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

Mathemat-
ics in Aristotle, Oxford 1949, 1f.). On Aristotle and Eudoxus’ astronomy, see Lloyd,
G. E. R. Metaphysics L 8, Aristotle’s Metaphysics Lambda, ed. by M. Frede, D.
Charles, Oxford 2000, 245–273.
8
Cat. 10a 11–24, Phys. 188a 25, Met. 1020a 35–b 8; Heath, T. L. The thirteen books
of Euclid’s Elements, Vol. 1, Oxford 1927, 177f.; Wehrli, comm. ad loc.
9
Cf. Arist.
Top. 101a 5–11, on the premises peculiar to geometry and her ‘sister

---

2.
The History of Geometry: on a quest for new evidence
169
selves. It is only natural, therefore, that a different science (êtéra filosofía)
deals with them, namely Aristotelian first philosophy.
10
Eudemus’ position is
thus very close to that of Plato and Aristotle, but in contrast to Plato, who re-
proaches the mathematicians for lack of interest in proving their principles
(
Resp. 510c–e), Eudemus seems to consider the division of labor between phil-
osophers and mathematicians as quite natural. Indeed, the mathematicians do
not want to prove their principles, not because they fail to think things through
or are lazy, but rather because such a position corresponds to the general rule
that no scientific discipline can prove its own principles. Proceeding from such
an understanding of the division of labor, one can suppose that when dealing
with subjects that are in the jurisdiction of mathematicians, Eudemus followed
their norms and criteria. Indeed, the mathematics found in his works does not
constitute any special type of philosophical mathematics; it is exactly what the
contemporary scientific community understood by this subject. Thus, Eude-
mus’ history of the exact sciences combines the Peripatetic conceptual frame-
work with the professional approach to the material of geometry, arithmetic,
and astronomy. It is this combination that makes him not only a reliable witness
to early Greek mathematics and (mathematical) astronomy, but also their first
true historian.
2.
The History of Geometry: on a quest for new evidence
The fragments from the
History of Geometry where Eudemus’ name is men-
tioned are not numerous. Two of them concern the theorems of Thales
(fr. 134–135), two the discoveries of Pythagoreans (fr. 136–137), one concerns
Oenopides (fr. 138), another two Antiphon’s squaring the circle and Hippo-
crates’ squaring the lunes (fr. 139–140). Yet another fragment deals with Archy-
tas’ solution to the problem of duplicating of the cube (fr. 141), and the last one
with Theaetetus’ theory of irrationals (fr. 141.I). The origin of these fragments
is rather accidental, and even taken together they are far from giving us an ad-
equate idea of what the
History of Geometry originally was like. The five frag-
ments from Proclus (fr. 134–138) deal with the theorems from Euclid’s book I,
on which Proclus comments. The fragment on the theory of irrationals is pre-
served in the Arabic version of Pappus’ commentary to Euclid’s book X
(fr. 140.I). Eutocius, commenting Archimedes’ book
On Measuring the Circle,
refers to attempts to square the circle (fr. 139); in another commentary he gives
(among many others) Archytas’ solution of the problem of duplicating the cube
(fr. 141). Finally, Simplicius, in his commentary on the passage in Aristotle’s
Physics that touches upon the quadrature of lunes, gives a long quotation from
sciences’. To reason correctly here, one has to follow the accepted definitions and
rules of construction.
10
Cf. Arist.
Met. 995b 4f., 996b 26f., 1005a 19f.

---

Chapter 5: The history of geometry
170
Eudemus on this matter (fr. 140).
11
Thus, five of the nine fragments concern the-
orems from Euclid’s book I, one fragment concerns theorems from book X, and
the rest deal with problems absent from the