20 
INTRODUCTORY 
letters. First there should be calculations specially devised 
as suitable for boys, which they should learn with amusement 
and pleasure, for example, distributions of apples or garlands 
where the same number is divided among more or fewer boys, 
or (distributions) of the competitors in boxing or wrestling 
matches on the plan of drawing pairs with byes, or by taking 
them in consecutive order, or in any of the usual ways 1 ; and 
again there should be games with bowls containing gold, 
bronze, and silver (coins?) and the like mixed together, 2 or the 
bowls may be distributed as undivided units; for, as I said, 
by connecting with games the essential operations of practical 
arithmetic, you supply the boy with wrnit will be useful to 
him later in the ordering of armies, marches and campaigns, 
as well as in household management; and in any case you 
make him more useful to himself and more wide awake. 
Then again, by calculating measurements of things which 
have length, breadth, and depth, questions on all of which 
the natural condition of all men is one of ridiculous and dis 
graceful ignorance, they are enabled to emerge from this 
state.’ 
It is true that these are Plato’s ideas of what elementary 
education should include; but it can hardly be doubted that 
such methods were actualty in use in Attica. 
Geometry and astronomy belonged to secondary education, 
which occupied the years between the ages of fourteen and 
eighteen. The pseudo-Platonic Axiochus attributes to Prodi 
cus a statement that, when a boy gets older, i. e. after he has 
1 The Greek of this clause is (biavopa'i) 7tvktcov kcu ttaXaiarav i<pe8peias 
re Kai crvXXrj^eas iv pepei Kai i(f)€t;ris Kat as irecfiVKacn yiyvecxdai. So far as 
1 can ascertain, iv pepei (by itself) and icfje^rjs have always been taken 
as indicating alternative methods, ‘ in turn and in consecutive order ’. 
But it is impossible to get any satisfactory contrast of meaning between 
‘ in turn ’ and ‘ in consecutive order ’. It is clear to me that we have 
here merely an instance of Plato’s habit of changing the order of words 
for effect, and that iv pepei must be taken with the genitives ifedpelas km 
avXXy^eas ; i.e. we must translate as if we had iv icfrebpeias re ko\ avXXi]- 
£ea)s pipei, ‘ by way of byes and drawings ’. This gives a proper distinction 
between (1) drawings with byes and (2) taking competitors in consecutive 
order. 
2 It is difficult to decide between the two possible interpretations 
of the phrase (jndXas dpa ypccroG KaL yeducoG kai dpyvpuv kcu roiovrav tivwv 
aXXav KepawvvTes. It may mean ‘ taking bowls made of gold, bronze, 
silver and other metals mixed together (in certain proportions) ’ or 
‘filling bowls with gold, bronze, silver, &c. (sc. objects such as coins) 
mixed together ’. The latter version seems to agree best with naigovres 
(making a game out of the process) and to give the better contrast to 
‘distributing the bowls as wholes' (dXas nas 8ia8i8dvTes). 
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3 See Isoc] 
§§ 261-8.