E. M. Cope, Commentary on the Rhetoric of Aristotle

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‘That (composition) which is (entirely) devoid of rhythm (has no measure) is indefinite (or, unlimited), but it ought to be limited, only not by metre (like verse): for the infinite (indefinite, unlimited) is displeasing and (i. e. because it) cannot be known. But everything is defined (or limited) by number; and the number (numerus in both its senses) of the structure of the language (prose composition) is rhythm, of which metres are so many sections’. Here we pass for a moment into Platonic metaphysics. The doctrine of the formless, vague, indefinite, unlimited, infinite of more or less, of degree; into which τὸ μέτριον order, harmony, measure, symmetry, law—the mean—are introduced by the limiting πέρας, the definite principle; coming originally from the Pythagoreans, is adopted and expounded by Plato in the Philebus, 23 E et seq. The principle is applied to the numbers or measures of music and composition, verse and prose, 26 A, ἐν δὲ ὀξεῖ καὶ βαρεῖ (the tones of music) καὶ ταχεῖ καὶ βραδεῖ, ἀπείροις οὖσιν, ἆρ᾽ οὐ ταὐτὰ ἐγγιγνόμενα ταῦτα (τὸ πέρας καὶ τὸ ἄπειρον) ἅμα πέρας τε ἀπειργάσατο καὶ μουσικὴν συμπάσαν τελεώτατα ξυνεστήσατο; From him Aristotle undoubtedly borrowed his conception of rhythm, as he did likewise his grand division of ὕλη, the informis materia, the potential, unenergized matter, the material cause of all things; and λόγος, the formal cause, that which gives form and substance to the brute matter, energizes or realizes it into complete existence, and is the original design, or conception in the mind of the Creator, the ‘what it was to be’, τὸ τί ἦν εἶναι: and also his doctrine of the ‘mean’. With ἄγνωστον τὸ ἄπειρον, compare Anal. Post. A 24, [86 a 5,] ἔστι δ᾽ ᾗ μὲν ἄπειρα οὐκ ἐπιστητά, ᾗ δὲ πεπέρανται ἐπιστητά. Metaph. B 4, 999 a 27, τῶν ἀπείρων πῶς ἐνδέχεται λαβεῖν ἐπιστήμην; κ.τ.λ.

On τὸ ἄρρυθμον ἀπέραντον, compare Cic. Orator, LXVIII 228, Hanc igitur, sive compositionem sive perfectionem sive numerum vocari placet, adhibere necesse est, si ornate velis dicere, non solum, quod ait Aristoteles et Theophrastus, ne infinite feratur ut flumen oratio, seq. On ῥυθμός, μέτρον, ‘measure of time’, Ib. § 227, sonantium omnium quae metiri auribus possumus.

περαίνεται...ἀριθμῷ πάντα] This axiom is doubtless derived ultimately from the Pythagoreans, who traced the laws of the universe in numbers and mathematical symbols. Καὶ πάντα γα μὰν τὰ γιγνωσκόμενα ἀριθμὸν ἔχοντι, οὐ γὰρ οἷόν τε οὐδὲν οὔτε νοηθῆμεν οὔτε γνωσθῆμεν ἄνευ τούτω, ap. Stobaeum, Böckh, Philolaos, p. 58. “The finite in number is the calculable, that which the mind can grasp, and handle; the infinite is the incalculable, that which baffles the mind, that which refuses to reduce itself to law, and hence remains unknowable.” Grant, Essay on Ar. Ethics, p. 202 (Ist ed. [p. 252, 3rd ed.]). Probl XIX 38, ῥυθμῷ δὲ χαίρομεν διὰ τὸ γνώριμον καὶ τεταγμένον ἀριθμὸν ἔχειν, καὶ κινεῖν ἡμᾶς τεταγμένως: οἰκειοτέρα γὰρ ἡ τεταγμένη κίνησις φύσει τῆς ἀτάκτου, ὥστε καὶ κατὰ φύσιν μᾶλλον. This illustrates ἀηδὲς...τὸ ἄπειρον. With ῥυθμὸς...οὗ τὰ μέτρα τμητά, comp. Poet. IV 7, τὰ γὰρ μέτρα ὅτι μόρια τῶν ῥυθμῶν ἐστί, φανερόν: i. e. metres, verses or systems of verses, are definite lengths or sections, into which the indefinite matter of rhythm is as it were cut. Similarly it is said, III 9. 3, that the period and all metres are measured by number.