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

op. cit. I, 86). Eudemus was not such a popular figure
that a late author would be interested in writing his biography; besides, what would a
biographer have as possible sources? It should be recalled that Archimedes’ bi-
ography, written by his student Heraclides, was first quoted by Eutocius (see below,
294f.). Biographies of Eudemus and Theophrastus are mentioned in the Arabic
sources (Rosenthal, F.
The classical heritage in Islam, Berkeley 1975, 36; cf. 4a
FHSG).
5
Gottschalk. Eudemus, 25ff. – A fragment of Eudemus’
Physics, written on Rhodes,
depicts a typical picture of a teacher lecturing to a group of students (fr. 88).
6
Fr. 143–144. Philodemus’
De pietate seems to have used Eudemus’ History of Theol-
ogy. See also below, 6.1, 8.1.

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Chapter 5: The history of geometry
168
To judge from his works, Eudemus received a good mathematical education
and was very competent in the problems of contemporary mathematics (which
is not always true of Aristotle).
7
This is also manifest in the fact that his histori-
es of the exact sciences are devoted to strictly mathematical problems and
methods, rather than to the philosophical interpretation of mathematics that
was so characteristic of Plato and his students – Speusippus, Xenocrates, and
Philip, as well as Aristotle. Certainly, a professional approach to mathematics
was not the only possibility for Eudemus: in his work
On Angle (fr. 30) he
treated an angle as a certain quality, i.e., in the spirit of Aristotle.
8
There is an
interesting fragment in Eudemus’
Physics (fr. 34) that is worth quoting in full to
demonstrate one of the possibilities of combining philosophical and mathemat-
ical approaches.
It is difficult to decide whether each science investigates and explains its own
principles, or each has some other science about its principles, or there exists a
science dealing with all the principles. For mathematicians display their own
principles and give its definition to every thing they talk about, so that a person
who does not know all this would look ridiculous if he tried to investigate what a
line is and every other mathematical object. As for the principles they talk about,
mathematicians do not attempt to demonstrate them, they even claim that it is not
their business to consider them (@ll^ oÿdé fasin aûtõn e£nai tañta ëpis-
kope$n), but, having reached agreement about them, they prove what follows
from them. If there exists some other science about the principles of geometry, as
well as those of arithmetic and the principles of every other science, then is it the
same for the principles of all the sciences, or for every science in particular?
However, whether there exists one general science of the principles or there are
different sciences for the principles of each particular science, it will be necessary
that these should have their own principles as well. Thus, it will again investigate
in the same way whether the principles it uses are its own or otherwise. And if the
principles every time prove different, they will go to infinity … But if they will
stop and there will be some sciences or even one specific science of the principles,
it will still remain to be investigated and explained why it is a science of its own
principles and those subordinate to it, whereas other sciences are not … This,
however, seems more appropriate for another branch of philosophy to examine in
details.
Thus, there exists an autonomous complex of mathematical disciplines in
which everything happens strictly according to the rules established by special-
ists.
9
Mathematicians, however, refuse to demonstrate their principles them-
7
Aristotle’s examples mainly concern elementary mathematics; the mathematical
discoveries of his time found little comment in his writings (Heath, T. L.