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

libros geometricarum enarrationum Gemini, the his-
torians of mathematics, beginning with Ramus, started to ascribe to Geminus a his-
tory of geometry that never actually existed. By the mid-19
th
century, this misunder-
standing was finally cleared up (Nesselmann, G.
Algebra der Griechen, Berlin 1842,
4f.; Schmidt. Philologische Beiträge, 79ff.), only to reappear in a slightly modified
form in Tannery and those who followed him.
63
On Geminus’ material in Proclus, see Tittel,
op. cit., 112f.
64
Procl.
In Eucl., 72.3ff., 77.2ff., 79.3ff., 200.22.
65
“This is the way in which other mathematicians also are accustomed to distinguish
lines, giving the property of each species. Apollonius, for instance, shows for each of
his conic lines what its property is, and Nicomedes likewise for the conchoids, Hip-
pias for the quadratrices, and Perseus for the spiric lines.” (Procl.
In Eucl, 356.6f,
transl. by G. Morrow; cf. 105.5, 15 on Apollonius).
66
Procl.
In Eucl., 41.6, 17; 181.18; cf. Papp. Coll. VIII, 1026.5f.; Eutoc. In Archim. de
plan. aequil., 266.1.
67
Procl.
In Eucl., 183.18; 74.22.
68
Plato (Procl.
In Eucl. 41.8, 103.21, 117.17, 192.12), Aristotle (33.21, 104.22, 188.7,

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Chapter 8: Historiography of science after Eudemus: a brief outline
292
called ‘founders of geometry’; their views on the classification of lines have
more weight than those of Apollonius.
69
Mathematical discoveries are touched
upon only once, in connection with the classification of various conic sec-
tions.
70
Interesting for the historian is also the note on how the geometers be-
fore Apollonius defined the cone and the three kinds of conic sections.
71
On the
whole, Qewría tõn maqhmátwn fully corresponded to its name and was
oriented not toward the history of mathematics, nor its particular problems, as
later in Pappus, but toward its methodology and philosophy, which is confirmed
by the ample use made of it in Proclus’ philosophical commentary to Euclid.
Pappus and Eutocius, who addressed their works to a professional audience,
show comparatively little concern for Geminus.
72
Posidonius’ and his students’ involvement with the exact sciences remained
only a short episode in the history of Stoicism; later Stoics returned to their
usual natural philosophy.
73
In the first century BC, mathematics gains a more
solid ground in other philosophical schools – re-emerging Aristotelianism,
Neopythagoreanism, Middle Platonism and later, particularly, Neoplatonism.
Though the late philosophical schools never showed any systematic interest in
the history of scientific knowledge, as distinct from an antiquarian interest, it is
to them that we owe the larger part of the surviving evidence on the history of
science in various kinds of introductions and commentaries, for example, in
Dercyllides, Nicomachus, Adrastus, Theon of Smyrna, Cleomedes, Porphyry,
Iamblichus, Proclus, and Simplicius. Still more valuable from this point of
view are the works of commentators and systematizers of mathematical sci-
ences, such as Hero, Menelaus, Sosigenes, Sporus, Pappus, and Eutocius. But
the fate of historico-scientific tradition in the Imperial period is outside the
scope of this book. The rich variety of sources of this time needs a detailed
192.10, 202.11), Speusippus (77.16, 179.15), Xenocrates (279.5), Chrysippus
(395.14), Posidonius (80.21, 143.8, 176.6), Stoics (77.3), Epicureans (322.6).
69
Procl.
In Eucl., 192.5f., 103.21f.
70
“Some of these sections, in particular the conic, were discovered by Menaechmus…
others by Perseus, who composed an epigram on his discovery.” (Procl.