CLASSIFICATION OF MATHEMATICS
13
accounting for
list of subjects
bus, Theon of
3i', arithmetic,
his order was
l with number
3 with number
. sphaeric were
dry with mag-
on. In Plato’s
same subjects,
metry, appear,
Dlid geometry,
of stereometry
was, however,
for of course
as a part of
3 and others,
ogical. Astro-
ire is therefore
for, after con-
e third dimen-
before passing
motion. But
n, namely that
studied. ‘ The
en discovered.’
cause no State
ffi are difficult,
ho do investi-
vithout whose
;ries. But, to
intendent, and
>w stand, those
prevented by
> i
now stand ’) in
tances’, i.e. so
long as the director has not the authority of the State behind
him: this seems to be the best interpretation in view of the
whole context; but it is possible, as a matter of construction,
to connect the phrase with the preceding words, in which case
the meaning would-be ‘and, even when such a superintendent
has been found, as is the case at present’, and Plato would
be pointing to some distinguished geometer among his con
temporaries as being actually available for the post. If Plato
intended this, it would presumably be either Archytas or
Eudoxus whom he had in mind.
It is again on a logical ground that Plato made harmonics
or music follow astronomy in his classification. As astronomy
is the motion of bodies (фора (Забои?) and appeals to the eye,
so there is a harmonious motion (kvappovto? фора), a motion
according to the laws of harmony, which appeals to the ear.
In maintaining the sisterhood of music and astronomy Plato
followed the Pythagorean view (cf. the passage of Archytas
above quoted and the doctrine of the ‘ harmony of the
spheres ’),
(a) Arithmetic and logistic.
By arithmetic Plato meant, not arithmetic in our sense, but
the science which considers numbers in themselves, in other
words, what we mean by the Theory of Numbers. He does
not, however, ignore the art of calculation (arithmetic in oui*
sense); he speaks of number and calculation {арсврог ка1
Хоу игрой) and observes that ‘ the art of calculation [Хоуиткр)
and arithmetic {арсврдтскд) are both concerned with number
those who have a natural gift for calculation (oi фугас Xoyc-
(ttlkol) have, generally speaking, a talent for learning of all
kinds, and even those who are slow are, by practice in it,
made smarter. 1 But the art of calculation (Хоусапкд) is only
preparatory to the true science; those who are to govern the
city are to get a grasp of Хоуихтскр, not in the popular
sense with a view to use in trade, but only for the pui’pose of
knowledge, until they are able to contemplate the nature^of
number in itself by thought alone. 2 This distinction between
арсврдтскр (the theory of numbers) and Xоусатскд (the art of
«■ 1 Republic, vii. 522 c, 525 A, 526 в.
2 lb. vii. 525 в, c.