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

Catalogue, to a time span smaller than one generation, i.e.,
10–15 years. We can, accordingly, date Oenopides’ birth at ca. 490–85 and his
floruit in the mid-fifth century.
154
Eudemus attributes to Oenopides two ele-
mentary geometrical constructions that later entered Euclid’s book I,
155
as well
as the last proposition of book IV concerning a regular fifteen-angled figure in-
scribed in the circle.
156
According to Eudemus, propositions I, 12 and IV, 16
were important not only for geometry, but also for mathematical astronomy; in
the first case, moreover, he refers to the opinion of Oenopides himself.
157
152
Neuenschwander. VB, 371f.
153
Plutarch says that Anaxagoras, while he was in prison, worked on the problem of
squaring the circle (59 A 38, cf. A 39). This evidence does not seem to come from
Eudemus.
154
The date of Anaxagoras’ birth must have been known to Aristotle (
Met. 984a 11f.)
and served him as a kind of starting point. Following Aristotle, Theophrastus noted
that Empedocles oÿ polù katópin toñ ^Anaxagórou gegonø~ (fr. 227a FHSG).
Here, as in Eudemus, “a little later” implies the difference of 10–15 years. Empe-
docles’ birth is usually dated to 490/85.
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To draw a perpendicular to a given straight line from a point outside it (I, 12); at a
point on a given straight line, to construct a rectilinear angle equal to a given recti-
linear angle (I, 23).
156
Fr. 138; Procl.
In Eucl., 283.7f., 269.8f. This also shows that book IV was written
before the middle of the fifth century.
157
On Oenopides’ mathematical astronomy, see below, 7.5.

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4. Early Greek geometry according to Eudemus
201
Eudemus’ familiarity with Oenopides’ work is further confirmed by the fact
that he points out an archaism in the formulation of I, 12: Oenopides called the
perpendicular katà gnømona, since the gnomon also stands at right angles to
the horizon.
The attention Eudemus pays to problems of terminology, which we already
noted when discussing a theorem of Thales (I, 5), is an additional proof of the
historical character of his work on mathematical sciences. Like a modern his-
torian of mathematics, Eudemus was interested not only in the discovery itself,
but also in details of the proof and its correspondence with demonstration cur-
rent in his own day, in peculiarities of terminology, connections with other
sciences, etc. This aspect of Eudemus’ works, testifying to his conscientious
approach to sources, is one of the guarantees that he avoided introducing arbit-
rary changes into his material unless he had to.
Oenopides was obviously not the first to have drawn a perpendicular to a
line or to have constructed a rectilinear angle. His propositions were conse-
quently regarded as the first attempt at a formal geometrical approach to these
constructions, deliberately limited to the use of compasses and ruler alone.
158
Disputing the latter opinion, Knorr denied the formal geometrical character of
Oenopides’ constructions, believing them to come from Oenopides’ astro-
nomical treatise that considered the construction of astronomical instruments
as well.
159
Knorr is right in maintaining that Oenopides is unlikely to have
written a special treatise on geometry. As an astronomer, he could use a
number of instruments, apart from ruler and compasses. But in cases where he
turned to geometrical constructions important for astronomy, Oenopides fol-
lowed the already existing formal requirements known to him, in particular,
from the Pythagorean compendium.
160
Obviously, Oenopides determined the
angle of the obliquity of the ecliptic empirically. But to give it an accurate geo-
metrical measure, he constructs a regular fifteen-angled figure inscribed in the
circle, in full accordance with the rules for the construction of polygons laid
out in book IV.
161
Another Ionian mathematician, Democritus, was a younger contemporary
of Oenopides, whom Democritus mentioned in one of his works (41 A 3). Like
Oenopides, Democritus was also associated with Pythagorean mathematics:
according to Glaucus of Rhegium, he had Pythagorean teachers (68 A 1.38 =
158
Heath.