§8.3Ἔστι δ᾿ ἐπιχειρεῖν τε χαλεπὸν καὶ ὑπέχειν ῥᾴδιον τὰς αὐτὰς ὑποθέσεις.
It is possible for the same theses to be difficult to attack and easy to defend.
Ἔστι δὲ τοιαῦτα τά τε φύσει πρῶτα καὶ τὰ ἔσχατα.
Such are those things which are first by nature and those which are ultimate.
Τὰ μὲν γὰρ πρῶτα ὅρου δεῖται, τὰ δ᾿ ἔσχατα διὰ πολλῶν περαίνεται βουλομένῳ τὸ συνεχὲς λαμβάνειν ἀπὸ τῶν πρώτων, ἢ σοφισματώδη φαίνεται τὰ ἐπιχειρήματα· ἀδύνατον γὰρ ἀποδεῖξαί τι μὴ ἀρξάμενον ἀπὸ τῶν οἰκείων ἀρχῶν καὶ συνείραντα μέχρι τῶν ἐσχάτων.
For the first things require definition, while the ultimates are concluded through many steps if one wishes to grasp the continuous line from the first things, or else the arguments appear sophistical; for it is impossible to demonstrate anything without starting from the appropriate principles and linking them together all the way to the ultimates.
Ὁρίζεσθαι μὲν οὖν οὔτ᾿ ἀξιοῦσιν οἱ ἀποκρινόμενοι, οὔτ᾿ ἂν ὁ ἐρωτῶν ὁρίζηται προσέχουσιν· μὴ γενομένου δὲ φανεροῦ τί ποτ᾿ ἐστὶ τὸ προκείμενον, οὐ ῥᾴδιον ἐπιχειρεῖν.
Now, those who answer do not demand to define, nor do they pay attention if the questioner defines; but when what is proposed is not made clear as to what it is, it is not easy to attack.
Μάλιστα δὲ τὸ τοιοῦτον περὶ τὰς ἀρχὰς συμβαίνει· τὰ μὲν γὰρ ἄλλα διὰ τούτων δείκνυται, ταῦτα δ᾿ οὐκ ἐνδέχεται δι᾿ ἑτέρων, ἀλλ᾿ ἀναγκαῖον ὁρισμῷ τῶν τοιούτων ἕκαστον γνωρίζειν.
And this sort of thing happens especially with regard to the principles; for other things are shown through these, but these cannot be shown through other things, but it is necessary to know each of such things by definition.
Ἔστι δὲ δυσεπιχείρητα καὶ τὰ λίαν ἐγγὺς τῆς ἀρχῆς· οὐ γὰρ ἐνδέχεται πολλοὺς πρὸς αὐτὰ λόγους πορίσασθαι, ὀλίγων ὄντων τῶν ἀνὰ μέσον αὐτοῦ τε καὶ τῆς ἀρχῆς, δι᾿ ὧν ἀνάγκη δείκνυσθαι τὰ μετὰ ταῦτα.
Those things which are extremely close to the principle are also difficult to attack; for it is not possible to provide many arguments against them, since there are few intermediate steps between them and the principle, through which those things after them must be shown.
Τῶν δὲ ὅρων δυσεπιχειρητότατοι πάντων εἰσὶν ὅσοι κέχρηνται τοιούτοις ὀνόμασιν, ἃ πρῶτον μὲν ἄδηλά ἐστιν εἴτε ἁπλῶς εἴτε πολλαχῶς λέγεται, πρὸς δὲ τούτοις μηδὲ γνώριμα πότερον κυρίως ἢ κατὰ μεταφορὰν ὑπὸ τοῦ ὁρισαμένου λέγεται.
And of definitions, the most difficult of all to attack are those that use such names which, in the first place, are unclear as to whether they are said simply or in many ways, and in addition to this, are not even known whether they are said by the definer properly or metaphorically.
Διὰ μὲν γὰρ τὸ ἀσαφῆ εἶναι οὐκ ἔχει ἐπιχειρήματα, διὰ δὲ τὸ ἀγνοεῖσθαι εἰ παρὰ τὸ κατὰ μεταφορὰν λέγεσθαι τοιαῦτ᾿ ἐστίν, οὐκ ἔχει ἐπιτίμησιν.
For on account of being obscure, they do not offer arguments, and on account of not knowing whether they are such because of being said metaphorically, they do not offer grounds for criticism.
Ὅλως δὲ πᾶν πρόβλημα, ὅταν ᾖ δυσεπιχείρητον, ἢ ὅρου δεῖσθαι ὑποληπτέον, ἢ τῶν πολλαχῶς ἢ τῶν κατὰ μεταφορὰν εἶναι λεγομένων, ἢ οὐ πόρρω τῶν ἀρχῶν, ἢ διὰ τὸ μὴ φανερὸν εἶναι πρῶτον ἡμῖν τοῦτ᾿ αὐτό, κατὰ τίνα ποτὲ τῶν εἰρημένων τρόπον ἐστὶν ὃ τὴν ἀπορίαν παρέχεται·
In general, when any problem is difficult to attack, one must suppose either that it needs definition, or that it is among things said in many ways or metaphorically, or that it is not far from the principles, or because of this very thing not being clear to us first, namely, by which of the mentioned ways it is that produces the difficulty.
φανεροῦ γὰρ ὄντος τοῦ τρόπου δῆλον ὅτι ἢ ὁρίζεσθαι ἂν δέοι ἢ διαιρεῖσθαι ἢ τὰς ἀνὰ μέσον προτάσεις πορίζεσθαι· διὰ τούτων γὰρ δείκνυται τὰ ἔσχατα.
For if the way is clear, it is obvious that one would have to either define, or divide, or provide the intermediate premises; for through these the ultimates are shown.
Πολλαῖς τε τῶν θέσεων μὴ καλῶς ἀποδιδομένου τοῦ ὁρισμοῦ οὐ ῥᾴδιον διαλέγεσθαι καὶ ἐπιχειρεῖν, οἷον πότερον ἓν ἑνὶ ἐναντίον ἢ πλείω· ὁρισθέντων δὲ τῶν ἐναντίων κατὰ τρόπον ῥᾴδιον συμβιβάσαι πότερον ἐνδέχεται πλείω τῷ αὐτῷ εἶναι ἐναντία ἢ οὔ.
And in many of the theses, when the definition is not well rendered, it is not easy to debate and attack, as for instance, whether one thing has one contrary or many; but once contraries are defined in a proper way, it is easy to bring to agreement whether it is possible for many contraries to belong to the same thing or not.
Τὸν αὐτὸν δὲ τρόπον καὶ ἐπὶ τῶν ἄλλων τῶν ὁρισμοῦ δεομένων.
And the same way holds also for other things that require definition.
Ἔοικε δὲ καὶ ἐν τοῖς μαθήμασιν ἔνια δι᾿ ὁρισμοῦ ἔλλειψιν οὐ ῥᾳδίως γράφεσθαι, οἷον καὶ ὅτι ἡ παρὰ τὴν πλευρὰν τέμνουσα τὸ ἐπίπεδον ὁμοίως διαιρεῖ τήν τε γραμμὴν καὶ τὸ χωρίον.
And it seems that in mathematics also, some things are not easily demonstrated because of a lack of definition, such as that the line which cuts the plane parallel to the side divides both the line and the area similarly.
Τοῦ δὲ ὁρισμοῦ ῥηθέντος εὐθέως φανερὸν τὸ λεγόμενον· τὴν γὰρ αὐτὴν ἀνταναίρεσιν ἔχει τὰ χωρία καὶ αἱ γραμμαί· ἔστι δ᾿ ὁρισμὸς τοῦ αὐτοῦ λόγου οὗτος.
But when the definition is stated, what is said becomes immediately clear; for the areas and the lines have the same mutual subtraction; and this is the definition of the same ratio.
Ἁπλῶς δὲ τὰ πρῶτα τῶν στοιχείων τιθεμένων μὲν τῶν ὁρισμῶν, οἷον τί γραμμὴ καὶ τί κύκλος, ῥᾷστα δεῖξαι, πλὴν οὐ πολλά γε πρὸς ἕκαστον ἔστι τούτων ἐπιχειρεῖν διὰ τὸ μὴ πολλὰ τὰ ἀνὰ μέσον εἶναι· ἂν δὲ μὴ τιθῶνται οἱ τῶν ἀρχῶν ὁρισμοί, χαλεπόν, τάχα δ᾿ ὅλως ἀδύνατον.
Simply, with regard to the first elements, if the definitions are laid down, as for instance, what a line is and what a circle is, it is easiest to demonstrate them, except that one cannot make many attacks against each of these, because there are not many intermediate steps; but if the definitions of the principles are not laid down, it is difficult, and perhaps altogether impossible.
Ὁμοίως δὲ τούτοις καὶ ἐπὶ τῶν κατὰ τοὺς λόγους ἔχει.
And it is the same with these as it is with matters concerning arguments.
Οὔκουν δεῖ λανθάνειν, ὅταν δυσεπιχείρητος ᾖ ἡ θέσις, ὅτι πέπονθέ τι τῶν εἰρημένων.
Therefore, it must not escape notice, when the thesis is difficult to attack, that it has suffered one of the things mentioned.
Ὅταν δ᾿ ᾖ πρὸς τὸ ἀξίωμα καὶ τὴν πρότασιν μεῖζον ἔργον διαλεγῆναι ἢ τὴν θέσιν, διαπορήσειεν ἄν τις πότερον θετέον τὰ τοιαῦτα ἢ οὔ.
But when it is a greater task to debate against the axiom and the premise than against the thesis, one might raise a difficulty whether such things should be granted or not.
Εἰ γὰρ μὴ θήσει ἀλλ᾿ ἀξιώσει καὶ πρὸς τοῦτο διαλέγεσθαι, μεῖζον προστάξει τοῦ ἐν ἀρχῇ κειμένου· εἰ δὲ θήσει, πιστεύσει ἐξ ἧττον πιστῶν.
For if he does not grant it but demands to debate against this too, he will enjoin a greater task than what was laid down in the beginning; but if he grants it, he will believe on the basis of things less believable.
Εἰ μὲν οὖν δεῖ μὴ χαλεπώτερον τὸ πρόβλημα ποιεῖν, θετέον, εἰ δὲ διὰ γνωριμωτέρων συλλογίζεσθαι, οὐ θετέον· ἢ τῷ μὲν μανθάνοντι οὐ θετέον, ἂν μὴ γνωριμώτερον ᾖ, τῷ δὲ γυμναζομένῳ θετέον, ἂν ἀληθὲς μόνον φαίνηται.
If, therefore, one must not make the problem more difficult, it should be granted, but if one must reason through things more familiar, it should not be granted; or rather, for the learner it should not be granted unless it is more familiar, but for the one who is practicing it should be granted if only it appears true.
Ὥστε φανερὸν ὅτι οὐχ ὁμοίως ἐρωτῶντί τε καὶ διδάσκοντι ἀξιωτέον τιθέναι.
So it is clear that one must not demand to grant things in the same way when questioning as when teaching.