NICOMACHUS
99
position
iclid by
has the
>rk with
ig them
iger de-
,ermined
done by
’ous and
>position
concrete
s in the
has been
low that
b left to
articular
ir makes
between
: he has
(ionic ’ as
a>b>c,
i observe
roduct of
ct of the
e true in
was not
o be, not
e subject
le theory
ost note-
ist of his
i to other
his hypo-
perties of
raculous;
in turgid
ic rather
bers that
interested Nicomachus. If the verbiage is eliminated, thg
mathematical content can be stated in quite a small com
pass. Little or nothing in the book is original, and, except
for certain definitions and refinements of classification, the
essence of it evidently goes back to the early Pythagoreans.
Its success is difficult to explain except on the hypothesis that
it was at first read by philosophers rather than mathemati
cians (Pappus evidently despised it), and afterwards became
generally popular at a time when there were no mathemati
cians left, but only philosophers who incidentally took an
interest in mathematics. But a success it undoubtedly was;
this is proved by the number of versions or commentaries
which appeared in ancient times. Besides the Latin transla
tion by Apuleius of Madaura (born about a.d. 125), of which
no trace remains, there was the version of Boetius (born about
480, died 524 A.D.); and the commentators include lamblichus
(fourth century), Heronas, 1 Asclepius of Tralles (sixth century),
Joannes Philoponus, Proclus. 2 The commentary of lamblichus
has been published, 3 as also that of Philoponus, 4 while that of
Asclepius is said to be extant in MSS. When (the pseudo-)
Lucian in his Philopatris (c. 12) makes Critias say to Triephon
‘ you calculate like Nicomachus ’, we have an indication that
the book was Avell known, although the remark may be less a
compliment than a laugh at Pythagorean subtleties. 5
Book I of the Introductio, after a philosophical prelude
(cc. 1-6), consists principally of definitions and laws of forma
tion. Numbers, odd and even, are first dealt with (c. 7); then
comes the subdivision of even into three kinds (1) evenly-even,
of the form 2 n , (2) even-odd, of the form 2 (2 n+ 1), and (3)
odd-even, of the form 2 m+1 (2 n+ 1), the last-named occupying
a sort of intermediate position in that it partakes of the
character of both the others. The odd is next divided into
three kinds : (1) ‘ prime and incomposite ’, (2) £ secondary and
1 v. Eutoc. in Archim. (ed. Heib. iii, p. 120. 22). 2 v. Suidas.
3 The latest edition is Pistelli’s (Teubner, 1894).
* Ed. Hoche, Heft 1, Leipzig, 1864, Heft 2, Berlin, 1867.
5 Triephon tells Critias to swear by the Trinity (‘One (proceeding) from
Three and Three from One ’), and Critias replies, ‘You would have me
learn to calculate, for your oath is mere arithmetic and you calculate
like Nicomachus of Gerasa. I do not know what you mean by your
“ One-Three and Three-One ”; I suppose you don’t mean the rerpanrixs
of Pythagoras or the oybods or the Tpia<ds ? ’
H 2