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

In Arch-
im. De sphaer. III, 56.4f.). It seems that Eutocius either was using a distorted
version of Eudoxus’ solution or simply failed to understand it. Leaving this
problem to the historians of mathematics,
195
we merely point out that Euto-
189
In Eucl., 67.2f. = fr. 22 Lasserre. Information on the discovery of proportions found
in Iamblichus (
In Nicom., 100.19–101.9) confirms the evidence of the Catalogue,
adding to it that Eudoxus called the fourth mean ‘subcontrary’. See above, 173ff.
190
4)
Schol. in Eucl., 280.7f., 282.12f. = fr. 32–33 Lasserre; 5) Eutoc. In Archim. De
sphaer., 56.4f., 90.7, 96.18 = fr. 24–25, 29 Lasserre; 6) Archim. Meth., 430.1f. =
fr. 61c Lasserre.
191
Heath.
 History 1, 323; Lasserre. Eudoxos, 162.
192
Met. 1026a 25–27, 1064b 8–9; 1077a 9–10, 1077b 17–18, cf. APr 85a 37; APo 74a
17–25. See Ross,
op. cit., 356f.; Heath. Mathematics, 222f.; Lasserre. Eudoxos,
166f.; Fiedler,
op. cit., 52ff.; Kouremenos, T. Aristotle’s mathematical matter and
Eudoxus’ proportion theory,
WS 109 (1996) 61ff.
193
Bretschneider,
op. cit., 168; Lasserre. Eudoxos, 176f.
194
Tannery.
Géométrie, 76; Heath. History 1, 325.
195
See Tannery, P. Sur les solutions du problème de Délos par Archytas et Eudoxe,
Mémoires scientifiques I, 53–61; Heath. History 1, 249f.; Böker, op. cit., 1207ff.;

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Chapter 5: The history of geometry
208
cius’ immediate source here was not Eudemus, but probably Eratosthenes’
Platonicus.
196
While no evidence has been left of the discoveries of Amyclas of Heraclea,
two of Eudoxus’ students, Menaechmus and Dinostratus, are known for their
research relating to the curves. Menaechmus solved the problem of doubling
the cube by finding two mean proportionals through the intersection of a hyper-
bola with a parabola,
197
while Dinostratus constructed the so-called quadratis-
sa, a curve used to square a circle.
198
It was traditionally thought that Menaech-
mus constructed the hyperbola and parabola by sectioning a cone.
199
Knorr,
however, doubts whether he might have developed even a rudimentary theory
of conic curves, believing that such a theory was hardly conceivable nearly half
a century before Euclid.
200
To this it ought to be objected that Menaechmus,
being a disciple of Eudoxus (born ca. 390), could hardly have been born before
375/70, and consequently is only a generation older than Euclid. Menaechmus’
solution was significantly revised by Eutocius as well as probably by his
source.
201
The latter could have been Eratosthenes, who relied on Eudemus and
considered the history of doubling the cube in detail.
202
By contrast, there is no reason to associate Eudemus with the evidence on
Menaechmus’ theoretical views in mathematics that we find in Geminus.
203
Lasserre.
Eudoxos, 163f.; Riddel, op. cit.; Knorr. AT, 52f.; idem. TS, 77ff. Knorr be-
lieved that the next solution, ascribed by Eutocius to Plato, could belong to Eudoxus.
Cf. Netz, R. Plato’s mathematical construction,
CQ 53 (2003) 500–509.
196
Wolfer,
op. cit., 51, believed that Platonicus did not reach Eutocius, however Euto-
cius did have two other texts of Eratosthenes at his disposal, which makes his fa-
miliarity with
Platonicus rather probable.
197
Eutoc.