a long passage from it, which he had found in Dercyllides (fr. 7–8 Isnardi Pa-
rente =
FGrHist 1008 F 2a–b = fr. 146 Smith).
94
Porphyry’s interest in the early theory of means is confirmed by his quotation from
Archytas (
In Ptol. harm., 92 = 47 B 2).
95
See above, 173 n. 28, 174 n. 33.

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3. The
Catalogue of geometers: from Eudemus to Proclus
189
he would have certainly mentioned it.
96
While the version referring the five
regular solids to Pythagoras was known before Proclus,
97
the idea that Pytha-
goras was the author of the theory of irrationals (tõn @lógwn pragmateía) is
not attested in any other ancient source. In this connection it has been long pro-
posed to change the reading tõn @lógwn pragmateía into tõn @nà lógwn
pragmateía, i.e., into the theory of proportions.
98
To judge from Iamblichus’
passages that connect Pythagoras with the discovery of proportions,
99
Porphyry
and, correspondingly, Eudemus wrote about tõn @nà lógwn pragmateía, not
tõn @lógwn pragmateía. This is confirmed both by Nicomachus and by the
obvious fact that Pythagoras did, indeed, study proportions.
100
What made Pro-
clus change the ‘theory of proportions’ into the ‘theory of irrationals’?
I suppose he did it for the same reason that made him remain silent about
the Pythagorean Hippasus, one of the important mathematicians of the early
fifth century. The late tradition connects with Hippasus two significant dis-
coveries: the construction of the dodecahedron inscribed in the sphere and the
discovery of irrationals. One part of the evidence (Clement of Alexandria,
Iamblichus) mentions Hippasus in this connection, the other speaks about
some anonymous Pythagorean.
101
At least two of the last group’s testimonies
concerning the discovery of irrationality are based on Eudemus: Pappus’ com-
mentary on book X of Euclid and the scholia to the same book.
102
To them we
should add the first scholium to book XIII that relates to the Pythagoreans the
discovery of the first three regular solids, including the dodecahedron. Does it
follow from this evidence that Eudemus referred to Pythagoreans in general,
without mentioning any names, while the late tradition filled in Hippasus’
name? If so, we are not in a position to determine who in fact was the author of
these discoveries. Besides, it means that Hippasus totally disappears from the
history of mathematics, since no other discoveries are ascribed to him. In other
96
This means that Porphyry most probably shared Eudemus’ view on the discovery of
the regular solids (