'What do you mean ?' I have observed this ignorance among my countrymen--they are like pigs--and I am heartily ashamed both on my own behalf and on that of all the Hellenes.

'In what respect ?' Let me ask you a question.

You know that there are such things as length, breadth, and depth?
'Yes.' And the Hellenes imagine that they are commensurable (1) with themselves, and (2) with each other; whereas they are only commensurable with themselves.

But if this is true, then we are in an unfortunate case, and may well say to our compatriots that not to possess necessary knowledge is a disgrace, though to possess such knowledge is nothing very grand.

'Certainly.' The discussion of arithmetical problems is a much better amusement for old men than their favourite game of draughts.
'True.' Mathematics, then, will be one of the subjects in which youth should be trained.