A history of Greek mathematics Vol.II from Aristarchus to Diophantus by Heath, Thomas Little, Sir, 1921

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.
224 SUCCESSORS OF THE GREAT GEOMETERS
to have been a sort of encyclopaedia of the subject. The
quotations of Proclus from Geminus's work do not stand
alone; we have other collections of extracts, some more and
some less extensive, and showing varieties of tradition according
to the channel through which they came down. The
scholia to Euclid's Elements, Book I, contain a considerable
part of the commentary on the Definitions of Book I, and are
valuable in that they give Geminus pure and simple, whereas
Proclus includes extracts from other authors. Extracts from
Geminus of considerable length are included in the Arabic
commentary by an-Nairizi (about A.D. 900) who got them
through the medium of Greek commentaries on Euclid,
especially that of Simplicius. It does not appear to be
doubted any longer that Aganis ' ' in an-Nairizi is really
Geminus ; this is inferred from the close agreement between
'
an-Nairizi's quotations from Aganis ' and the corresponding
passages in Proclus ; the difficulty caused by the fact
that Simplicius calls Aganis ' socius noster ' is met by the
suggestion that the particular word socius is either the
result of the double translation from the Greek or means
nothing more, in the mouth of Simplicius, than ' colleague
in the sense of a worker in the same field, or ' authority \
A few extracts again are included in the Anonymi variae
collectiones in Hultsch's Heron, Nos. 5-14 give definitions of
geometry, logistic, geodesy and their subject-matter, remarks
on bodies as continuous magnitudes, the three dimensions as
'
principles ' of geometry, the purpose of geometry, and lastly
on optics, with its subdivisions, optics proper, Gatoptriea and
o-KT}uoypa(f>LKrj, scene-painting (a sort of perspective), with some
fundamental principles of optics, e.g. that all light travels
along straight lines (which are broken in the cases of reflection
and refraction), and the division between optics and natural
philosophy (the theory of light), it
being the province of the
latter to investigate (what is a matter of indifference to optics)
whether (1) visual rays issue from the eye, (2) images proceed
from the object and impinge on the eye, or (3) the intervening
air is aligned or compacted with the beam-like breath or
emanation from the eye.
Nos. 80-6 again in the same collection give the Peripatetic
explanation of the name mathematics, adding that the term