---
title: "The E at Delphi · De E apud Delphos"
author: "Plutarch"
translator: "R. Kippax, rev. William W. Goodwin"
languages: [grc, en]
shelf: "Philosophy"
section: 1 of 2
url: https://scriptura.si/works/plutarch-e-at-delphi/1/
cite: "Plutarch, tr. R. Kippax, rev. William W. Goodwin, The E at Delphi · De E apud Delphos, section 1. Scriptura (scriptura.si), https://scriptura.si/works/plutarch-e-at-delphi/1/"
---

# The E at Delphi · De E apud Delphos

*Plutarch, tr. R. Kippax, rev. William W. Goodwin*

What does the letter E carved at Delphi mean? A dialogue that ends in “Thou art”: the being of the god.

> Greek: ed. Grēgorios N. Vernardakēs, from the Perseus Digital Library (canonical-greekLit, tlg0007.tlg090, CC BY-SA 4.0).

> English: R. Kippax, rev. William W. Goodwin, from the Perseus Digital Library (tlg0007.tlg090.perseus-eng4). Notes are not included.

> Rows follow the references the two texts share (chapters and sections), cut where both reach the end of a sentence.

## 1. Sections 1–10

Source: https://scriptura.si/works/plutarch-e-at-delphi/1/ · cite a paragraph as https://scriptura.si/works/plutarch-e-at-delphi/1/#p-N

[¶0] 1. I HAPPENED not long since, dear Serapion, on certain not unelegant verses, which Dicaearchus supposes Euripides to have spoken to King Archelaus:
I’m poor, you rich, I’ll therefore nothing give;
Lest me or fool or beggar you believe.
For he who out of his little estate makes small presents to those that have great possessions does them no pleasure; nay, being not believed to give even that little for nothing, he incurs the suspicion of being of a sordid and ungenerous disposition. But since pecuniary presents are both in bounty and beauty far inferior to such as proceed from learning and wisdom, it is honorable both to make such presents, and at our giving them, to desire suitable returns from the receivers. I therefore, sending to you,—and through you to our friends in those parts,—as a first-fruit offering, some discourses concerning the Pythian affairs, confess that I do in requital expect others, both more and better, from you, as being persons conversant in a great city, and enjoying more leisure amongst many books and conferences of all sorts. For indeed our good Apollo seems to cure and solve such difficulties as occur in the ordinary management of our life, by giving his oracles to those that resort to him; but as for those which concern learning, he leaves and proposes them to that faculty of the soul which is naturally addicted to the study of philosophy, imprinting in it a desire leading to truth; as is manifest both in many other matters. and in the consecration of this inscription EI. For it is not probable. that it was by chance or by a lottery (as it were) of letters that this word alone was placed in the principal seat in the God’s temple, and received the dignity of a sacred donary and spectacle; but it is highly credible that those who at the beginning philosophized concerning this God gave it that station, either as. seeing it in some peculiar and extraordinary power, or using it as a symbol to signify some other thing worthy of our attention. Having therefore often formerly declined and avoided this discourse, when proposed in the school, I was lately surprised by my own children as I was debating with certain strangers, who were on their departure out of Delphi, so that I could not in civility hold them in suspense nor yet refuse discoursing with them, since they were exceeding earnest to hear something. Being therefore set down by the temple, I began myself to search into some things, and to ask them concerning others, being by the place and the very talk put in mind of those things we had heretofore, when Nero passed through these parts, heard Ammonius and some others discourse; the same difficulty having been then likewise in this very place propounded.

> Greek: 1. στιχιδίοις τισὶν οὐ φαύλως ἔχουσιν, ὦ φίλε Σαραπίων, ἐνέτυχον πρῴην, ἃ Δικαίαρχος Εὐριπίδην οἴεται πρὸς Ἀρχέλαον εἰπεῖν·
ʼοὐ βούλομαι πλουτοῦντι. δωρεῖσθαι πένης,
μὴ μʼ ἄφρονα κρίνῃς ἢ διδοὺς αἰτεῖν δοκῶ.
χαρίζεται; μὲν γὰρ οὐδὲν ὁ διδοὺς ἀπʼ ὀλίγων μικρὰ τοῖς πολλὰ κεκτημένοις, ἀπιστούμενος δʼ ἀντὶ μηδενὸς διδόναι κακοηθείας καὶ ἀνελευθερίας προσλαμβάνει δόξαν. ὅρα δὴ ὅσον ἐλευθεριότητι καὶ κάλλει τὰ χρηματικὰ δῶρα λείπεται τῶν ἀπὸ λόγου σοφίας, ἃ καὶ διδόναι καλόν ἐστι καὶ διδόντας ἀνταιτεῖν ὅμοια παρὰ τῶν λαμβανόντων. ἐγὼ γοῦν πρὸς σὲ καὶ διὰ σὲ τοῖς αὐτόθι φίλοις τῶν Πυθικῶν λόγων ἐνίους ὥσπερ ἀπαρχὰς; ἀποστέλλων, ὁμολογῶ προσδοκᾶν ἑτέρους καὶ πλείονας καὶ βελτίονας παρʼ ὑμῶν, ἅτε δὴ καὶ πόλει χρωμένων μεγάλῃ καὶ σχολῆς μᾶλλον ἐν βιβλίοις πολλοῖς καὶ παντοδαπαῖς διατριβαῖς εὐπορούντων. ὁ δʼ οὖν φίλος Ἀπόλλων ἔοικε τὰς μὲν περὶ τὸν βίον ἀπορίας ἰᾶσθαι καὶ διαλύειν θεμιστεύων τοῖς χρωμένοις, τὰς δὲ περὶ τὸν λόγον αὐτὸς ἐνιέναι καὶ προβάλλειν τῷ φύσει φιλοσόφῳ, τῆ ψυχῇ ὄρεξιν ἐμποιῶν ἀγωγὸν ἐπὶ τὴν ἀλήθειαν, ὡς ἄλλοις τε πολλοῖς δῆλόν ἐστι καὶ τῇ τοῦ Ε καθιερώσει. τοῦτο γὰρ εἰκὸς οὐ κατὰ τύχην οὐδʼ οἷον ἀπὸ κλήρου τῶν γραμμάτων μόνον ἐν προεδρίᾳ παρὰ τῷ θεῷ γενέσθαι καὶ λαβεῖν ἀναθήματος τάξιν ἱεροῦ καὶ θεάματος ἀλλʼ ἢ δύναμιν αὐτοῦ κατιδόντας ἰδίαν καὶ περιττὴν ἢ συμβόλῳ χρωμένους πρὸς ἕτερόν τι τῶν ἀξίων σπουδῆς τοὺς ἐν ἀρχῇ περὶ τὸν θεὸν φιλοσοφήσαντας, οὕτω προσέσθαι. πολλάκις οὖν ἄλλοτε τὸν λόγον ἐν τῇ σχολῇ προβαλλόμενον ἐκκλίνας ἀτρέμα καὶ παρελθὼν, ἔναγχος ὑπὸ τῶν υἱῶν ἐλήφθην ξένοις τισὶ συμφιλοτιμούμενος, οὓς εὐθὺς ἐκ Δελφῶν ἀπαίρειν μέλλοντας οὐκ ἦν εὐπρεπὲς παράγειν οὐδὲ παραιτεῖσθαι, πάντως ἀκοῦσαί τι προθυμουμένους. ὡς δὲ καθίσας παρὰ τὸν νεὼν τὰ μὲν αὐτὸς ἠρξάμην ζητεῖν, τὰ δʼ ἐκείνους ἐρωτᾶν, ὑπὸ τοῦ τόπου καὶ τῶν λόγων αὐτῶν· ἃ πάλαι ποτὲ καθʼ ὃν καιρὸν ἐπεδήμει Νέρων ἠκούσαμεν Ἀμμωνίου καί τινων ἄλλων διεξιόντων, ἐνταῦθα τῆς αὐτῆς ἀπορίας ὁμοίως ἐμπεσούσης.

[¶1] 2. Since therefore this God is no less a philosopher than a prophet, Ammonius seemed to all of us rightly to apply every one of his names to this purpose, and to teach that he is Pythius (or a questionist) to those who begin to learn and enquire; Delius and Phanaeus (or a manifester and prover) to those to whom somewhat of the truth is already manifest and shines forth; Ismenius (or knowing) to those that have acquired knowledge; and Leschenorius (or discoursing) when they practise and enjoy their science, making use of it to discourse and philosophize with one another. Now, forasmuch as to philosophize implies to enquire, to wonder, and to doubt, it is probable (he said) that many of the things that concern God are not unfitly concealed under enigmas, and require that one should ask the reason why, and seek to be instructed in the causes, —as, why of all wood fir only is burnt in the eternal fire, why the laurel only is used in fumigations, why there are erected but two statues of the Fates, they being everywhere else thought to be three, why no woman is permitted to have access to the oracle, what is the reason of the tripod, and other such like things, which, being proposed to those who are not altogether irrational and soulless, allure and incite them to consider, hear, and discourse something about them. And do but behold how many questions these inscriptions, “Know thyself” and “Nothing too much,” have set afoot amongst the philosophers, and what a multitude of discourses has sprung up from each of them, as from a seed; than neither of which, I think the matter now in question to be less fruitful.

> Greek: 2. ὅτι μὲν γὰρ οὐχ ἧττον ὁ θεὸς φιλόσοφος ἢ μάντις, ἐδόκει πᾶσιν ὀρθῶς πρὸς τοῦτο τῶν ὀνομάτων ἕκαστον Ἀμμώνιος τίθεσθαι καὶ διδάσκειν, ὡς Πύθιος μέν ἐστι τοῖς ἀρχομένοις μανθάνειν καὶ διαπυνθάνεσθαι· Δήλιος δὲ καὶ Φαναῖος οἷς ἤδη τι δηλοῦται καὶ ὑποφαίνεται τῆς ἀληθείας· Ἰσμήνιος δὲ τοῖς ἔχουσι τὴν ἐπιστήμην, καὶ Λεσχηνόριος ὅταν ἐνεργῶσι καὶ ἀπολαύωσι χρώμενοι τῷ διαλέγεσθαι καὶ φιλοσοφεῖν πρὸς ἀλλήλους. ἐπεὶ δὲ τοῦ φιλοσοφεῖν ἔφη τὸ ζητεῖν τὸ· θαυμάζειν καὶ ἀπορεῖν, εἰκότως τὰ πολλὰ τῶν περὶ τὸν θεὸν ἔοικεν αἰνίγμασι κατακεκρύφθαι, καὶ λόγον τινὰ ποθοῦντα διὰ τί καὶ διδασκαλίαν τῆς αἰτίας· οἷον ἐπὶ τοῦ πυρὸς τοῦ ἀθανάτου, τὸ κάεσθαι μόνον αὐτόθι τῶν, ξύλων ἐλάτην καὶ δάφνην ἐπιθυμιᾶσθαι, καὶ τὸ δύο Μοίρας ἱδρῦσθαι πανταχοῦ τριῶν νομιζομένων, τὸ μηδεμιᾷ γυναικὶ πρὸς τὸ χρηστήριον εἶναι προσελθεῖν· καὶ τὸ τοῦ τρίποδος, καὶ ὅσα τοιαῦτα, τοῖς μὴ παντάπασιν ἀλόγοις καὶ ἀψύχοις ὑφειμένα δελεάζει καὶ παρακαλεῖ πρὸς τὸ σκοπεῖν τι καὶ ἀκούειν καὶ διαλέγεσθαι περὶ αὐτῶν. ὅρα δὲ καὶ ταυτὶ τὰ προγράμματα, τὸ γνῶθι σαυτόν καὶ τὸ μηδὲν ἄγαν, ὅσας ζητήσεις κεκίνηκε φιλοσόφους καὶ ὅσον λόγων πλῆθος ἀφʼ ἑκάστου καθάπερ ἀπὸ σπέρματος ἀναπέφυκεν· ὧν οὐδενὸς ἧττον οἶμαι γόνιμον λόγων εἶναι τὸ νῦν ζητούμενον.

[¶2] 3. Ammonius having spoken thus, Lamprias the Delphian said: The reason indeed which we have heard of this is plain and very short; for they say that those Sages, who were by some called Sophisters, were but five, Chilo, Thales, Solon, Bias, and Pittacus. But after that Cleobulus the tyrant of the Lindians, and Periander the Corinthian, though wholly destitute of virtue and wisdom, had by their power, friends, and courtesy forced a reputation, they usurped the name of Sages, and set forth and dispersed all over Greece certain sentences and sayings, not unlike to those which had been spoken by the five former wise men. The five, however, being discontented at this, would not reprove their arrogancy, nor openly contest and enter into quarrels for glory with men of so great power; but assembling here together, and consulting with one another, they consecrated the letter E, which is in the order of the alphabet the fifth, and signifies five in number, protesting of themselves before the God that they were but five, and rejecting and abdicating the sixth and seventh as not belonging to them. Now that these things are not spoken beside the cushion, any one might understand who should have heard those who have care of the temple naming the golden EI the EI of Livia, the wife of Augustus Caesar; and the brazen one the El of the Athenians; but the first and ancientest of all, which is the wooden one, they call the EI of the Sages, as not being of any one, but the common dedication of them all.

> Greek: 3. εἰπόντος δὲ ταῦτα τοῦ Ἀμμωνίου; Λαμπρίας ὁ ἀδελφὸς εἶπε καὶ μὴν ὃν ἡμεῖς ἀκηκόαμεν λόγον ἁπλοῦς τίς ἐστι καὶ κομιδῇ βραχύς. λέγουσι γὰρ ἐκείνους; τοὺς σοφοὺς ὑπʼ ἐνίων δὲ σοφιστὰς προσαγορευθέντας αὐτοὺς μὲν εἶναι πέντε, Χίλωνα καὶ Θαλῆν καὶ Σόλωνα καὶ Βίαντα καὶ Πιττακόν· ἐπεὶ δὲ Κλεόβουλος ὁ Λινδίων τύραννος, εἶτα Περίανδρος ὁ Κορίνθιος, οὐδὲν αὐτοῖς ἀρετῆς μετὸν οὐδὲ σοφίας, ἀλλὰ δυνάμει καὶ φίλοις καὶ χάρισι καταβιαζόμενοι τὴν δόξαν, ἐνέβαλον εἰς τοὔνομα τῶν σοφῶν καί τινας γνώμας καὶ λόγους ἐξέπεμπον καὶ διέσπειρον εἰς τὴν Ἑλλάδα τοῖς ὑπʼ ἐκείνων λεγομένοις ὁμοίους· δυσχεράναντας ἄρα τοὺς ἄνδρας ἐξελέγχειν μὲν οὐκ ἐθέλειν τὴν ἀλαζονείαν οὐδὲ φανερῶς ὑπὲρ δόξης ἀπεχθάνεσθαι καὶ διαμάχεσθαι πρὸς ἀνθρώπους μέγα δυναμένους, ἐνταῦθα δὲ συνελθόντας αὐτοὺς καθʼ αὑτοὺς καὶ διαλεχθέντας ἀλλήλοις, ἀναθεῖναι τῶν γραμμάτων ὃ τῇ τε τάξει πέμπτον ἐστὶ καὶ τοῦ ἀριθμοῦ τὰ πέντε δηλοῖ, μαρτυρομένους μὲν ὑπὲρ αὑτῶν πρὸς τὸν θεὸν ὅτι πέντʼ εἰσί, τὸν δʼ ἕβδομον καὶ τὸν ἕκτον ἀποποιουμένους καὶ ἀποβάλλοντας ὡς οὐ προσήκοντας αὑτοῖς· ὅτι δʼ οὐκ ἀπὸ σκοποῦ ταῦτα λέγεται, γνοίη τις ἂν ἀκούσας τῶν κατὰ τὸ ἱερὸν τὸ μὲν χρυσοῦν Λιβίοις τῆς Καίσαρος γυναικὸς ὀνομαζόντων, τὸ δὲ χαλκοῦν Ἀθηναίων τὸ δὲ πρῶτον καὶ παλαιότατον τῇ δʼ οὐσίᾳ ξύλινον ἔτι νῦν τῶν σοφῶν καλοῦσιν, ὡς οὐχ ἑνὸς ἀλλὰ κοινὸν ἀνάθημα πάντων γενόμενον.

[¶3] 4. At this Ammonius gently smiled, supposing Lamprias to have delivered an opinion of his own, but to have feigned that he had heard the story from others, lest he might be obliged to give an account of it. But another of those that were present said that this had some affinity with what a certain Chaldean stranger had lately babbled, to wit, that there are in the alphabet seven letters rendering a perfect sound of themselves, and in the heavens seven stars moved by their own proper motion, not bound or linked to that of the others; that E is from the beginning the second in order of the vowels, and the sun the second of the planets, or next to the moon, and that the Greeks do unanimously (so to speak) repute Apollo to be the same with the sun. But these things, said he, wholly savor of his counting-table and his trifling. But Lamprias, it seems, was not sensible of his having stirred up all those of the temple against his discourse. For there was not a man of the Delphians who knew any thing of what he said; but they all alleged the common and current opinion, holding that neither the sight nor the sound of this writing, but the word alone as it was written, contained some symbol or secret signification.

> Greek: 4. ὁ μὲν οὖν Ἀμμώνιος ἡσυχῆ διεμειδίασεν, ὑπονοήσας ἰδίᾳ τὸν Λαμπρίαν δόξῃ κεχρῆσθαι, πλάττεσθαι δʼ, ἱστορίαν καὶ ἀκοὴν ἑτέρων πρὸς τὸ ἀνυπεύθυνον. ἕτερος δέ τις ἔφη τῶν παρόντων, ὡς ὅμοια ταῦτʼ ἐστὶν οἷς πρῴην ὁ Χαλδαῖος ἐφλυάρει ξένος, ἑπτὰ μὲν εἶναι τὰ φωνὴν ἰδίαν ἀφιέντα τῶν γραμμάτων, ἑπτὰ δὲ τοὺς κίνησιν αὐτοτελῆ καὶ ἀσύνδετον ἐν οὐρανῷ κινουμένους ἀστέρας εἶναι δὲ τῇ τάξει δεύτερον τὸ τʼ Ε τῶν φωνηέντων ἀπʼ ἀρχῆς καὶ τὸν ἥλιον ἀπὸ σελήνης τῶν πλανήτων· ἡλίῳ δʼ Ἀπόλλωνα τὸν αὐτὸν ὡς ἔπος εἰπεῖν πάντας Ἕλληνας νομίζειν. ἀλλὰ ταυτὶ μέν ἔφη παντάπασιν ἐκ πίνακος καὶ πυλαίας. ὁ δὲ Λαμπρίας ἔλαθεν, ὡς ἔοικε, τοὺς ἀφʼ ἱεροῦ κινήσας ἐπὶ τὸν αὑτοῦ λόγον. ἃ μὲν γὰρ ἐκεῖνος εἶπεν, οὐδεὶς ἐγίγνωσκε Δελφῶν· τὴν δὲ κοινὴν καὶ περιηγητικὴν δόξαν εἰς τὸ μέσον προῆγον, οὔτε τὴν ὄψιν ἀξιοῦντες οὔτε τὸν φθόγγον ἀλλὰ τοὔνομα μόνον τοῦ γράμματος ἔχειν τι σύμβολον.

[¶4] 5. 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.

> Greek: 5. 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.

[¶5] 6. 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.

> Greek: 6. 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.

[¶6] 7. 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.

> Greek: 7. 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.

[¶7] 8. I answered therefore that Eustrophus has excellently solved the difficulty by number. For (said I) since all number is distributed into even and odd, unity is in efficacy common to them both,—for that being added to an even number, it makes it odd, and to an odd, it makes it even, two constituting the beginning of the even, and three of the odd. Now the number of five, composed of these two, is deservedly honored, as being the first compound made of the first simple numbers, and is called the marriage, for the resemblance of the odd with the male, and the even with the female. For in the divisions of the numbers into equal parts, the even, being wholly separated, leaves a certain capacious beginning and space in itself; but in the odd, suffering the same thing, there always remains a middle, of generative distribution, by which it is more fruitful than the other, and being mixed is always master, never mastered. For by the mixture of both, even and odd together, there is never produced an even number but always an odd. But which is more, either of them added to and compounded with itself shows the difference; for no even joined with another even ever produced an odd, or went forth of its proper nature, being through weakness unable to generate another and imperfect. But odd numbers mixed with odd do, through their being every way fruitful, produce many even ones. Time does not now permit us to set down the other powers and differences of numbers. Therefore have the Pythagoreans, through a certain resemblance, said that five is the marriage of the first male and the first female number. This also is it for which it is called Nature, by the multiplication of itself determining again into itself. For as Nature, taking a grain of wheat for seed and diffusing it, produces many forms and species between, by which she brings her work to an end, but at last she shows again a grain of wheat, restoring the beginning in the end of all; so, while the rest of the numbers, when they are multiplied into others, terminate by the increase only those of five and six, multiplied by themselves, bring back and preserve themselves. For six times six makes thirty-six, and five times five makes twenty-five. And again, six does this once, and only after one manner, to wit, when it is squared. But this indeed befalls five both by multiplication and by composition with itself, to which being added, it alternatively makes itself and ten; and this as far as all number can extend, this number imitating the beginning or first Cause which governs the universe. For as that first Cause, preserving the world by itself, does reciprocally perfect itself by the world, as Heraclitus says of fire, “Fire turns to all things, and all things to fire;” and as money is changed for gold, and gold for money; so the congress of five with itself is framed by Nature to produce nothing imperfect or strange, but has limited changes; for it either generates itself or ten, that is, either what is proper to itself, or what is perfect.

> Greek: 8. εἶπον οὖν κάλλιστα τὸν Εὔστροφον τῷ ἀριθμῷ λύειν τὴν ἀπορίαν; ἐπεὶ γάρ ἔφην εἰς τὸ ἄρτιον νενεμημένου παντὸς ἀριθμοῦ καὶ τὸ περιττὸν τὸν ἡ μὲν μονὰς ἀμφοτέρων ἐπίκοινός ἐστι τῇ δυνάμει (διὸ καὶ προστιθεμένη τὸν μὲν περιττὸν ἀριθμὸν ἄρτιον ποιεῖ τὸν δʼ ἄρτιον περιττόν̓) ἀρχὴν δὲ τοῦ μὲν ἀρτίου τὰ δύο τοῦ δὲ περιττοῦ τὰ τρία ποιοῦνται, τὰ δὲ πέντε γεννᾶται τούτων πρὸς ἀλλήλους μιγνυμένων εἰκότως; ἔσχηκε τιμὴν πρῶτος ἐκ πρώτων ἀποτελούμενος, καὶ γάμος ἐπωνόμασται τῇ τοῦ ἀρτίου πρὸς τὸ θῆλυ περιττοῦ δʼ αὖ πρὸς τὸ ἄρρεν ὁμοιότητι· ταῖς γὰρ εἰς ἴσα τομαῖς τῶν ἀριθμῶν, ὁ μὲν ἄρτιος πάντῃ διιστάμενος ὑπολείπει τινὰ δεκτικὴν ἀρχὴν οἷον ἐν ἑαυτῷ καὶ χώραν, ἐν δὲ τῷ περιττῷ ταὐτὸ παθόντι μέσον ἀεὶ περίεστι τῆς νεμήσεως γόνιμον· ᾗ γονιμώτερός ἐστι τοῦ ἑτέρου, καὶ μιγνύμενος ἀεὶ κρατεῖ κρατεῖται δʼ οὐδέποτε γίγνεται γὰρ ἐξ ἀμφοῖν κατʼ οὐδεμίαν μῖξιν ἄρτιος ἀλλὰ κατὰ πάσας περιττός. ἔτι δὲ μᾶλλον αὐτὸς ἐπιβάλλων αὑτῷ καὶ συντιθέμενος δείκνυσι τὴν διαφορὰν ἑκάτερος· ἄρτιος μὲν γὰρ οὐδεὶς ἀρτίῳ συνελθὼν περισσὸν παρέσχεν οὐδʼ ἐξέβη τὸ οἰκεῖον ὑπʼ ἀσθενείας ἄγονος ὢν ἑτέρου καὶ ἀτελής περισσοὶ δὲ μιγνύμενοι περισσοῖς ἀρτίους πολλοὺς διὰ τὸ πάντῃ γόνιμον ἀποτελοῦσι. τὰς δʼ ἄλλας οὐκ ἄν τις ἐν καιρῷ νῦν ἐπεξίοι δυνάμεις καὶ διαφορὰς τῶν ἀριθμῶν. ὡς οὖν ἄρρενός τε τοῦ πρώτου καὶ θήλεος ὁμιλίᾳ τὰ πέντε γιγνόμενα γάμον οἱ Πυθαγόρειοι προσεῖπον. ἔστι δʼ καὶ φύσις λέλεκται τῷ περὶ αὑτὸν πολυπλασιασμῷ πάλιν εἰς ἑαυτὸν περαίνων. ὡς γὰρ ἡ φύσις λαβοῦσα πυρὸν ἐν σπέρματι καὶ χεαμένη πολλὰ μὲν ἐν μέσῳ φύει σχήματα καὶ εἴδη, διʼ ὧν ἐπὶ τέλος ἐξάγει τὸ ἔργον, ἐπὶ πᾶσι δὲ πυρὸν ἀνέδειξεν ἀποδοῦσα τὴν ἀρχὴν ἐν τῷ τέλει τοῦ παντός· οὕτω τῶν λοιπῶν ἀριθμῶν, ὅταν αὑτοὺς πολλαπλασιάσωσιν, εἰς ἑτέρους τελευτώντων τῇ αὐξήσει, μόνος ὁ τῶν πέντε καὶ ἓξ γενόμενος τοσαυτάκις αὑτοὺς ἀναφέρουσι καὶ ἀνασῴζουσιν. ἑξάκις γὰρ τὰ ἓξ τριακονταὲξ, καὶ πεντάκις τὰ πέντε εἰκοσιπέντε γίγνεται. καὶ πάλιν ὁ μὲν τῶν ἓξ ἅπαξ τοῦτο ποιεῖ καὶ μοναχῶς αὐτὸς ἀφʼ ἑαυτοῦ τετράγωνος γιγνόμενος· τῇ δὲ πεμπάδι καὶ τοῦτο μὲν συμβέβηκε κατὰ πολυαπλασιασμόν, ἰδίως δὲ τὸ κατὰ σύνθεσιν ἢ ἑαυτὴν ἢ τὴν δεκάδα ποιεῖν παρὰ μέρος ἐπιβάλλουσαν αὑτῇ, καὶ τοῦτο γίγνεσθαι μέχρι παντὸς, ἀπομιμουμένου τοῦ ἀριθμοῦ τὴν τὰ ὅλα διακοσμοῦσαν ἀρχήν. ὡς γὰρ ἐκείνην φυλάττουσαν ἐκ μὲν ἑαυτῆς τὸν κόσμον ἐκ δὲ τοῦ κόσμου πάλιν αὖ ἑαυτὴν ἀποτελεῖν πυρὸς τʼ ἀνταμείβεσθαι πάντα φησὶν ὁ Ἡράκλειτος καὶ πῦρ ἁπάντων, ὅκωσπερ χρυσοῦ χρήματα καὶ χρημάτων χρυσός· οὕτως ἡ τῆς πεμπάδος πρὸς ἑαυτὴν σύνοδος οὐδὲν οὔτʼ ἀτελὲς οὔτʼ ἀλλότριον γεννᾶν πέφυκεν, ἀλλʼ ὡρισμένας ἔχει μεταβολάς· ἢ γὰρ αὑτὴν ἢ τὴν δεκάδα γεννᾷ, τουτέστιν ἢ τὸ οἰκεῖον ἢ τὸ τέλειον.

[¶8] 9. Now if any one shall say, What is all this to Apollo? we will answer, that it concerns not Apollo only, but Bacchus also, who has no less to do with Delphi than Apollo himself. For we have heard the divines, partly in verse partly in prose, saying and singing, that the God is of his own nature incorruptible and eternal, but yet, through a certain fatal decree and reason, suffers changes of himself, having sometimes his nature kindled into a fire, and making all things alike, and otherwhiles becoming various, in different shapes, passions, and powers, like unto the World, and is named by this best-known of names. But the wiser, concealing from the vulgar the change into fire, call him both Apollo from his unity and Phoebus from his purity and unpollutedness. But as for the passion and change of his conversion into winds, water, earth, stars, and the various kinds of plants and animals, and its order and disposition, this they obscurely represent as a certain distraction and dismembering; and they now call him Dionysus, Zagreus, Nyctelius, and Isodaetes, exhibiting and chanting forth certain corruptions, disparitions, deaths, and resurrections, which are all riddles and fables suited to the said mutations. To Dionysus or Bacchus they sing dithyrambic verses, full of passions and change, joined with a certain wandering and agitation backwards and forwards; for, as Aeschylus says,
The dithyramb, whose sounds are dissonant,’Tis fit should wait on Bacchus.
But to Apollo they sing the well-ordered paean and a discreet song. And Apollo both in their sculptures and statues they always make to be young and never declining to old age; but Dionysus they represent in many shapes and forms. Lastly, to the one they attribute equality, order, and unmixed gravity; but to the other, a certain unequal mixture of sports, petulancy, gravity, and madness, surnaming him,
Evius Bacchus, who to rage incites
Women on tops of mountains, and delights
In frantic worship.
Thus they not unfitly touch the property of both changes. Now because the time of the revolutions in these changes is not equal, but that of the one which they call Koros (that is, satiety) is longer, and that of the other named Chresmosyne (or want) shorter; observing in this the proportion, they all the rest of the year use in their sacrifices the paean; but at the beginning of winter, rousing up the dithyramb, and laying the paean to rest, they do for three months invocate Bacchus instead of Apollo, esteeming the creation of the world to be the same in proportion of time to the conflagration of it as three to one.

> Greek: 9. ἐὰν οὖν ἔρηταί τις, τί ταῦτα πρὸς τὸν Ἀπόλλωνα, φήσομεν οὐχὶ μόνον ἀλλὰ καὶ πρὸς τὸν Διόνυσον, ᾧ τῶν Δελφῶν οὐδὲν ἧττον ἢ τῷ Ἀπόλλωνι μέτεστιν. ἀκούομεν οὖν τῶν θεολόγων τὰ μὲν ἐν ποιήμασι τὰ δʼ ἄνευ μέτρου λεγόντων καὶ ὑμνούντων, ὡς ἄφθαρτος ὁ θεὸς καὶ ἀίδιος πεφυκώς, ὑπὸ δή τινος εἱμαρμένης γνώμης καὶ λόγου μεταβολαῖς ἑαυτοῦ χρώμενος, ἄλλοτε μὲν εἰς πῦρ ἀνῆψε τὴν φύσιν πάνθʼ ὁμοιώσας πᾶσιν, ἄλλοτε δὲ παντοδαπὸς ἔν τε μορφαῖς καὶ ἐν πάθεσι καὶ δυνάμεσι διαφόροις γιγνόμενος, ὡς γίγνεται νῦν, κόσμος ὀνομάζεται δὲ τῷ γνωριμωτάτῳ τῶν ὀνομάτων. κρυπτόμενοι δὲ τοὺς πολλοὺς οἱ σοφώτεροι τὴν μὲν εἰς πῦρ μεταβολὴν Ἀπόλλωνά τε τῇ μονώσει Φοῖβόν τε τῷ καθαρῷ καὶ ἀμιάντῳ καλοῦσι. τῆς δʼ εἰς πνεύματα καὶ ὓδωρ καὶ γῆν καὶ ἄστρα καὶ φυτῶν ζῴων τε γενέσεις τροπῆς αὐτοῦ καὶ διακοσμήσεως τὸ μὲν πάθημα καὶ τὴν μεταβολὴν διασπασμόν τινα καὶ διαμελισμὸν αἰνίττονται· Διόνυσον δὲ καὶ Ζαγρέα καὶ Νυκτέλιον καὶ Ἰσοδαίτην αὐτὸν ὀνομάζουσι, καὶ φθοράς τινας καὶ ἀφανισμοὺς οἱ τὰς ἀποβιώσεις καὶ παλιγγενεσίας, οἰκεῖα ταῖς εἰρημέναις μεταβολαῖς αἰνίγματα καὶ μυθεύματα περαίνουσι· καὶ ᾅδουσι τῷ μὲν διθυραμβικὰ μέλη παθῶν μεστὰ καὶ μεταβολῆς πλάνην τινὰ καὶ διαφόρησιν ἐχούσης·
μιξοβόαν γὰρ Αἰσχύλος φησὶ πρέπει
διθύραμβον ὁμαρτεῖν
σύγκωμον Διονύσῳ;
τῷ δὲ παιᾶνα, τεταγμένην καὶ σώφρονα μοῦσαν. ἀγήρων τε τοῦτον ἀεὶ καὶ νέον ἐκεῖνον δὲ πολυειδῆ καὶ πολύμορφον ἐν γραφαῖς καὶ πλάσμασι δημιουργοῦσι· καὶ ὅλως τῷ μὲν ὁμοιότητα καὶ τάξιν καὶ σπουδὴν ἄκρατον, τῷ δὲ μεμιγμένην τινὰ παιδιᾷ καὶ ὕβρει καὶ σπουδῇ καὶ μανίᾳ προσφέροντες ἀνωμαλίαν, εὔιον ὀρσιγύναικα μαινομέναις Διόνυσον ἀνθέοντα τιμαῖς ἀνακαλοῦσιν, οὐ φαύλως ἑκατέρας μεταβολῆς τὸ οἰκεῖον λαμβάνοντες. ἐπεὶ δʼ οὐκ ἴσος τῶν περιόδων ἐν ταῖς μεταβολαῖς χρόνος, ἀλλὰ μείζων ὁ τῆς ἑτέρας ἣν κόρον· καλοῦσιν, ὁ δὲ τῆς χρησμοσύνης ἐλάττων, τὸ κατὰ λόγον τηροῦντες ἐνταῦθα τὸν μὲν ἄλλον ἐνιαυτὸν παιᾶνι χρῶνται περὶ τὰς θυσίας, ἀρχομένου δὲ χειμῶνος ἐπεγείραντες διθύραμβον τὸν δὲ παιᾶνα καταπαύσαντες, τρεῖς μῆνας ἀντʼ ἐκείνου τοῦτον κατακαλοῦνται τὸν θεὸν· ὅπερ τρία πρὸς ἕν, τοῦτο τὴν διακόσμησιν οἰόμενοι χρόνῳ πρὸς τὴν ἐκπύρωσιν εἶναι.

[¶9] 10. But these things have perhaps had more than sufficient time spent on them. This, however, is evident, that they properly attribute to this God the number of five, saying that it sometimes of itself produces itself like fire, and other whiles the number of ten, like the world. But do we think that this number is not also concerned with music, which is of all things most acceptable to this God For the chiefest operation of harmony is, as one may say, about symphonies. Now that these are five and no more, reason convinces even him who will by his senses without reasoning make trial either on strings or pipe-holes. For all these accords take their original in proportions of number; and the proportion of the symphony diatessaron is sesquitertial, of diapente sesquialter, of diapason duple, of diapason with diapente triple, and of disdiapason quadruple. But as for that which, transcending all measures, the musicians add to these, naming it diapason with diatessaron, it is not fit we should receive it, gratifying the unreasonable pleasure of the ear against proportion, which is as the law. I may therefore let pass the five positions of the tetrachords, and also the five first,—whether they are to be called tones, tropes, or harmonies,—according to the changes of which by rising or falling, either to more or less, the rest are bases or trebles. And, whereas there are many or rather infinite intervals, are not five of them only used in music, to wit, diesis, hemitonion, tons, triemitonion, and ditonon? Nor is there in the voice any other space, either greater or less, that, being distinguished by base or treble, comes into melody.

> Greek: 10. ἀλλὰ ταῦτα μὲν ἱκανοῦ καιροῦ μᾶλλον ἀπομεμήκυνται· δῆλον δʼ ὅτι συνοικειοῦσιν αὐτῷ τὴν πεμπάδα, νῦν μὲν αὐτὴν ἑαυτὴν ὡς τὸ πῦρ αὖθις δὲ τὴν δεκάδα ποιοῦσαν ἐξ ἑαυτῆς ὡς τὸν κόσμον. τῆς δὲ δὴ μάλιστα κεχαρισμένης τῷ θεῷ μουσικῆς οὐκ οἰόμεθα τούτῳ τῷ ἀριθμῷ· μετεῖναι; τὸ γὰρ πλεῖστον ὡς ἔνι εἰπεῖν ἔργον ἁρμονικῆς περὶ τὰς συμφωνίας ἐστίν. αὗται δʼ ὅτι πέντε καὶ οὐ πλείους, ὁ λόγος ἐξελέγχει τὸν ἐν χορδαῖς καὶ τρυπήμασι ταῦτα θηρᾶν ἀλόγως τῇ αἰσθήσει βουλόμενον. πᾶσαι γὰρ ἐν λόγοις τὴν γένεσιν ἀριθμῶν λαμβάνουσιν· καὶ λόγος ἐστὶ τῆς μὲν διὰ τεσσάρων ἐπίτριτος, τῆς δὲ διὰ πέντε ἡμιόλιος, διπλάσιος δὲ τῆς διὰ πασῶν, τῆς δὲ διὰ πασῶν καὶ διὰ πέντε τριπλάσιος, τῆς δὲ δὶς διὰ πασῶν τετραπλάσιος. ἣν δὲ ταύταις ἐπεισάγουσιν οἱ ἁρμονικοὶ διὰ πασῶν καὶ διὰ τεσσάρων ὀνομάζοντες, ἔξω μέτρου βαίνουσαν, οὐκ ἄξιόν ἐστι δέχεσθαι, τῆς ἀκοῆς τῷ ἀλόγῳ παρὰ τὸν λόγον ὥσπερ νόμον χαριζομένους. ἵνα τοίνυν ἀφῶ πέντε τετραχόρδων θέσεις, καὶ πέντε τοὺς πρώτους, εἴτε τόνους ἢ τρόπους; εἴθʼ ἁρμονίας χρὴ καλεῖν, ὧν ἐπιτάσει καὶ ὑφέσει τρεπομένων κατὰ τὸ μᾶλλον καὶ ἧττον αἱ λοιπαὶ βαρύτητές εἰσι καὶ ὀξύτητες ἆρʼ οὐχὶ πολλῶν, μᾶλλον δʼ ἀπείρων διαστημάτων ὄντων, τὰ μελῳδούμενα μόνα πέντʼ ἐστί, δίεσις καὶ ἡμιτόνιον καὶ τόνος καὶ τριημιτόνιον καὶ δίτονον, ἄλλο δʼ οὐδὲν οὔτε μικρότερον οὔτε μεῖζον ἐν φωναῖς χωρίον ὀξύτητι καὶ βαρύτητι περατούμενον μελῳδητόν ἐστι;