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

In Eucl., 65.15f.). The anonymous scholia to book V of the El-
ements twice call Eudoxus the author of this book (280.7f., 282.12f.); here too
Eudemus may be the source.
The last proposition of book IV, on the fifteen-angled figure inscribed in the
circle, deserves special attention. Proclus, relying on the earlier commentaries
on Euclid, notes that the
Elements contains more than a few theorems and prob-
lems useful for astronomy, e.g. problem IV, 16 (269.8f.). The same is said here
about problem I, 12, which belongs to Oenopides: “he thought it useful in as-
tronomy” (283.7f.). Since, as we noted, the latter reference goes back to Eude-
mus, one can suspect that the former remark has the same origin, too. This sup-
position gains probability if we remember that Oenopides was the very astron-
omer who first measured the angle of the obliquity of the ecliptic (41 A 7). Pro-
clus explains that by inscribing the side of the fifteen-angled figure in the circle
we get the angle between the celestial equator and the zodiacal circle, i.e., 24°.
The confirming evidence can be found in a short but regrettably error-ridden
summary from Eudemus’
History of Astronomy: “Oenopides was the first who
found the obliquity of the zodiacal circle”,
20
whereas “the others found that the
angle between the zodiacal circle and the celestial equator is equal to the side of
the fifteen-angled figure, or 24°.” (fr. 145). As K. von Fritz showed long ago,
both statements pertaining to the zodiac originally referred to Oenopides.
21
Therefore, Proclus’ evidence on the astronomical significance of the problem
IV, 16 also goes back to Eudemus, although Proclus mentions neither his, nor
Oenopides’ name.
22
18
Fr. 136. See van Pesch,
op. cit., 79; Heath. Elements I, 36.
19
Schol. in Eucl., 273.3–13, 654.3f. See Burkert. L & S, 450; Neuenschwander. VB,
372f.
20
Diels’ correction, lóxwsi~ instead of manuscript diázwsi~ (Theon. Exp., 198.15 =
41A7), is fully justified by the parallels in Aëtius, Diodorus, and Macrobius (41A7):
they mention lóxwsi~, or oblique circle. Cf. Panchenko, D. Who found the zodiac?,
Antike Naturwissenschaft und ihre Rezeption, Vol. 9 (1999) 33–44.
21
Fritz, K. von. Oenopides,
RE 17 (1937) 2260f. They came to be separated when Oe-
nopides’ name was taken out of context and placed at the beginning of the chro-
nological list of astronomers: Oenopides, Thales, Anaximander, Anaximenes,
others. See also Gundel, H. Zodiakos,
RE 10 A (1972) 490; Waerden, B. L. van der.
Die Pythagoreer: Religiöse Bruderschaft und Schule der Wissenschaft, Zurich 1979,
348f., and below, 7.5.
22
The style of IV, 16 differs from the other propositions of book IV, so it seems to be a

---

Chapter 5: The history of geometry
172
In fr. 141.I from the Arabic translation of Pappus, overlooked in Wehrli’s
first edition, Eudemus speaks about Theaetetus’ contribution to the theory of ir-
rationals. This fragment was added to the second edition, but Wehrli, following
Burkert, does not include in it the preceding note on the Pythagoreans. It is
clear from the text, however, that Eudemus thought that Theaetetus had con-
tinued and developed the already existing theory of irrationals. Hence, the
preceding note (omitted by Wehrli), “This science had its origin in the school of
Pythagoras, but underwent important development at the hands of Theaete-
tus”,
23
perfectly fits in Eudemus’ context.
24
Among the predecessors of
Theaetetus, at least one person should have been mentioned: his Pythagorean
teacher Theodorus, who is named in the