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

On Pythagorean Numbers
(fr. 28 Tarán), the material he was interested in was very far from the real prob-
lems of contemporary mathematics and his approach could in no way be de-
scribed as professional.
106
Speusippus, Xenocrates, and Hermodorus are no ex-
ceptions. Strictly speaking, none of Plato’s immediate students achieved any-
thing remarkable in mathematics. If we look at the sciences as a whole, then it
is only Aristotle who achieves any real success; and significantly, that success
was primarily in biology, i.e., in an area that was
not studied at the Academy.
Philip was known as an astronomer; the
Suda attributes to him a number of
mathematical and astronomical writings, which we know practically only by
101
For lists of the Academics, see Lasserre.
Léodamas, I T 2–9; Gaiser. Academica,
181f.; Dorandi.
Filodemo, 135. The only exception is Amyclas, who is discussed
above.
102
Although Eudemus was the major authority on the exact sciences, Dicaearchus on
geography, and Aristoxenus on musical theory, no one has yet come to the con-
clusion that Aristotle himself taught these sciences at the Lyceum.
103
Cherniss, H.
The riddle of the early Academy, Berkeley 1945, 60ff.
104
On the Pythagorean origin of the quadrivium, see above, 63.
105
See above, 89 f. n. 37–41.
106
See Zhmud. Philolaus, 263ff. Speusippus, in particular, believed that, in a sense, an
equilateral triangle has only one angle (fr. 28 Tarán).

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3. Mathematics at the Academy
103
their titles.
107
It is hardly possible to prove whether Philip really was the author
of all these books; Neugebauer expressed serious doubts about the authenticity
of the majority of astronomical treatises.
108
Only in some cases have Tarán and
Lasserre succeeded in linking the flimsy surviving evidence with titles known
only from the
Suda.
109
Paradoxically, most of the astronomical material con-
nected with Philip’s name relates to the so-called parapegma, i.e., to observa-
tional astronomy and meteorology, which his teacher, Plato, held in very low
opinion (
Res. 529a–530c) and could hardly have encouraged Philip to study
them. What is significant, however, is that we do not know about any dis-
coveries Philip personally made in astronomy.
110
Specifically, in the
Epinomis,
written by Philip, there are no astronomical ideas that cannot be found in the
Ti-
maeus or the Republic,
111
and there is nothing astronomically original at all. In
short, if Philip really was converted by Plato to study the exact sciences and
worked under the latter’s guidance, then the results of this work seem rather
poor.
Tradition connects two interesting astronomical hypotheses with another
Academic, Heraclides Ponticus, who later collaborated with Aristotle (fr. 104–
110). One of these hypotheses – that Venus and Mercury rotate around the sun,
which in turn rotates around the earth – is based on an incorrect interpretation
of the sources, as Evans and Neugebauer showed.
112
The other hypothesis – that
the Earth rotates on its own axis – has nothing in common with Platonic astron-
omy.
113
In all probability, Heraclides borrowed it from the Pythagorean Ec-
107
IV, 733. 24–34 Adler = 20 T 1 Lasserre. Mathematics: ^Ariqmhtiká, Mesóthte~,
Perì polugønwn @riqmõn; astronomy: Perì planhtõn, Perì megéqou~ 1líou
kaì sel2nh~ kaì g4~ aV, Perì ëkleíyew~ sel2nh~, Perì t4~ @postásew~ 1líou
kaì sel2nh~; meteorology: Perì @strapõn, Perì @némwn; optics: ’Optikõn bV,
’Enoptikõn bV.
108
Neugebauer.