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

RE Suppl. 7 (1940) 371–372; Tarán, L. Proclus on the Old
Academy,
Proclus. – Lecteur et interprète des Anciens, ed. by J. Pépin, H.D. Saffrey,
Paris 1987, 273. Lasserre himself admitted this (
Léodamas, 24, 445).
50
D. L. III, 24 = Favor. fr. 25 Mensching. Cf. “Plato, it is said, taught this method to
Leodamas, who also is reported to have made many discoveries in geometry by
means of it.” (Procl.
In Eucl., 211.18f.). Whereas Favorinus calls Plato the dis-
coverer of analysis (prõto~ eıshg2sato), Proclus only says that he passed it
(paradédwke) to Leodamas. See Mensching, E. Favorinus von Arelate, Berlin
1963, 103f. On probable reasons for confusions in Favorinus and Proclus, see Heath.
History 1, 291; Cherniss. Plato as mathematician, 418f.
51
So in Philodemus (col.VI) and in Theon of Smyrna, whose list is preserved in Arabic
translation (Gaiser.
Academica, 439f., 444).
52
Mathieu, B. Archytas de Tarent pythagoricien et ami de Platon,
BAGB (1987)
239–255; Zhmud.
Wissenschaft, 73.

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2. The
Catalogue of geometers about mathematicians of Plato’s time
93
which is one of the forms of analysis, Leodamas must have been 45–55 years
old. If he was at least five years older than Archytas (which the order in which
the names in the
 Catalogue are arranged seems to suggest) then, accordingly,
he must have been 50–60. Is this not too late to study analysis, even under such
a teacher as Plato?
53
The improbability of such an apprenticeship is increased by the following.
1) One should hardly attach any importance to Favorinus’ statement about
analysis, which is repeated by Proclus, since elsewhere, referring to an anony-
mous source (which might have been Eudemus), Proclus attributes the dis-
covery of the method of reduction (@pagwg2), i.e., one of the earliest forms of
analysis, to Hippocrates of Chios.
54
2) Plato himself, describing the method ëx
ûpoqésew~, says that it was already in use by geometers (rai
polláki~
skopoñntai, Men. 86e); the method he describes is identical to
the method of reduction, which Hippocrates used in trying to solve the problem
of the duplication the cube.
55
3) To study analysis on the basis of the
Meno (or
the whole of Plato’s works) would not only be embarrassing for the not very
young Leodamas, but utterly impossible: despite endless interpretations of this
passage, a clear understanding of what Plato had in mind has not been achieved
to this day.
56
Despite the mention of Archytas in the Academic legend about the dupli-
cation of the cube, there is no information whatsoever about whether he ever
went to Athens.
57
Sources talk about his friendship with Plato, who visited him
several times in Magna Graecia. But he was never Plato’s pupil, rather vice
versa: Plato learned a lot from him. Archytas’ influence on Plato has been re-
peatedly noted,
58
but no one has yet succeeded in tracing the opposite influence.
53
Relying on the
Catalogue, Mensching, op. cit., 104f., suggested that Leodamas was
born about 435/30 and considered Favorinus’ statement “more than implausible”.
Lasserre eventually comes to the conclusion that it was Leodamas who influenced
Plato, rather than vice versa (
Léodamas, 457f.), but it is scarcely possible to verify
this assertion either.
54
In Eucl., 212.24–213.11; see below, 175, 203.
55
Knorr.
AT, 71f.
56
The old literature is given in Heiberg, I. L. Jahresberichte,