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

Catalogue, and of Porphyry in the second one. Yet this
picture is far from being correct: both introductions to Proclus’ commentary
contain material from both Geminus and Porphyry.
85
What makes Porphyry the
most preferable candidate?
1) In his
Commentary, Proclus refers five times to Porphyry’s work
86
that
was, in all probability, a commentary to Euclid’s book I.
87
In any case, the last
of Proclus’ quotations covers five pages and could have been taken only from a
special work on the
Elements.
88
Such a commentary, written by the Neoplaton-
a sufficient proof that the
Catalogue is preceded and followed by Geminus’ material,
Tannery does not bring any specific arguments in favor of his authorship.
81
On Neoplatonic influence on Pappus, see Mansfeld.
Prolegomena, 99ff.
82
Papp.
Coll. III, 86.19f.; V, 352.10f. Both times he is named ô qeiótato~ Plátwn.
83
On Pappus’ attitude toward philosophers, see Cuomo, S.
Pappus of Alexandria and
the mathematics of late Antiquity, Cambridge 2000.
84
Tannery. Eudème, 171f.
85
Proclus refers to Porphyry’s Súmmikta zht2mata in the same second introduction,
where the
Catalogue is located (In Eucl., 56.24). The direct references, however, do
not give an adequate picture. In the first introduction, Proclus borrows extensively
from Iamblichus, whose name never occurs in the entire
Commentary. See Mueller,
I. Iamblichus and Proclus’ Euclid commentary,
Hermes 115 (1987) 334–348.
86
255.12–14, 297.1–298.3, 315.11–316.13, 323.5–326.5, 347.20–352.14 = fr. 482–486
Smith.
87
Tannery. Eudème, 170f.; van Pesch,
op. cit., 127f.; Heath. History 2, 529; idem. El-
ements 1, 24; Mueller, I. Mathematics and philosophy in Proclus’ commentary on
book I of Euclid’s Elements,
Proclus, 311f. Mansfeld’s suggestion (Prolegomena,
24) that this work was a part of Súmmikta zht2mata is not convincing. According
to Porphyry’s biographer Eunapius, he studied all branches of knowledge, including
arithmetic, geometry, and music (
Vit. Soph., p. 457 Wright).
88
Porphyry’s
Elements are mentioned in Arabic sources (422 T Smith), according to
which they had been translated into Syriac and consisted of one book (I am grateful

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3. The
Catalogue of geometers: from Eudemus to Proclus
187
ist Porphyry, could explain both the Platonism of the second part of the
Cata-
logue and its interest in the predecessors of Euclid. Characteristically enough, it
is in the passages devoted to the two figures of particular importance to Por-
phyry – Pythagoras and Plato – that his influence is the most easily traced.
2) Proclus twice refers to Eudemus immediately after Porphyry, the first time in
the space of one page (297.4–298.10 and 299.3, on prop. XIV and XV), and the
second time in the very same line (352.14, on prop. XXVI). This reinforces the
probability that Porphyry’s commentary included references to Eudemus’ book
(in both cases theorems attributed to Thales are in question).
89
3) Porphyry was the author of a commentary on Ptolemy’s
Harmonics con-
taining the only extant fragment from Eudemus’
History of Arithmetic (fr. 142).
4) The passage from the
Catalogue relating to Pythagoras (65.15f.) contains
Neoplatonic terms and partly coincides with the passage from the work by Por-
phyry’s student Iamblichus (
De comm. math. sc., 70.1f.). This work makes a
brief mention of Theodorus and Hippocrates (77.24f.), which is missing in the
parallel passage of his biography of Pythagoras (
VP 89). This remark is very
similar to the place in the
Catalogue where both mathematicians are also men-
tioned in one sentence (66.4f.). It looks as though Iamblichus used the same
source as Proclus,
90
i.e., Porphyry. The same source must be the origin of Iam-
blichus’ information on the development of the theory of means from Pythago-
ras to Eratosthenes.
91
5) Porphyry wrote a history of philosophy that starts from its Oriental pre-
cursors, moves up to Thales and other Presocratics, and ends with Plato, i.e., it
embraces practically the same period as the
Catalogue.
92
Porphyry’s attitude
toward Plato’s system as the consummation of the whole of earlier philosophy
to Maroun Aouad for his assistance on this point). The book could hardly have been
a commentary on Euclid.
89
This does not necessarily mean (
pace Tannery. Eudème, 170f.) that in these two
cases Proclus used Eudemus through Porphyry. It is equally possible that Porphyry’s
references prompted Proclus to look in Eudemus’ book. Simplicius also used Eude-
mus’
History of Geometry and Physics both directly and indirectly, through Alex-
ander of Aphrodisias’ commentary on Aristotle’s
Physics (e.g., fr. 43, 82b, 140). See
Knorr.
AT, 29ff.; Sharples, R.W. Eudemus’ Physics: Change, place and time, Eude-
mus of Rhodes, 114f.
90
Björnbo, A. A. Hippokrates von Chios,
RE 8 (1913) 1782; Burkert. L & S, 458 n. 59.
We find in this remark two ‘progressive’ terms, ëpididónai and proagage$n, so
characteristic of the
Catalogue. See below, 212 n. 222.
91
See above, 173f.
92
filósofo~ îstoría ën biblíoi~ dV = fr. 193–224 Smith. Apart from the fragments,
only one part of book I is preserved, containing the
Life of Pythagoras. The Cata-
logue shares with the Life of Pythagoras the idea that geometry comes from Egypt
and arithmetic from Phoenicia (
In Eucl., 65.3f.; Porph. VP 6), but this can be found
already in Plato (
Leg. 747a–c); cf. Strab. 16,2.24, 17,1.3. See also Panchenko, D.
˙Omoio~ and ômoióth~ in Thales and Anaximander, Hyperboreus 1.1 (1994) 40
n. 36.

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Chapter 5: The history of geometry
188
is very close to the ‘Platocentrism’ of the second part of the
Catalogue, where
the construction of the five Platonic bodies is called the final goal (télo~) of the
whole
Elements (68.18f.). This provides additional support to the hypothesis
that Porphyry was the principal intermediary between Eudemus and Proclus.
93
Thus, we find in Porphyry exactly what is missing in Geminus that would
have enabled us to consider him the compiler of the
Catalogue: a predisposition
to Platonism, obvious knowledge of Eudemus’ works, interest in the intellec-
tual history of the classical period in general and in Euclid’s predecessors in