A history of Greek mathematics - Wilbourhall.org

GEMINUS 223
An upper limit for his date is furnished by the fact that he
wrote a commentary on or exposition of Posidonius's work
nepl fi€T€dopcou ;
on the other hand, Alexander Aphrodisiensis
(about a.d. 210) quotes an important passage from an 'epitome'
of this egrjyrja-is by Geminus. The view most generally
accepted is that he was a Stoic philosopher, born probably
in the island of Rhodes, and a pupil of Posidonius, and that
he wrote about 73-67 B.C.
Of Geminus's works that which has most interest for us
is a comprehensive work on mathematics. Proclus, though
he makes great use of it, does not mention its title, unless
indeed, in the passage where, after quoting from Geminus
a classification of lines which never meet, he says ' these
remarks I have selected from the (piXoKaXta of Geminus', 1
the word (piXoKaXia is a title or an alternative title.
Pappus,
however, quotes a work of Geminus ' on the classification of
the mathematics' (kv tS> irepl rfjs tqov fjLaOrjfidrcoy radons),
while Eutocius quotes from the sixth book of the doctrine of
'
the mathematics ' (ev tS> Zkto) rr]s tS>v fiaOrjfiaTcoy Oeoopias).
The former title corresponds well enough to the long extract
on the division of the mathematical sciences into arithmetic,
geometry, mechanics, astronomy, optics, geodesy, canonic
(musical harmony) and logistic which Proclus gives in his
first prologue, and also to the fragments contained in the
Anonymi variae collectiones published by Hultsch in his
edition of Heron ; but it does not suit most of the other
passages borrowed by Proclus. The correct title was most
probably that given by Eutocius, The Doctrine, or Theory,
of the Mathematics) and Pappus probably refers to one
particular section of the work, say the first Book. If the
sixth Book treated of conies, as we may conclude from
Eutocius's reference, there must have been more Books to
follow; for Proclus has preserved us details about higher
curves, which must have come later. If again Geminus
finished his work and wrote with the same fullness about the
other branches of mathematics as he did about geometry,
there must have been a considerable number of Books
altogether. It seems to have been designed to give a complete
view of the whole science of mathematics, and in fact
1
Proclus on Eucl. I, p. 177. 24.