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

Met. 984a 7; Theophr. fr. 225 FHSG, cf. Aët. I,3.11, IV,3.4 = 18 A 9.
104
Fr. 90. See above, 174 n. 31.
105
In Nicom., 100.23, 113.17, 116.4.
106
This tradition is widely presented in Iamblichus, including the work used by Proclus
(
De comm. math. sc., 77.18f., cf. VP 88, 246–247).
107
See above, 189 n. 102. The scholia repeat Pappus.
108
Coll. III, 84.1f.; see above, 173 n. 28.
109
Coll.IV, 272.15f. On Pappus’ method of working with sources, see Knorr. TS, 227ff.
We should not exclude the possibility that Hippasus’ name was already omitted from
Pappus’ source. He mentions Eudemus only once and most likely used his works at
second hand.

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4. Early Greek geometry according to Eudemus
191
4. Early Greek geometry according to Eudemus
We will now try to bring together the data contained in Eudemus’ fragments, in
the
Catalogue, and in the evidence we relate to the History of Geometry. This
does not imply the reconstruction of early Greek geometry on the basis of
Eudemus’ writings. Such a reconstruction, involving a detailed analysis of all
available sources on the subject, does not belong to the historiography of Greek
mathematics. Our goal is more modest: we seek to get a general picture of
what,
whom, and how Eudemus’ History of Geometry is written about. Different parts
of this picture can be reconstructed more or less reliably, depending in each
case on the character of evidence at our disposal. Probably the most difficult
question concerns the origin of Eudemus’ information on the geometers of the
sixth and the early fifth century. Although we know that he used the works of
Oenopides, Hippocrates, Archytas, Theaetetus, Eudoxus, and Eudoxus’ stu-
dents, it is very hard to say definitively which of them contained any infor-
mation on the earliest mathematicians.
Like most of his predecessors, Eudemus considered Egypt a birthplace of
geometry and explained the discipline’s appearance there with the practical
needs of land surveying (
In Eucl., 64.17f. = fr. 133). In its development, ge-
ometry passes through three stages: aÍsqhsi~, logismó~, and noñ~ (65.1f.).
These can be related to the tripartite scheme of
Metaphysics A (ëmpeiría,
técnh, and ëpist2mh) and interpreted respectively as the acquisition of practi-
cal skill in land surveying, the emergence of a practically oriented applied dis-
cipline, and its further transformation into a theoretical science. Eudemus ap-
peared to attribute the first two stages to Egypt and the third to Greek mathe-
matics.
He interprets the passing of knowledge from one culture to another within
the framework of two traditional formulas: prõto~ eûret2~ and máqhsi~
(mímhsi~) – eÛresi~ (
2.3
). Thales, having visited Egypt, was the first to bring
geometry to Greece and discovered many things in it himself. Regrettably, the
stereotypes Eudemus used are still popular in the historiography of science. It is
very probable that the Greeks did in fact borrow from Egypt a lot of knowledge
needed for land surveying and building, the more so since early Greek archi-
tecture and sculpture bear obvious traces of Egyptian influence. It is hard to be-
lieve, however, that the Greeks would have waited for Thales to get from Egypt
the practical knowledge they needed. Stone building in Greece was resumed in
the eighth century, Naucratis was founded in the mid-seventh century, and the
famous architects Theodorus, Chersiphron, and Metagenes were Thales’ con-
temporaries. The passage from empirical to theoretical geometry is indeed con-
nected with Thales, but the practical knowledge he relied on must have been of
a Greek, rather than Egyptian origin.
According to Eudemus, Thales 1) was the first to prove that the diameter di-
vides the circle into two equal parts (Eucl. I, def. 17); 2) was the first to learn
and state (ëpist4sai kaì eıpe$n) that the angles at the base of any isosceles

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Chapter 5: The history of geometry
192
triangle are equal (I, 5), calling them, in the archaic manner,