MATHEMATICS IN GREEK EDUCATION 
21 
3ially devised 
Ii amusement 
;s or garlands 
)r fewer boys, 
or wrestling 
, or by taking 
»1 ways 1 ; and 
itaiuing gold, 
gether, 2 or the 
for, as I said, 
as of practical 
1 be useful to 
nd campaigns, 
any case you 
wide awake, 
things which 
i all of which 
ulous and dis- 
rge from this 
lat elementary 
3 doubted that 
lary education, 
f fourteen and 
butes to Prodi- 
.e. after he has 
aXauTTobv f(j)e8pelas 
•vecrdai. So far as 
Iways been taken 
onsecutive order’, 
meaning between 
i me that we have 
the order of words 
litives e(p(8peias Ka'i 
8peias re kch itvWt]- 
proper distinction 
itors in consecutive 
fie interpretations 
v Kal toiovtcov tivcov 
le of gold, bronze, 
i proportions) ’ or 
icts such as coins) 
best with naiCovns 
better contrast to 
0. 
passed the primary stage under the paidagogos, grammatistes, 
and paidotrihes, he comes under the tyranny of the ‘ critics ’, 
the geometers, the tacticians, and a host of other masters. 1 
Teles, the philosopher, similarly, mentions arithmetic and 
geometry among the plagues of the lad. 2 It would appear 
that geometry and astronomy were newly introduced into the 
curriculum in the time of Isocrates. ‘ I am so far he says, 3 
‘ from despising the instruction which our ancestors got, that 
I am a supporter of that which has been established in our 
time, I mean geometry, astronomy, and the so-called eristic 
dialogues.’ Such studies, even if they do no other good, 
keep the young out of mischief, and in Isocrates’s opinion no 
other subjects could have been invented more useful and 
more fitting; but they should be abandoned by the time that 
the pupils have reached man’s estate. Most people, he says, 
think them idle, since (say they) they are of no use in private 
or public affairs; moreover they are forgotten directly because 
they do not go with us in our daily life and action, nay, they 
are altogether outside everyday needs. He himself, however, 
is far from sharing these views. True, those who specialize in 
such subjects as astronomy and geometry get no good from 
them unless they choose to teach them for a livelihood; and if 
they get too deeply absorbed, they become unpractical and 
incapable of doing ordinary business; but the study of these 
subjects up to the proper point trains a boy to keep his atten 
tion fixed and not to allow his mind to wander; so, being 
practised in this way and having his wits sharpened, he will be 
capable of learning more important matters with greater ease 
and speed. Isocrates will not give the name of 4 philosophy ’ to 
studies like geometry and astronomy, which are of no imme 
diate use for producing an orator or man of business; they 
are rather means of training the mind and a preparation for 
philosophy. They are a more manly discipline than the sub 
jects taught to boys, such as literary study and music, but in 
other respects have the same function in making them quicker 
to learn greater and more important subjects. 
1 Axiochus, 366 e. 
2 Stobaeus, Ed. iv. 34, 72 (vol. v, p. 848, 19 sq., Wachsmuth and 
Hense). 
See Isocrates, Punathenciicus, §§ 26—8 1238 b—d) i ITfol aiTitoireais, 
§§261-8.