A history of Greek mathematics - Wilbourhall.org

222 SUCCESSORS OF THE GREAT GEOMETERS
from them cannot be proved without the admission of something
else as well which has not been included in the said
principles, and he intended by means of these criticisms to
destroy the whole of geometry. 1
We can understand, therefore,
that the tract of Posidonius was a serious work.
A definition of the centre of gravity by one ' Posidonius a
Stoic ' is quoted in Heron's Mechanics, but, as the writer goes
on to say that Archimedes introduced a further distinction, we
may fairly assume that the Posidonius in question is not
Posidonius of Rhodes, but another, perhaps Posidonius of
Alexandria, a pupil of Zeno of Cittium in the third century
B.C.
We now come to
Geminus, a very important authority on
many questions belonging to the history of mathematics, as is
shown by the numerous quotations from him in Proclus's
Commentary on Euclid, Book I. His date and birthplace are
uncertain, and the discussions on the subject now form a whole
literature for which reference must be made to Manitius's
edition of the so-called Gemini elementa astronomiae (Teubner,
1898) and the article 'Geminus' in Pauly-Wissowa's Real-
Encyclopadie. The doubts begin with his name. Petau, who
included the treatise mentioned in his Uranologion (Paris,
1630), took it to be the Latin Geminus. Manitius, the latest
editor, satisfied himself that it was Geminus, a Greek name,
judging from the fact that it consistently appears with the
properispomenon accent in Greek {Teiuvos), while it is also
found in inscriptions with the spelling Pe/xe^o?; Manitius
suggests the derivation from ye/z, as 'EpyTvos from epy, and
'A\e£tvos from aAe£ ; he compares also the unmistakably
Greek names 'IktIvos, Kparivos. Now, however, we are told
(by Tittel) that the name is, after all, the Latin Ge'mmus,
that re/jLiuo? came to be so written through false analogy
with 'AXegivos, &c, and that Te^elvos, if the reading is
correct, is also wrongly formed on the model of Avrccvelvo^,
Aypnnrdva. The occurrence of a Latin name in a centre
of Greek culture need not surprise us, since Romans settled in
such centres in large numbers during the last century B.C.
Geminus, however, in spite of his name, was thoroughly Greek.
1
Proclus on Eucl. I, pp. 214. 18-215. 13, p. 216. 10-19, p. 217. 10-23.