§85ΣΩ. οὐκοῦν ἐστιν αὕτη γραμμὴ ἐκ γωνίας εἰς γωνίαν τέμνουσα δίχα ἕκαστον τούτων τῶν χωρίων;
SOC. Therefore, is this not a line stretching from corner to corner, cutting each of these areas in half?
ΠΑΙ. ναί.
BOY. Yes.
ΣΩ. οὐκοῦν τέτταρες αὗται γίγνονται γραμμαὶ ἴσαι, περιέχουσαι τουτὶ τὸ χωρίον;
SOC. So there are these four equal lines, enclosing this area?
ΠΑΙ. γίγνονται γάρ.
BOY. Indeed they are.
ΣΩ. σκόπει δή·
SOC.
πηλίκον τί ἐστιν τοῦτο τὸ χωρίον;
Consider then: how large is this area?
ΠΑΙ. οὐ μανθάνω.
BOY. I don't understand.
ΣΩ. οὐχὶ τεττάρων ὄντων τούτων ἥμισυ ἑκάστου ἑκάστη ἡ γραμμὴ ἀποτέτμηκεν ἐντός;
SOC. Since there are these four areas, has not each line cut off inside half of each of them?
ἢ οὔ;
Or not?
ΠΑΙ. ναί.
BOY. Yes.
ΣΩ. πόσα οὖν τηλικαῦτα ἐν τούτῳ ἔνεστιν;
SOC. How many such halves, then, are contained in this area?
ΠΑΙ. τέτταρα.
BOY. Four.
ΣΩ. πόσα δὲ ἐν τῷδε;
SOC. And how many in this one?
ΠΑΙ. δύο.
BOY. Two.
ΣΩ. τὰ δὲ τέτταρα τοῖν δυοῖν τί ἐστιν;
SOC. And what is four in relation to two?
ΠΑΙ. διπλάσια.
BOY. Double.
ΣΩ. τόδε οὖν ποσάπουν γίγνεται;
SOC. Then how many feet does this area become?
ΠΑΙ. ὀκτώπουν.
BOY. Eight feet.
ΣΩ. ἀπὸ ποίας γραμμῆς;
SOC. From what line?
ΠΑΙ. ἀπὸ ταύτης.
BOY. From this one.
ΣΩ. ἀπὸ τῆς ἐκ γωνίας εἰς γωνίαν τεινούσης τοῦ τετράποδος;
SOC. From the one stretching from corner to corner of the four-foot square?
ΠΑΙ. ναί.
BOY. Yes.
ΣΩ. καλοῦσιν δέ γε ταύτην διάμετρον οἱ σοφισταί·
SOC. And the sophists call this the diagonal.
ὥστʼ εἰ ταύτῃ διάμετρος ὄνομα, ἀπὸ τῆς διαμέτρου ἄν, ὡς σὺ φῄς, ὦ παῖ Μένωνος, γίγνοιτʼ ἂν τὸ διπλάσιον χωρίον.
So, if "diagonal" is its name, then from the diagonal, as you say, boy of Meno, the double area would be produced.
ΠΑΙ. πάνυ μὲν οὖν, ὦ Σώκρατες.
BOY. Absolutely, Socrates.
ΣΩ. τί σοι δοκεῖ, ὦ Μένων;
SOC. What do you think, Meno?
ἔστιν ἥντινα δόξαν οὐχ αὑτοῦ οὗτος ἀπεκρίνατο;
Is there any opinion this boy expressed that was not his own?
ΜΕΝ. οὔκ, ἀλλʼ ἑαυτοῦ.
MEN. No, they were all his own.
ΣΩ. καὶ μὴν οὐκ ᾔδει γε, ὡς ἔφαμεν ὀλίγον πρότερον.
SOC. And yet, he did not know, as we said a little while ago.
ΜΕΝ. ἀληθῆ λέγεις.
MEN. You speak the truth.
ΣΩ. ἐνῆσαν δέ γε αὐτῷ αὗται αἱ δόξαι· ἢ οὔ;
SOC. But these opinions were in him, were they not?
ΜΕΝ. ναί.
MEN. Yes.
ΣΩ. τῷ οὐκ εἰδότι ἄρα περὶ ὧν ἂν μὴ εἰδῇ ἔνεισιν ἀληθεῖς δόξαι περὶ τούτων ὧν οὐκ οἶδε;
SOC. So in one who does not know, there are true opinions about those things which he does not know, regarding whatever he may not know?
ΜΕΝ. φαίνεται.
MEN. It appears so.
ΣΩ. καὶ νῦν μέν γε αὐτῷ ὥσπερ ὄναρ ἄρτι ἀνακεκίνηνται αἱ δόξαι αὗται·
SOC.
εἰ δὲ αὐτόν τις ἀνερήσεται πολλάκις τὰ αὐτὰ ταῦτα καὶ πολλαχῇ, οἶσθʼ ὅτι τελευτῶν οὐδενὸς ἧττον ἀκριβῶς ἐπιστήσεται περὶ τούτων.
And now, indeed, these opinions have just been stirred up in him like a dream; but if someone asks him these same questions many times and in many ways, you know that in the end he will understand these things no less accurately than anyone else.
ΜΕΝ. ἔοικεν.
MEN. It seems so.
ΣΩ. οὐκοῦν οὐδενὸς διδάξαντος ἀλλʼ ἐρωτήσαντος ἐπιστήσεται, ἀναλαβὼν αὐτὸς ἐξ αὑτοῦ τὴν ἐπιστήμην;
SOC. Therefore, without anyone teaching him but only asking questions, he will know, recovering the knowledge himself from within himself?
ΜΕΝ. ναί.
MEN. Yes.
ΣΩ. τὸ δὲ ἀναλαμβάνειν αὐτὸν ἐν αὑτῷ ἐπιστήμην οὐκ ἀναμιμνῄσκεσθαί ἐστιν;
SOC. And is recovering knowledge in oneself not recollecting?
ΜΕΝ. πάνυ γε.
MEN. Certainly.
ΣΩ. ἆρʼ οὖν οὐ τὴν ἐπιστήμην, ἣν νῦν οὗτος ἔχει, ἤτοι ἔλαβέν ποτε ἢ ἀεὶ εἶχεν;
SOC. Then, must he not have either acquired at some time or always possessed the knowledge which he now has?
ΜΕΝ. ναί.
MEN. Yes.
ΣΩ. οὐκοῦν εἰ μὲν ἀεὶ εἶχεν, ἀεὶ καὶ ἦν ἐπιστήμων· εἰ δὲ ἔλαβέν ποτε, οὐκ ἂν ἔν γε τῷ νῦν βίῳ εἰληφὼς εἴη.
SOC. Therefore, if he always possessed it, he was also always knowledgeable; but if he acquired it at some time, he could not have acquired it in this present life.
ἢ δεδίδαχέν τις τοῦτον γεωμετρεῖν;
Or has someone taught him geometry?
οὗτος γὰρ ποιήσει περὶ πάσης γεωμετρίας ταὐτὰ ταῦτα, καὶ τῶν ἄλλων μαθημάτων ἁπάντων.
For he will do these same things regarding all geometry, and all other branches of learning.
ἔστιν οὖν ὅστις τοῦτον πάντα δεδίδαχεν;
Is there, then, anyone who has taught him all this?
δίκαιος γάρ που εἶ εἰδέναι, ἄλλως τε ἐπειδὴ ἐν τῇ σῇ οἰκίᾳ γέγονεν καὶ τέθραπται.
For you ought to know, especially since he was born and brought up in your house.
ΜΕΝ. ἀλλʼ οἶδα ἔγωγε ὅτι οὐδεὶς πώποτε ἐδίδαξεν.
MEN. But I know well that no one has ever taught him.
ΣΩ. ἔχει δὲ ταύτας τὰς δόξας, ἢ οὐχί;
SOC. But he has these opinions, does he not?
ΜΕΝ. ἀνάγκη, ὦ Σώκρατες, φαίνεται.
MEN. It is necessary, Socrates, so it appears.