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

Schol. In Eucl., 654.3). Cf. below, n. 97.
97
See e.g. Aët. II,6.5 = 44 A 15. For other evidence, see Sachs, E.
Die fünf platonischen
Körper, Berlin 1917, 8ff. The five regular solids are mentioned in Speusippus’ On
Pythagorean Numbers (fr. 28 Tarán), which was probably the original source of this
version (Burkert.
L & S, 71; cf. Tarán. Speusippus, 256f.). Later it can be found in do-
xography (Sachs,
op. cit., 65f.). If Achilles’ version (Dox., 334 not.), which is par-
allel to Aëtius, goes back to Posidonius (Sachs,
op. cit., 10, 51f.; Burkert. L & S, 70
n. 113), then the latter, unlike Eudemus, ascribed all the five regular solids to the Py-
thagoreans.
98
DK I, 98.23; Heath. History 1, 84f. This reading is attested only in one manuscript of
Proclus, all the others have tõn @lógwn pragmateía: Stamatis, E. S. Die Entde-
ckung der Inkommensurabilität durch Pythagoras,
Platon 29 (1977) 188. On this,
see Zhmud.
Wissenschaft, 158f.
99
See above, 173f.
100
See above, 173f., 174 n. 31.
101
For the evidence and its analysis, see Zhmud.
Wissenschaft, 170f.
102
Papp.
Comm., 63f.; Schol. in Eucl., 415.7, 416.13, 417.12f. See above, 172 n. 24.

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Chapter 5: The history of geometry
190
words, if Eudemus and his contemporaries did not know the mathematician
Hippasus, he did not exist.
Meanwhile, Aristotle and Theophrastus knew Hippasus as a philosopher;
103
Aristoxenus referred to his acoustical experiment based on mathematical pro-
portions;
104
and Iamblichus, relying on the tradition that most likely derives
from Eudemus, likewise connected his name with the first three proportions.
105
Thus, the Pythagorean Hippasus who took up philosophy, harmonics, and
mathematics did not merely exist but was known in the late fourth century. On
the other hand, Eudemus mentioned the discovery of the irrationals and the
construction of the dodecahedron by the Pythagoreans. I therefore believe that
the late tradition assigning these discoveries to Hippasus contains a historical
core and might go back to Eudemus. But if Eudemus named Hippasus, then
why is his name missing from the
Catalogue and not mentioned in Proclus at
all? There is at least one important reason for such an omission. Proclus at-
tributed to Pythagoras the very discoveries that the other authors associate with
Hippasus: the theory of irrationals and the construction of all five regular
solids, including the dodecahedron. Therefore, there was no place left in the
Catalogue for the mathematician Hippasus. One might surmise that Proclus
chose to trust the tradition that persistently connected Hippasus with plagiarism
and with divulging the Pythagorean secrets
106
and to sacrifice this figure by ‘re-
turning’ his discoveries to Pythagoras.
The omission of Hippasus’ name in Pappus, who referred to an anonymous
Pythagorean discoverer of the irrationals,
107
can be explained in a simpler way.
Pappus was not particularly concerned with naming the authors of the math-
ematical discoveries he presented in his work. While Nicomachus says that the
first three means “came down to Plato and Aristotle from Pythagoras”, Pappus,
quoting him, omits all the names.
108
This is not the only example: in book IV
of the
Collectio, Pappus presents three methods of angle trisection and two
methods of dividing an angle in a given proportion, without any attribution.
109
103
Arist.