ἔστι γάρ ὡς ὑπολαμβάνουσι Δελφοὶ καὶ τότε προηγορῶν ἔλεγε Νίκανδρος ὁ ἱερεὺς σχῆμα καὶ μορφὴ τῆς πρὸς τὸν, θεὸν ἐντεύξεως, καὶ τάξιν ἡγεμονικὴν ἐν τοῖς ἐρωτήμασιν ἔχει τῶν χρωμένων ἑκάστοτε καὶ διαπυνθανομένων, εἰ νικήσουσιν, εἰ γαμήσουσιν, εἰ συμφέρει πλεῖν, εἰ γεωργεῖν, εἰ ἀποδημεῖν. τοῖς δὲ διαλεκτικοῖς χαίρειν ἔλεγε σοφὸς ὁ θεός, οὐδὲν οἰομένοις ἐκ τοῦ εἰ μορίου καὶ τοῦ μετʼ αὐτοῦ ἀξιώματος πρᾶγμα γίγνεσθαι, πάσας τὰς ἐρωτήσεις ὑποτεταγμένας τούτῳ καὶ νοῶν ὡς πράγματα καὶ προσιέμενος. ἐπεὶ δʼ ἴδιον τὸ ἐρωτᾶν ὡς μάντιν ἐστὶν ἡμῖν καὶ τὸ εὔχεσθαι κοινὸν ὡς πρὸς θεὸν, οὐχ ἧττον οἴονται τῆς πευστικῆς τὴν εὐκτικὴν τὸ γράμμα περιέχειν δύναμιν· εἰ γὰρ ὤφελον φησὶν ἕκαστος τῶν εὐχομένων. καὶ Ἀρχίλοχος εἰ γὰρ ὣς ἐμοὶ γένοιτο χεῖρα Νεοβούλης θιγεῖν. καὶ τοῦ εἴθε τὴν δευτέραν συλλαβὴν παρέλκεσθαί φασιν, οἷον τὸ Σώφρονος ἃμα τέκνων θην δευομένα· καὶ τὸ Ὁμηρικὸν ὥς θην καὶ σὸν ἐγὼ λύσω μένος· ἐν δὲ τῷ εἰ τὸ εὐκτικὸν καὶ ἀποχρώντως δηλοῦσθαι.
For the syllable EI (if) is, as the Delphians conceive it, and as Nicander the priest (who was then present) also said, a conveyance and form of prayer to the God, and has the leading place in the questions of those who at every turn use it, asking if they shall overcome, if they shall marry, if it is convenient to go to sea, if to till the ground, if to travel. And the wise God, bidding adieu to the logicians, who think nothing at all can be made of this particle EI and any clause following it, understands and admits all interrogations annexed to it, as real things. Now, because it is proper for us to consult him as a prophet, and common to pray to him as a God, they suppose that this word has no less a precatory than an interrogatory power. For every one who prays or wishes says, εἰ γὰρ ὤφελον, O if I were, c. And Archilochus has also this expression: If I might be so happy as to touch / My Neobule’s hand. / And they say that the second syllable in the word εἴθε is redundant like θήν in this of Sophron, Ἅμα τέκνων θὴν δευομένα, desiring also children; and in this of Homer, Ὡς θὴν καὶ σὸν ἐγὼ λύσω μένος, as I will also foil thy strength; but in the word EI there is sufficiently declared an optative power.
ταῦτα τοῦ Νικάνδρου διελθόντος, οἶσθα γὰρ δὴ Θέωνα τὸν ἑταῖρον, ἤρετο τὸν Ἀμμώνιον, εἰ διαλεκτικῇ παρρησίας μέτεστιν οὕτω περιυβρισμένῃ ἀκηκουίᾳ· τοῦ δʼ Ἀμμωνίου λέγειν παρακελευομένου καὶ βοηθεῖν, ἀλλʼ ὅτι μέν ἔφη διαλεκτικώτατος ὁ θεός ἐστιν, οἱ πολλοὶ τῶν χρησμῶν δηλοῦσιν τοῦ γὰρ αὐτοῦ δήπουθέν ἐστι καὶ λύειν καὶ ποιεῖν ἀμφιβολίας. ἔτι δʼ, ὥσπερ Πλάτων ἔλεγε, χρησμοῦ δοθέντος ὅπως τὸν ἐν Δήλῳ βωμὸν διπλασιάσωσιν, ὃ τῆς ἄκρας; ἕξεως περὶ γεωμετρίαν ἔργον ἐστίν, οὐ τοῦτο προστάττειν τὸν θεὸν ἀλλὰ καὶ γεωμετρεῖν διακελεύεσθαι τοῖς Ἕλλησιν · οὕτως ἄρα χρησμοὺς ἀμφιβόλους ἐκφέρων ὁ θεὸς αὔξει καὶ συνίστησι διαλεκτικὴν ὡς ἀναγκαίαν τοῖς μέλλουσιν ὀρθῶς αὐτοῦ συνήσειν. ἐν δὲ διαλεκτικῇ δήπου μεγίστην ἔχει δύναμιν ὁ συναπτικὸς οὑτοσὶ σύνδεσμος, ἅτε δὴ τὸ λογικώτατον σχηματίζων ἀξίωμα · πῶς γὰρ τοιοῦτο τὸ συνημμένον, εἴ γε τῆς μὲν ὑπάρξεως τῶν πραγμάτων ἔχει καὶ τὰ θηρία γνῶσιν, ἀκολούθου δὲ θεωρίαν καὶ κρίσιν ἀνθρώπῳ μόνῳ παραδέδωκεν ἡ φύσις; ὅτι γάρ ἡμέρα καὶ φῶς ἔστιν αἰσθάνονται δήπου καὶ λύκοι καὶ κύνες καὶ ὄρνιθες· ὅτι δʼ εἰ ἡμέρα, φῶς ἔστιν οὐδὲν ἄλλο συνίησι πλὴν ἄνθρωπος, ἡγουμένου καὶ λήγοντος ἐμφάσεώς τε καὶ συναρτήσεως τούτων πρὸς ἄλληλα καὶ σχέσεως καὶ διαφορᾶς μόνος ἔχων ἔννοιαν, ἐξ αἱ ἀποδείξεις τὴν κυριωτάτην ἀρχὴν λαμβάνουσιν. ἐπεὶ τοίνυν φιλοσοφία μέν ἐστι περὶ ἀλήθειάν ἀληθείας δὲ φῶς ἀπόδειξις ἀποδείξεως δʼ ἀρχὴ τὸ συνημμένον, εἰκότως ἡ τοῦτο συνέχουσα καὶ ποιοῦσα δύναμις ὑπὸ σοφῶν ἀνδρῶν τῷ μάλιστα τὴν ἀλήθειαν ἠγαπηκότι θεῷ καθιερώθη· καὶ μάντις μὲν ὁ θεὸς μαντικὴ δὲ τέχνη περὶ τὸ μέλλον ἐκ τῶν παρόντων ἢ παρῳχημένων. οὐδενὸς γὰρ. οὔτʼ ἀναίτιος ἡ γένεσις οὔτʼ ἄλογος ἡ πρόγνωσις· ἀλλʼ ἐπεὶ πάντα τοῖς γεγονόσι τὰ γιγνόμενα τά τε γενησόμενα τοῖς γιγνομένοις ἕπεται καὶ συνήρτηται κατὰ διέξοδον ἀπʼ ἀρχῆς εἰς τέλος περαίνουσαν, ὁ τὰς αἰτίας εἰς ταὐτὸ συνδεῖν τε πρὸς ἄλληλα καὶ συμπλέκειν φυσικῶς ἐπιστάμενος οἶδε καὶ προλέγειν τὰ τʼ ἐόντα τὰ τʼ ἐσσόμενα πρὸ τʼ ἐόντα. καὶ καλῶς Ὅμηρος πρῶτον ἔταξε τὰ παρόντα εἶτα τὸ μέλλον καὶ τὸ παρῳχημένον· ἀπὸ γὰρ τοῦ ὄντος ὁ συλλογισμὸς κατὰ τὴν τοῦ συνημμένου δύναμιν, ὡς εἰ τόδʼ ἐστί, τόδε προηγεῖται καὶ πάλιν εἰ τόδʼ ἐστί, τόδε γενήσεται τὸ γὰρ τεχνικὸν καὶ λογικὸν ὥσπερ εἴρηται γνῶσις ἀκολουθίας, τὴν δὲ πρόσληψιν ἡ αἴσθησις τῷ λόγῳ δίδωσιν. ὅθεν, εἰ καὶ γλίσχρον εἰπεῖν, οὐκ ἀποστρέψομαι τοῦτον εἶναι τὸν τῆς ἀληθείας τρίποδα τὸν λόγον, ὃς τὴν τοῦ λήγοντος πρὸς τὸ προηγούμενου ἀκολουθίαν θέμενος εἶτα προσλαβὼν τὴν ὕπαρξιν ἐπάγει τὸ συμπέρασμα τῆς ἀποδείξεως. τὸν οὖν Πύθιον, εἰ δὴ μουσικῇ θʼ ἣδεται καὶ κύκνων φωναῖς καὶ κιθάρας ψόφοις, τί θαυμαστόν ἐστι διαλεκτικῆς φιλίᾳ τοῦτʼ ἀσπάζεσθαι τοῦ λόγου τὸ μέρος καὶ ἀγαπᾶν, ᾧ μάλιστα καὶ πλείστῳ προσχρωμένους ὁρᾷ τοὺς φιλοσόφους; ὁ δʼ Ἡρακλῆς, οὔπω τὸν Προμηθέα λελυκὼς οὐδὲ τοῖς περὶ τὸν Χείρωνα καὶ Ἄτλαντα σοφισταῖς διειλεγμένος ἀλλὰ νέος ὢν καὶ κομιδῇ Βοιώτιος, ἀναιρῶν τὴν διαλεκτικὴν καὶ καταγελῶν τοῦ εἰ τὸ πρῶτον, τὸ δεύτερον ὑποσπᾶν ἔδοξε βίᾳ τὸν τρίποδα καὶ διαμάχεσθαι πρὸς τὸν θεὸν ὑπὲρ τῆς τέχνης· ἐπεὶ προϊών γε τῷ χρόνῳ καὶ οὗτος ἔοικε μαντικώτατος ὁμοῦ γενέσθαι καὶ διαλεκτικώτατος.
Nicander having delivered these words, our friend Theon, whom you know, asked Ammonius if he might have liberty to plead for logic, which was so highly injured. And Ammonius bidding him speak and defend it, he said: Now that this God is a most expert logician many of his oracles show; for it is, to wit, the part of the same artist to dissolve and frame ambiguities. Moreover, as Plato said, when an oracle was given to the Greeks that they should double the altar in Delos, which is a work of the utmost perfection in geometry, that the God did not order the doing of that very thing, but commanded the Greeks to apply themselves to geometry; so the same God, by giving ambiguous oracles, honors and recommends logic, as necessary to those who desire to understand him aright. Now this conjunction El, or if, has a very great efficacy in logic, as forming the most rational proposition; for how can it be otherwise, since the very brutes have indeed the knowledge of the substance of things, but to man only has Nature given the consideration and judgment of consequence? For that there is both day and light, wolves and dogs and birds are sensible. But that if it is day there must be light, no other animal understands but man, who only has the conception of antecedent and consequent, of the significance and connection of these things with one another, and of their habitude and difference, from which demonstrations take their principal beginnings. Now since philosophy is conversant about truth, since the light of truth is demonstration, and the beginning of demonstration this connection of propositions; the faculty which contains and effects this was by wise men, with good reason, consecrated to the God who most of all loves truth. Now the God indeed is a prophet, and the art of prophesying is a divination concerning the future from things that are present and past. For neither is the original of any thing without a cause, nor the foreknowledge of any thing without reason. But since all things that are done follow and are connected to those that have been done, and those that shall be done to those that are done, according to the progress proceeding from the beginning to the end; he who knows how to look into the causes of this together, and naturally connect them one with another, knows also and divines What things now are, shall be, or e’er have been. And Homer indeed excellently well places first things that are present, and afterwards what is future and past. For by the very nature of the connection the argument is based on that which now is. Thus, if this is, that preceded; and again, if this is, that shall be. For the knowledge of the consequence is, as has been said, an artificial and rational thing; but sense gives the assumption to reason. Whence (though it may seem indecent to say it) I will not be afraid to aver this, that the tripod of truth is reason, which recognizes the dependence of the consequent on the antecedent, and then, assuming the reality of the antecedent, infers the conclusion of the demonstration. If then the Pythian Apollo delights in music, and is pleased with the singing of swans and the harmony of the lute, what wonder is it that, for the sake of logic, he embraces and loves this argumentative particle, which he sees the philosophers so much and so frequently to use? Hercules indeed, not having yet unbound Prometheus, nor conversed with the sophisters that were with Chiron and Atlas, but being still a young man and a plain Boeotian, at first abolished logic and derided this word EI; but afterwards he seemed by force to have seized on the tripod, and contended with our God himself for the pre-eminence in this art; for being grown up in age, he appeared to be the most expert both in divination and logic.
παυσαμένου δὲ τοῦ Θέωνος, Εὔστροφον Ἀθηναῖον οἶμαι τὸν εἰπόντα εἶναι πρὸς ἡμᾶς ὁρᾷς, ὡς ἀμύνει τῇ διαλεκτικῇ Θέων προθύμως, μονονοὺ τὴν λεοντῆν ἐπενδυσάμενος; οὕτως οὐδʼ ἡμᾶς τοὺς πάντα συλλήβδην πράγματα καὶ φύσεις καὶ ἀρχὰς θείων ὁμοῦ καὶ ἀνθρωπείων ἐν ἀριθμῷ τιθεμένους, καὶ πολὺ μάλιστα τῶν καλῶν καὶ τιμίων τοῦτον ἡγεμόνα ποιουμένους καὶ κύριον, εἰκὸς ἡσυχίαν ἄγειν, ἀλλʼ ἀπάρξασθαι τῷ θεῷ τῆς φίλης μαθηματικῆς, αὐτὸ μὲν ἐφʼ ἑαυτοῦ μήτε δυνάμει μήτε μορφῇ μήτε τῷ ῥήματι τὸ Ε τῶν ἄλλων στοιχείων διαφέρειν ἡγουμένους, ὡς δὲ μεγάλου πρὸς τὰ ὅλα καὶ κυρίου σημεῖον ἀριθμοῦ τετιμῆσθαι τῆς πεμπάδος, ἀφʼ οὗ τὸ ἀριθμεῖν οἱ σοφοὶ πεμπάζειν ὠνόμαζον. ταῦτα δὲ πρὸς ἡμᾶς ἔλεγεν οὐ παίζων ὁ Εὔστροφος, ἀλλʼ ἐπεὶ τηνικαῦτα προσεκείμην τοῖς μαθήμασιν ἐμπαθῶς, τάχα δʼ ἔμελλον εἰς πάντα τιμήσειν τὸ μηδὲν ἄγαν ἐν Ἀκαδημείᾳ γενόμενος.
Theon having ended his speech, I think it was Eustrophus the Athenian who said to us: Do you not see how valiantly Theon vindicates logic, having, in a manner, got on the lion’s skin? So it is not right even for us—who comprehensively place all the affairs, nature, and principles of things both divine and human in number, and make it most especially the author and lord of honest and estimable things—to be at quiet, but we must willingly offer the first-fruits of our dear mathematics to the God; since we think that this letter E does not of itself differ from the other letters either in power, figure, or expression, but that it has been preferred as being the sign of that great number which has an influence over all things, called the Quinary (or Pemptas), from which the Sages have expressed the art of numbering by the verb πεμπτάζειν (signifying to account by fives). Now Eustrophus spake these things to us, not in jest, but because I did at that time studiously apply myself to the mathematics, and perhaps also in every thing to honor that saying, Nothing too much, as having been conversant in the Academy.
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