§7.819ΑΘ. φοβοῦμαι μὲν καὶ ταῦτα ἃ σὺ νῦν λέγεις, μᾶλλον δʼ ἔτι δέδοικα τοὺς ἡμμένους μὲν αὐτῶν τούτων τῶν μαθημάτων, κακῶς δʼ ἡμμένους.
ATH.: I fear indeed those things which you now say, but I fear still more those who have touched these very studies, but have touched them badly.
οὐδαμοῦ γὰρ δεινὸν οὐδὲ σφοδρὸν ἀπειρία τῶν πάντων οὐδὲ μέγιστον κακόν, ἀλλʼ ἡ πολυπειρία καὶ πολυμαθία μετὰ κακῆς ἀγωγῆς γίγνεται πολὺ τούτων μείζων ζημία.
For complete ignorance of everything is nowhere a terrible or intense thing, nor the greatest evil, but great experience and much learning with bad guidance becomes a much greater damage than these.
ΚΛ. ἀληθῆ λέγεις.
CL.: You speak the truth.
ΑΘ. τοσάδε τοίνυν ἑκάστων χρὴ φάναι μανθάνειν δεῖν τοὺς ἐλευθέρους, ὅσα καὶ πάμπολυς ἐν Αἰγύπτῳ παίδων ὄχλος ἅμα γράμμασι μανθάνει.
ATH.: Therefore, one must say that the free citizens ought to learn so much of each of these as a very great crowd of children in Egypt learn at the same time as their letters.
πρῶτον μὲν γὰρ περὶ λογισμοὺς ἀτεχνῶς παισὶν ἐξηυρημένα μαθήματα μετὰ παιδιᾶς τε καὶ ἡδονῆς μανθάνειν, μήλων τέ τινων διανομαὶ καὶ στεφάνων πλείοσιν ἅμα καὶ ἐλάττοσιν ἁρμοττόντων ἀριθμῶν τῶν αὐτῶν, καὶ πυκτῶν καὶ παλαιστῶν ἐφεδρείας τε καὶ συλλήξεως ἐν μέρει καὶ ἐφεξῆς καὶ ὡς πεφύκασι γίγνεσθαι.
For first, in regard to calculation, they learn studies simply devised for children with play and pleasure: distributions of certain apples and crowns, adapting the same numbers to larger and smaller groups, and also matches and pairings of boxers and wrestlers in turn and in order, and as they naturally occur.
καὶ δὴ καὶ παίζοντες, φιάλας ἅμα χρυσοῦ καὶ χαλκοῦ καὶ ἀργύρου καὶ τοιούτων τινῶν ἄλλων κεραννύντες, οἱ δὲ καὶ ὅλας πως διαδιδόντες, ὅπερ εἶπον, εἰς παιδιὰν ἐναρμόττοντες τὰς τῶν ἀναγκαίων ἀριθμῶν χρήσεις, ὠφελοῦσι τοὺς μανθάνοντας εἴς τε τὰς τῶν στρατοπέδων τάξεις καὶ ἀγωγὰς καὶ στρατείας καὶ εἰς οἰκονομίας αὖ, καὶ πάντως χρησιμωτέρους αὐτοὺς αὑτοῖς καὶ ἐγρηγορότας μᾶλλον τοὺς ἀνθρώπους ἀπεργάζονται·
And further, while playing, by mixing bowls of gold and bronze and silver and other such things together, and some also distributing them as wholes, as I said, fitting the uses of necessary numbers into play, they benefit the learners in regard to both the arrays, leaderships, and campaigns of armies, and again in regard to household management; and in every way they render the men more useful to themselves and more awake.
μετὰ δὲ ταῦτα ἐν ταῖς μετρήσεσιν, ὅσα ἔχει μήκη καὶ πλάτη καὶ βάθη, περὶ ἅπαντα ταῦτα ἐνοῦσάν τινα φύσει γελοίαν τε καὶ αἰσχρὰν ἄγνοιαν ἐν τοῖς ἀνθρώποις πᾶσιν, ταύτης ἀπαλλάττουσιν.
And after these things, in measurements, in as many things as have length, breadth, and depth, they rid them of a certain ridiculous and shameful ignorance that is naturally present in all men concerning all these things.
ΚΛ. ποίαν δὴ καὶ τίνα λέγεις ταύτην;
CL.: What sort of ignorance indeed, and what is this that you speak of?
ΑΘ. ὦ φίλε Κλεινία, παντάπασί γε μὴν καὶ αὐτὸς ἀκούσας ὀψέ ποτε τὸ περὶ ταῦτα ἡμῶν πάθος ἐθαύμασα, καὶ ἔδοξέ μοι τοῦτο οὐκ ἀνθρώπινον ἀλλὰ ὑηνῶν τινων εἶναι μᾶλλον θρεμμάτων, ᾐσχύνθην τε οὐχ ὑπὲρ ἐμαυτοῦ μόνον, ἀλλὰ καὶ ὑπὲρ ἁπάντων τῶν Ἑλλήνων.
ATH.: O dear Clinias, I myself indeed, having heard about our condition concerning these things quite late, was utterly amazed, and it seemed to me that this is not human, but belongs rather to some swinish creatures; and I was ashamed not only on my own behalf, but also on behalf of all the Greeks.
ΚΛ. τοῦ πέρι;
CL.: Concerning what?
λέγʼ ὅτι καὶ φῄς, ὦ ξένε.
Say what you mean, O stranger.
ΑΘ. λέγω δή· μᾶλλον δὲ ἐρωτῶν σοι δείξω.
ATH.: I will say indeed; or rather, by questioning I will show you.
καί μοι σμικρὸν ἀπόκριναι· γιγνώσκεις που μῆκος;
And answer me a small thing: you know length, I suppose?
ΚΛ. τί μήν;
CL.: Why, of course.
ΑΘ. τί δέ;
ATH.: And what of breadth?
πλάτος;
CL.: Absolutely.
ΚΛ. πάντως. ΑΘ. ἦ καὶ ταῦτα ὅτι δύʼ ἐστόν, καὶ τρίτον τούτων βάθος;
ATH.: And that these are two things, and a third besides them, depth?
ΚΛ. πῶς γὰρ οὔ;
CL.: For how not?
ΑΘ. ἆρʼ οὖν οὐ δοκεῖ σοι ταῦτα εἶναι πάντα μετρητὰ πρὸς ἄλληλα;
ATH.: Does it not seem to you, then, that all these are measurable against one another?
ΚΛ. ναί.
CL.: Yes.
§7.820ΑΘ. μῆκός τε οἶμαι πρὸς μῆκος, καὶ πλάτος πρὸς πλάτος, καὶ βάθος ὡσαύτως δυνατὸν εἶναι μετρεῖν φύσει.
ATH.: And length against length, I suppose, and breadth against breadth, and depth likewise, is by nature possible to measure.
ΚΛ. σφόδρα γε.
CL.: Very much so.
ΑΘ. εἰ δʼ ἔστι μήτε σφόδρα μήτε ἠρέμα δυνατὰ ἔνια, ἀλλὰ τὰ μέν, τὰ δὲ μή, σὺ δὲ πάντα ἡγῇ, πῶς οἴει πρὸς ταῦτα διακεῖσθαι;
ATH.: But if some things are possible neither very much nor slightly, but some are and others are not, while you think that all are, how do you think you are disposed toward these things?
ΚΛ. δῆλον ὅτι φαύλως.
CL.: Clearly, in a bad state.
ΑΘ. τί δʼ αὖ μῆκός τε καὶ πλάτος πρὸς βάθος, ἢ πλάτος τε καὶ μῆκος πρὸς ἄλληλα;
ATH.: And what again of length and breadth against depth, or breadth and length against one another?
ἆρʼ οὐ διανοούμεθα περὶ ταῦτα οὕτως Ἕλληνες πάντες, ὡς δυνατά ἐστι μετρεῖσθαι πρὸς ἄλληλα ἁμῶς γέ πως;
Do we not, all of us Greeks, think about these things in this way, that they are capable of being measured against one another in some way or other?
ΚΛ. παντάπασι μὲν οὖν.
CL.: Absolutely indeed.
ΑΘ. εἰ δʼ ἔστιν αὖ μηδαμῶς μηδαμῇ δυνατά, πάντες δʼ, ὅπερ εἶπον, Ἕλληνες διανοούμεθα ὡς δυνατά, μῶν οὐκ ἄξιον ὑπὲρ πάντων αἰσχυνθέντα εἰπεῖν πρὸς αὐτούς· ὦ βέλτιστοι τῶν Ἑλλήνων, ἓν ἐκείνων τοῦτʼ ἐστὶν ὧν ἔφαμεν αἰσχρὸν μὲν γεγονέναι τὸ μὴ ἐπίστασθαι, τὸ δʼ ἐπίστασθαι τἀναγκαῖα οὐδὲν πάνυ καλόν;
ATH.: But if, on the contrary, they are in no way and by no means possible, while all of us Greeks, as I said, think they are possible, is it not worth being ashamed on behalf of all, and saying to them: 'O best of Greeks, this is one of those things which we said it is shameful not to understand, but to understand what is necessary is nothing very grand'?
ΚΛ. πῶς δʼ οὔ;
CL.: Of course.
ΑΘ. καὶ πρὸς τούτοις γε ἄλλα ἔστιν τούτων συγγενῆ, ἐν οἷς αὖ πολλὰ ἁμαρτήματα ἐκείνων ἀδελφὰ ἡμῖν ἐγγίγνεται τῶν ἁμαρτημάτων.
ATH.: And in addition to these indeed, there are other things akin to these, in which in turn many errors akin to those errors occur among us.
ΚΛ. ποῖα δή;
CL.: Of what sort indeed?
ΑΘ. τὰ τῶν μετρητῶν τε καὶ ἀμέτρων πρὸς ἄλληλα ᾗτινι φύσει γέγονεν.
ATH.: The matters of things commensurable and incommensurable with respect to one another, in whatever nature they have been made.
ταῦτα γὰρ δὴ σκοποῦντα διαγιγνώσκειν ἀναγκαῖον ἢ παντάπασιν εἶναι φαῦλον, προβάλλοντά τε ἀλλήλοις ἀεί, διατριβὴν τῆς πεττείας πολὺ χαριεστέραν πρεσβυτῶν διατρίβοντα, φιλονικεῖν ἐν ταῖς τούτων ἀξίαισι σχολαῖς.
For it is necessary to examine and distinguish these, or to be altogether worthless; and, by always proposing them to one another, spending time in a pursuit far more pleasant than that of board-games for old men, to compete in studies worthy of these.
ΚΛ. ἴσως· ἔοικεν γοῦν ἥ τε πεττεία καὶ ταῦτα ἀλλήλων τὰ μαθήματα οὐ πάμπολυ κεχωρίσθαι.
CL.: Perhaps; at least the board-game and these studies seem not to be very far separated from one another.
ΑΘ. ταῦτα τοίνυν ἐγὼ μέν, ὦ Κλεινία, φημὶ τοὺς νέους δεῖν μανθάνειν· καὶ γὰρ οὔτε βλαβερὰ οὔτε χαλεπά ἐστιν, μετὰ δὲ παιδιᾶς ἅμα μανθανόμενα ὠφελήσει μέν, βλάψει δὲ ἡμῖν τὴν πόλιν οὐδέν.
ATH.: These things therefore, O Clinias, I indeed say that the young must learn; for they are neither harmful nor difficult, and being learned at the same time as play, they will indeed benefit, and will in no way harm our city.
εἰ δέ τις ἄλλως λέγει, ἀκουστέον.
But if anyone says otherwise, he must be listened to.
ΚΛ. πῶς δʼ οὔ;
CL.: Of course.
ΑΘ. ἀλλὰ μὴν ἂν οὕτω ταῦτα ἔχοντα φαίνηται, δῆλον ὡς ἐγκρινοῦμεν αὐτά, μὴ ταύτῃ δὲ φαινόμενα ἔχειν ἀποκριθήσεται.
ATH.: But indeed, if these things appear to be so, it is clear that we shall admit them; but if they do not appear to be so, they will be excluded.
ΚΛ. δῆλον· τί μήν;
CL.: Clear; how not?
ΑΘ. οὐκοῦν νῦν, ὦ ξένε, κείσθω ταῦτα ὡς ὄντα τῶν δεόντων μαθημάτων, ἵνα μὴ διάκενα ἡμῖν ᾖ τὰ τῶν νόμων;
ATH.: Therefore, now, O stranger, let these things be established as being among the necessary studies, so that our laws may not have gaps?
κείσθω μέντοι καθάπερ ἐνέχυρα λύσιμα ἐκ τῆς ἄλλης πολιτείας, ἐὰν ἢ τοὺς θέντας ἡμᾶς ἢ καὶ τοὺς θεμένους ὑμᾶς μηδαμῶς φιλοφρονῆται.
Let them, however, be laid down like pledges redeemable from the rest of the constitution, if they should in no way show friendliness either to us who lay them down, or to you who receive them.
ΚΛ. δικαίαν λέγεις τὴν θέσιν.
CL.: You speak of a just condition.
ΑΘ. ἄστρων δὴ τὸ μετὰ ταῦτα ὅρα τὴν μάθησιν τοῖς νέοις, ἂν ἡμᾶς ἀρέσκῃ λεχθεῖσα ἢ καὶ τοὐναντίον.
ATH.: Next, then, consider the study of the stars for the young, whether it pleases us when spoken of, or the contrary.
ΚΛ. λέγε μόνον.
CL.: Just speak.
ΑΘ. καὶ μὴν θαῦμά γε περὶ αὐτά ἐστιν μέγα καὶ οὐδαμῶς οὐδαμῇ ἀνεκτόν.
ATH.: And indeed, there is a great wonder concerning them, and one that is by no means in any way tolerable.