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

On Velocities developed Archytas’ research,
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conceiving
every planet as fixed to a rotating sphere, whose axis, in turn, is linked with an-
other sphere, etc. The curve resulting from the rotation of these spheres can be
regarded as the intersection of the inner sphere with the cylinder. This construc-
tion is very similar to the one that helped Archytas solve the problem of dupli-
cating the cube. Here the necessary curve is made by the intersection of the
three rotating bodies – the cone, the torus, and the half-cylinder (47 A 14).
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Thus, the Pythagorean tradition contained all the mathematical elements
necessary for the development of Eudoxus’ theory. Eudoxus’ book
On Velo-
cities was most likely written during the last period of his activity, when he was
living in Cnidus,
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and it is only reasonable to suppose that Plato knew nothing
about it. Theoretically, he
 might have learned about the basics of Eudoxus’ as-
tronomical system in 350 when the
 Timaeus was already written and the Laws
had not yet been finished. However, no one has succeeded in finding in the
Laws convincing evidence of his knowledge of the system of homocentric
spheres, so Eudoxus’ influence on Plato remains as unproved
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as Plato’s in-
fluence on Eudoxus.
Let us return to the point where Diogenes Laertius talks about Eudoxus’ sec-
ond visit to Athens from Cyzicus, where he had his own school with a large
it must have been existed already by the mid-fourth century. Thus, Archytas who is
known to work on mechanics (47 A 10a; Athen. Mechan.
De machinis, 5.1; D. L.
VIII, 83), is the best possible candidate for its founder. See also Cambiano, G. Archi-
mede meccanico e la meccanica di Archita,
Elenchos 19 (1998) 291–324, and below,
129 n. 45.
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Krafft.
Mechanik, 145f.; Neugebauer. HAMA, 678. Not accidentally, Archytas’ defi-
nition of astronomy begins with perì tã~ tõn Ástrwn tacutãto~ (cf. Pl. Phaed.
98a;
Gorg. 451c), and he attributes to his Pythagorean predecessors a ‘clear knowl-
edge’ of this subject (47 B 1).
85
Heath.
History 1, 333f.; Knorr. AT, 54f. Riddell, R. C. Eudoxian mathematics and
Eudoxian spheres,
AHES 20 (1979) 1–19.
86
Lasserre.
Eudoxos, 142, 193.
87
Ibid., 181f.; Tarán, L.
Academica: Plato, Philip of Opus and the Pseudo-Platonic
Epinomis, Philadelphia 1975, 107. Mittelstraß, op. cit., 133ff., although a keen ad-
herent of the idea of such an influence (he relied on the old chronology for Eudoxus),
nevertheless admitted that Plato did not change his former astronomical system, as
proposed in the
Republic and Timaeus, and that only by some occasional hints in the
Laws can we conclude that Plato was acquainted with Eudoxus’ theory. The fact re-
mains, however, that the most important elements of Eudoxus’ theory are missing
from the
Laws, primarily the idea that all planets are attached to spheres by which
they rotate. Is it possible to be under the influence of Eudoxus’ theory and not men-
tion a sphere at all? Besides, there are no traces of Eudoxus’ theory even in the
Epi-
nomis Philip wrote after Plato’s death (Tarán. Academica, 110; Knorr. Plato and
Eudoxus, 323). Cf. Gregory, A. Eudoxus, Callippus and the astronomy of the
Ti-
maeus, Ancient approaches to Plato’s Timaeus, ed. by R.W. Sharples, A. Sheppard,
London 2003, 5–28.

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2. The
Catalogue of geometers about mathematicians of Plato’s time
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number of pupils (VIII, 87). I believe it was this group of Eudoxus’ students
that formed the main body of ‘Academic mathematicians’ of the younger gen-
eration.
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After Eudoxus, the