§83ΣΩ. θεῶ δὴ αὐτὸν ἀναμιμνῃσκόμενον ἐφεξῆς, ὡς δεῖ ἀναμιμνῄσκεσθαι.
SOC. Watch him now recollecting in order, as one ought to recollect.
σὺ δέ μοι λέγε· ἀπὸ τῆς διπλασίας γραμμῆς φῂς τὸ διπλάσιον χωρίον γίγνεσθαι;
And you, tell me: do you say that from the double line the double area is produced?
τοιόνδε λέγω, μὴ ταύτῃ μὲν μακρόν, τῇ δὲ βραχύ, ἀλλὰ ἴσον πανταχῇ ἔστω ὥσπερ τουτί, διπλάσιον δὲ τούτου, ὀκτώπουν·
I mean something like this: not long this way and short that way, but let it be equal in every direction just like this one, but double the size of this, of eight feet.
ἀλλʼ ὅρα εἰ ἔτι σοι ἀπὸ τῆς διπλασίας δοκεῖ ἔσεσθαι.
But see if it still seems to you to come from the double line.
ΠΑΙ. ἔμοιγε.
BOY. Yes, to me at least.
ΣΩ. οὐκοῦν διπλασία αὕτη ταύτης γίγνεται, ἂν ἑτέραν τοσαύτην προσθῶμεν ἐνθένδε;
SOC. Therefore, does this line not become double this other one, if we add another of the same length from this end?
ΠΑΙ. πάνυ γε.
BOY. Certainly.
ΣΩ. ἀπὸ ταύτης δή, φῄς, ἔσται τὸ ὀκτώπουν χωρίον, ἂν τέτταρες τοσαῦται γένωνται;
SOC. From this line, then, you say, the eight-foot area will be produced, if four such lines are made?
ΠΑΙ. ναί.
BOY. Yes.
ΣΩ. ἀναγραψώμεθα δὴ ἀπʼ αὐτῆς ἴσας τέτταρας.
SOC. Let us construct, then, from it four equal lines.
ἄλλο τι ἢ τουτὶ ἂν εἴη ὃ φῂς τὸ ὀκτώπουν εἶναι;
Would it be anything else than this which you say is the eight-foot area?
ΠΑΙ. πάνυ γε.
BOY. Certainly.
ΣΩ. οὐκοῦν ἐν αὐτῷ ἐστιν ταυτὶ τέτταρα, ὧν ἕκαστον ἴσον τούτῳ ἐστὶν τῷ τετράποδι;
SOC. Therefore, are there not in it these four areas, each of which is equal to this four-foot one?
ΠΑΙ. ναί.
BOY. Yes.
ΣΩ. πόσον οὖν γίγνεται; οὐ τετράκις τοσοῦτον;
SOC. How many, then, does it become? Is it not four times as much?
ΠΑΙ. πῶς δʼ οὔ;
BOY. Of course it is.
ΣΩ. διπλάσιον οὖν ἐστιν τὸ τετράκις τοσοῦτον;
SOC. Is four times as much, then, the same as double?
ΠΑΙ. οὐ μὰ Δία.
BOY. No, by Zeus.
ΣΩ. ἀλλὰ ποσαπλάσιον;
SOC. But how many times?
ΠΑΙ. τετραπλάσιον.
BOY. Four times.
ΣΩ. ἀπὸ τῆς διπλασίας ἄρα, ὦ παῖ, οὐ διπλάσιον ἀλλὰ τετραπλάσιον γίγνεται χωρίον.
SOC. Therefore, boy, from the double line not a double but a fourfold area is produced.
ΠΑΙ. ἀληθῆ λέγεις.
BOY. You speak the truth.
ΣΩ. τεττάρων γὰρ τετράκις ἐστὶν ἑκκαίδεκα.
SOC. For four times four is sixteen.
οὐχί;
Is it not?
ΠΑΙ. ναί.
BOY. Yes.
ΣΩ. ὀκτώπουν δʼ ἀπὸ ποίας γραμμῆς;
SOC. But from what line does the eight-foot area come?
οὐχὶ ἀπὸ μὲν ταύτης τετραπλάσιον;
Is it not a fourfold area from this one?
ΠΑΙ. φημί.
BOY. I agree.
ΣΩ. τετράπουν δὲ ἀπὸ τῆς ἡμισέας ταυτησὶ τουτί;
SOC. And this four-foot area is from the half of this side?
ΠΑΙ. ναί.
BOY. Yes.
ΣΩ. εἶεν·
SOC.
τὸ δὲ ὀκτώπουν οὐ τοῦδε μὲν διπλάσιόν ἐστιν, τούτου δὲ ἥμισυ;
Very well; and is the eight-foot area not double this one, and half of that other one?
ΠΑΙ. ναί.
BOY. Yes.
ΣΩ. οὐκ ἀπὸ μὲν μείζονος ἔσται ἢ τοσαύτης γραμμῆς, ἀπὸ ἐλάττονος δὲ ἢ τοσησδί;
SOC. Will it not then come from a line larger than this one, but smaller than that one?
ἢ οὔ;
Or not?
ΠΑΙ. ἔμοιγε δοκεῖ οὕτω.
BOY. It seems so to me.
ΣΩ. καλῶς·
SOC.
τὸ γάρ σοι δοκοῦν τοῦτο ἀποκρίνου. καί μοι λέγε·
Excellent; answer what seems so to you.
οὐχ ἥδε μὲν δυοῖν ποδοῖν ἦν, ἡ δὲ τεττάρων;
And tell me: was this line not of two feet, and that other of four?
ΠΑΙ. ναί.
BOY. Yes.
ΣΩ. δεῖ ἄρα τὴν τοῦ ὀκτώποδος χωρίου γραμμὴν μείζω μὲν εἶναι τῆσδε τῆς δίποδος, ἐλάττω δὲ τῆς τετράποδος.
SOC. Therefore, the line of the eight-foot area must be longer than this two-foot line, but shorter than the four-foot one.
ΠΑΙ. δεῖ.
BOY. It must.
ΣΩ. πειρῶ δὴ λέγειν πηλίκην τινὰ φῂς αὐτὴν εἶναι.
SOC. Try now to tell me how long you say it is.
ΠΑΙ. τρίποδα.
BOY. Three feet.
ΣΩ. οὐκοῦν ἄνπερ τρίπους ᾖ, τὸ ἥμισυ ταύτης προσληψόμεθα καὶ ἔσται τρίπους;
SOC. Therefore, if it is three feet, we shall add half of this line and it will be three feet?
δύο μὲν γὰρ οἵδε, ὁ δὲ εἷς· καὶ ἐνθένδε ὡσαύτως δύο μὲν οἵδε, ὁ δὲ εἷς· καὶ γίγνεται τοῦτο τὸ χωρίον ὃ φῄς.
For these are two feet, and this is one; and on that side likewise, these are two, and this is one; and this produces the area you mean.
ΠΑΙ. ναί.
BOY. Yes.
ΣΩ. οὐκοῦν ἂν ᾖ τῇδε τριῶν καὶ τῇδε τριῶν, τὸ ὅλον χωρίον τριῶν τρὶς ποδῶν γίγνεται;
SOC. Therefore, if it is three feet this way and three feet that way, does the whole area not become three times three feet?
ΠΑΙ. φαίνεται.
BOY. It appears so.
ΣΩ. τρεῖς δὲ τρὶς πόσοι εἰσὶ πόδες;
SOC. And how many feet are three times three?
ΠΑΙ. ἐννέα.
BOY. Nine.
ΣΩ. ἔδει δὲ τὸ διπλάσιον πόσων εἶναι ποδῶν;
SOC. But how many feet was the double area supposed to be?
ΠΑΙ. ὀκτώ.
BOY. Eight.
ΣΩ. οὐδʼ ἄρʼ ἀπὸ τῆς τρίποδός πω τὸ ὀκτώπουν χωρίον γίγνεται.
SOC. Therefore, the eight-foot area does not come from the three-foot line either.
ΠΑΙ. οὐ δῆτα.
BOY. Certainly not.
§84ΣΩ. ἀλλʼ ἀπὸ ποίας;
SOC. But from what line?
πειρῶ ἡμῖν εἰπεῖν ἀκριβῶς· καὶ εἰ μὴ βούλει ἀριθμεῖν, ἀλλὰ δεῖξον ἀπὸ ποίας.
Try to tell us precisely; and if you do not want to calculate, at least point out from what line.
ΠΑΙ. ἀλλὰ μὰ τὸν Δία, ὦ Σώκρατες, ἔγωγε οὐκ οἶδα.
BOY. But by Zeus, Socrates, I at least do not know.
ΣΩ. ἐννοεῖς αὖ, ὦ Μένων, οὗ ἐστιν ἤδη βαδίζων ὅδε τοῦ ἀναμιμνῄσκεσθαι;
SOC. Do you notice again, Meno, where he is now on the path of recollecting?
ὅτι τὸ μὲν πρῶτον ᾔδει μὲν οὔ, ἥτις ἐστὶν ἡ τοῦ ὀκτώποδος χωρίου γραμμή, ὥσπερ οὐδὲ νῦν πω οἶδεν, ἀλλʼ οὖν ᾤετό γʼ αὐτὴν τότε εἰδέναι, καὶ θαρραλέως ἀπεκρίνετο ὡς εἰδώς, καὶ οὐχ ἡγεῖτο ἀπορεῖν·
At first he did not know, just as he still does not know now, what the line of the eight-foot area is; yet at that time he thought he knew it, and answered confidently as if he knew, and did not think he was at a loss.
νῦν δὲ ἡγεῖται ἀπορεῖν ἤδη, καὶ ὥσπερ οὐκ οἶδεν, οὐδʼ οἴεται εἰδέναι.
But now he feels that he is at a loss, and just as he does not know, so he does not even think he knows.
ΜΕΝ. ἀληθῆ λέγεις.
MEN. You speak the truth.
ΣΩ. οὐκοῦν νῦν βέλτιον ἔχει περὶ τὸ πρᾶγμα ὃ οὐκ ᾔδει;
SOC. Therefore, is he not now in a better position regarding the matter which he did not know?
ΜΕΝ. καὶ τοῦτό μοι δοκεῖ.
MEN. That also seems so to me.
ΣΩ. ἀπορεῖν οὖν αὐτὸν ποιήσαντες καὶ ναρκᾶν ὥσπερ ἡ νάρκη, μῶν τι ἐβλάψαμεν;
SOC. In making him hesitate and making him numb like the numb-fish, have we done him any harm?
ΜΕΝ. οὐκ ἔμοιγε δοκεῖ.
MEN. Not to me at least.
ΣΩ. προὔργου γοῦν τι πεποιήκαμεν, ὡς ἔοικε, πρὸς τὸ ἐξευρεῖν ὅπῃ ἔχει·
SOC. At any rate, we have done something useful, as it seems, for discovering how the matter stands.
νῦν μὲν γὰρ καὶ ζητήσειεν ἂν ἡδέως οὐκ εἰδώς, τότε δὲ ῥᾳδίως ἂν καὶ πρὸς πολλοὺς καὶ πολλάκις ᾤετʼ ἂν εὖ λέγειν περὶ τοῦ διπλασίου χωρίου, ὡς δεῖ διπλασίαν τὴν γραμμὴν ἔχειν μήκει.
For now he would search gladly since he does not know, whereas then he would easily have thought he spoke well, even before many people and many times, about the double area, saying that it must have a line of double length.
ΜΕΝ. ἔοικεν.
MEN. It seems so.
ΣΩ. οἴει οὖν ἂν αὐτὸν πρότερον ἐπιχειρῆσαι ζητεῖν ἢ μανθάνειν τοῦτο ὃ ᾤετο εἰδέναι οὐκ εἰδώς, πρὶν εἰς ἀπορίαν κατέπεσεν ἡγησάμενος μὴ εἰδέναι, καὶ ἐπόθησεν τὸ εἰδέναι;
SOC. Do you think, then, that he would have attempted to search or learn this which he thought he knew though he did not know, before he fell into difficulty and realized he did not know, and longed to know?
ΜΕΝ. οὔ μοι δοκεῖ, ὦ Σώκρατες.
MEN. It does not seem so to me, Socrates.
ΣΩ. ὤνητο ἄρα ναρκήσας;
SOC. Was he benefited, then, by being numb?
ΜΕΝ. δοκεῖ μοι.
MEN. It seems so to me.
ΣΩ. σκέψαι δὴ ἐκ ταύτης τῆς ἀπορίας ὅτι καὶ ἀνευρήσει ζητῶν μετʼ ἐμοῦ, οὐδὲν ἀλλʼ ἢ ἐρωτῶντος ἐμοῦ καὶ οὐ διδάσκοντος·
SOC. Now watch how from this state of difficulty he will also discover, by searching with me, while I do nothing but ask questions and do not teach.
φύλαττε δὲ ἄν που εὕρῃς με διδάσκοντα καὶ διεξιόντα αὐτῷ, ἀλλὰ μὴ τὰς τούτου δόξας ἀνερωτῶντα.
Watch if you find me teaching and explaining to him, instead of asking for his own opinions.
λέγε γάρ μοι σύ· οὐ τὸ μὲν τετράπουν τοῦτο ἡμῖν ἐστι χωρίον;
Now, you tell me: is this not our four-foot area?
μανθάνεις;
Do you understand?
ΠΑΙ. ἔγωγε.
BOY. Yes.
ΣΩ. ἕτερον δὲ αὐτῷ προσθεῖμεν ἂν τουτὶ ἴσον;
SOC. And we could add to it this other equal area?
ΠΑΙ. ναί.
BOY. Yes.
ΣΩ. καὶ τρίτον τόδε ἴσον ἑκατέρῳ τούτων;
SOC. And a third one here, equal to each of these?
ΠΑΙ. ναί.
BOY. Yes.
ΣΩ. οὐκοῦν προσαναπληρωσαίμεθʼ ἂν τὸ ἐν τῇ γωνίᾳ τόδε;
SOC. Therefore, could we also fill up this corner space?
ΠΑΙ. πάνυ γε.
BOY. Certainly.
ΣΩ. ἄλλο τι οὖν γένοιτʼ ἂν τέτταρα ἴσα χωρία τάδε;
SOC. Would they then become anything else than these four equal areas?
ΠΑΙ. ναί.
BOY. Yes.
ΣΩ. τί οὖν; τὸ ὅλον τόδε ποσαπλάσιον τοῦδε γίγνεται;
SOC. What then? How many times larger than this one does this whole area become?
ΠΑΙ. τετραπλάσιον.
BOY. Four times.
ΣΩ. ἔδει δέ γε διπλάσιον ἡμῖν γενέσθαι· ἢ οὐ μέμνησαι;
SOC. But we were supposed to get a double one; or do you not remember?
ΠΑΙ. πάνυ γε.
BOY. Certainly.