ἐγχειρίσαι αὐτὸ τῷ καθηγητῇ ὃς δὴ ἆθλον προύθηκε τῷ περὶ τὸ σονέττιον ἀριστεύσαντι. Εὔχομαί σοι γενέσθαι τὰ ἀρισ‐ τεῖα· εἴπερ ἀξιώτατοί γε στεφανωθῆναι οἱ κατὰ τὸ μεσονύ κτιον ἐπὶ τῆς ̓Αρτούρου ἕδρας αἰθριάσαντες. Σὺ δὲ δὴ μή τώθαζε· ἔμοιγε οὐ μεταμελήσειεν ἄνποτε τῆς εὐσε βοῦς θεραπείας, τῆς πρὸς τὴν ἁγνὴν τῆς μεσονυκτίας ὥρας κυνηγέτιδα, καθ ̓ ὃν χρόνον σὺ δὴ ἔκεισο ῥέγκων ἐν τοῖς στρώ‐ μασι, τὴν ψυχὴν ἔχων μεμαγ γανευμένην ὑπὸ τῶν ἀλόγων φασμάτων, οὓς οἱ ἄνθρωποι καλοῦσιν ὀνείρους. ADDITIONAL WORDS AND PHRASES. Accuracy—ἀκρίβεια, -ας, ἡ. The argument—ὑπόθεσις, εως, ἡ. To appear before the public—παριέναι εἰς τὰ πλήθη. An author-συγγραφεύς, -εως, δ. Composition—σύνθεσις, σύν ταξις, -εως, ἡ. Conciseness—τὸ σύντομον. Dignity-σεμνότης, -ητος, ή. Edition—ἔκδοσις, -εως, ἡ. Eloquenceἡ περὶ τοὺς λόγους δεινότης. Emendation- διόρθωσις, -εως, ἡ. Εxhibition of literary talentἐπίδειξις, -εως, ἡ. A fancy or notion—νόημα, ατος, τό. Fluency—εὔροια, -ας, ἡ. A forid writer-λογοδαίδαλος. Literary man-φιλόλογος, -ου, ὁ. Literary man superficial-σοφιστής, -ου, ὁ. Manuscript χειρόγραφον, -ου, τό. Neatness—κομψότης, ητος, ἡ. Proof —τεκμήριον, -ου, τό. Propriety—τὸ πρέπον, -οντος. cension of the text-διασκευή, -ῆς, ἡ. Simile-εἰκών, -όνος, ἡ. Sketch—ὑποτύπωσις, -εως, ἡ. Style-χαρακτήρ, -ῆρος, Subject of discourse—τὸ ὑποκείμενον, -ου. Tasteφιλοκαλία, -ας, ἡ. Turgidity-ὄγκος, -ου, ὁ. Weight-τὸ ἐμβριθές, -ους. Wit—εὐτραπελία, -ας, ἡ. Coarse wit, buf foonery--βωμολοχία, -ας, ἡ. ὁ. A re 58 DIALOGUE FOURTEENTH. ON ARITHMETIC AND MATHEMATICS. Will you never be done bending over these circles and triangles, and wasting your brain on the barren relations of space and time? My dear Sir, you talk of what you do not understand. Mathematics is, next to poetry, the purest element in which the soul delights to move. What figure is this you were looking at so intently, and puzzling about ? You are an ignoramus. I am not puzzling, only enjoying the beautiful demonstration of the famous forty-seventh proposition of the First Book of Euclid. Read the proposition. In every right-angled triangle the square of the side subtending the right angle is equal to the squares of the two sides containing the right angle. Hold ! hold! I already 1 πέφυκα, to have a natural genius for doing anything. J. 668. 2 Idiomatic use of ris.-J. 659, 4; C. 28, a. feel quite confused. But why do you call this proposition famous ? Because they say Pythagoras first found out the demonstration. Do you believe that? Why not? The Samian was unquestionably a great mathematician,andtaught that the first principle of all things is number. What could he mean by that? I hate arithmetic ; and, to confess the truth, am constantly confounding addition and subtraction in my calculations. I am sorry for you ; for here you plainly confess that you have a weak brain, and claim near relationship with certain savage tribes who cannot count above twenty. Well; don't bother me about figures: at the same time, I should be very glad to hear what Pythagoras meant by making number the first principle. He meant, what any man of sense may see, that all things in the world are measured and calculated. Is there any calculation in the clouds? Yes; every drop of water, as the chemists will tell you, is composed of cer κάτω ἕλκεις μοι τὰ διανοήματα. Ταύτην δὲ δὴ τὴν πρότασιν διὰ τί εἶπες περιβόητον ; Διότι τὸν Πυθαγόραν φασὶ πρῶτον τὴν ἀπόδειξιν ἐξευρεῖν. Μῶν σὺ ταῦτα πιστεύεις ; Πιστεύω δῆτα· καὶ γὰρ ἦν ὁ Σάμιος ὡς ἀληθῶς δεινὸς περὶ τὴν μάθησιν, διδάσκων γε τὴν τῶν ὅλων ἀρχὴν εἶναι τὸν ἀριθμόν. Ταῦτα δὲ τί βουλόμενος ἀπεφήνατο; Μῖσῶ τὴν ἀριθμητικήν· καὶ, ἵνα λέγω τὰ ἀληθῆ, λογιζόμενος ἀεὶ λανθάνω οὐ διακρί νων τὴν τε ἀφαίρεσιν καὶ τὴν προσθήκην. Ελυπήθην ἀκούων· ταῦτα γὰρ λέγων δῆλος εἶ ὁμολογούμενος πάνυ μαλακῇ χρῆσθαι τῇ διανοίᾳ, ὥστε δικαίως ἀποδέξασθαι ἀγρίων τινῶν φύλων τὴν συγγένειαν, τῶν μὴ δυναμένων πεμπάζειν ὑπὲρ τοὺς εἴκοσι. Εἶεν· ἐμὲ δὲ μὴ κόπτε τοῖς ἀριθ. μοῖς· οὐ μὴν ἀλλὰ ὅ γε Πυθαγό ρας τί ποτε ἐβούλετο θεὶς ἀρχὴν τὸν ἀριθμὸν μάλα ἡδέως ἂν ἀκούσαιμι. Ἐκεῖνο γοῦν ἐβούλετο, τοῖς γε νοῦν ἔχουσιν δῆλον, τὸ ἅπανθ ̓ ὅσα ἐν τῷ κόσμῳ ἀριθμοῖς τισι καὶ μέτροις ῥυθμίζεσθαι. Μῶν ῥυθμός νεφέλαις ; Καὶ μάλα γε· σταγὼν γὰρ ὕδατος πολλοστὴ, ὡς διδάσκουσιν οἱ χημικοὶ, σύγκειται ἐξ ὡρισ τις ἐστὶν ἐν ταῖς 1 As in Latin ut vera dicam; but the infin. also, with os is used in Greek.-J. 893, d. tain fixed measures of two gases, oxygen and hydrogen ; and, in fact, the whole of chemistry is nicely quantitative, and depends on arithmetic. And must I then be an arithmetician in order to study chemistry? Of course. Time and Space, which you call empty relations, are no doubt empty in themselves, but, like bottles, can easily be filled with good wine. Nothing exists which is not contained by these universal forms. μένων τινῶν μέτρων δυεῖν ἀέρων, δηλαδὴ τοῦ ὀξυγόνου καὶ τοῦ ὑδρογόνου· ὅλως δὲ δὴ σύμ πᾶσα ἡ χημικὴ κατὰ τὸ πόσον ὁρίζεται ἀκριβῶς, καὶ ἐξήρτηται τῆς ἀριθμητικῆς. Εἶτα, νὴ Δία, καὶ ἐμὲ μέλλοντα μελετῶν τὰ χημικὰ δεῖ πάντως διαπονεῖσθαι τὰ περὶ τοὺς ἀριθμούς ; Κομιδῆ μὲν οὖν· ὁ γὰρ δὴ χρόνος καὶ οἱ ὡρισμένοι τόποι οὓς κενοὺς λέγεις, καθ ̓ αὑτοὺς τῷ ὄντι διάκενοί εἰσιν, ῥᾳδίως δὲ, καθάπερ οἱ ἀσκοὶ, οὐ πολλῷ πόνῳ ἀγαθοῦ οἴνου ἂν ἐκπληρωθεῖεν. Ολως δὴ ἐν τῇ τῶν ὅλων συστάσει ὑπάρχει οὐδὲν ὅ τι οὐχ ὁρίζουσιν ὁ τε χρόνος καὶ οἱ τόποι. Εἶτα, περὶ τοῦ νοῦ τί ποτε λέγεις ; Ἐκεῖνο δὴ συγχωρῶ, μὴ δύνασ θαι μετρηθῆναι τὰς διανοίας δακτύλων γε λογισμῷ· δὲ μὴν ἀλλὰ ὅ γε νοῦς οὐχ οἷός τε ἐστὶν ἐνεργεῖν χωρὶς τοῦ ποῦ καὶ τοῦ πότε. Τοιγάρτοι ὡς ἐμοῦ ἠλιθίου ἀποβησομένου, μὴ σπουδάσαντος1 περὶ τήν τε μάθησιν καὶ τοὺς ἀριθμούς, οὕτως ἔχεις τὴν γνώμην ; Ἐκεῖνο δήπου ἀποφαίνομαι, ἄνευ τῶν μέτρων τούτων τῶν πάντα περιεχόντων οὐχ οἷους τε εἶναι τοὺς ἀνθρώπους ἐξακριβοῦν ὁποιανδήποτε ἐπιστήμην. Πάτ ρεστι δήπουθεν μετὰ χρηστῶν Γερμανῶν ἐν μεταφυ σικοῖς τισι κενώμασιν ἔνθα καὶ ἔνθα μετεωρίζεσθαι. τῶν Σὺ δὲ μὴ κακολόγει τὰ μετα 1 μὴ, with aor. part. =nisi, with perf. subj.-J. 646, 2 ; F. 276 ; C. 48, 1. physics; that is a vulgar habitude of the English mind. Then don't speak you against mathematics. The next time I see you I hope to find you not ignorant of the difference between 9 +2 and 9 -2, and perhaps even advanced to the comprehension of the great mystery of (a+b)2=a2 + b2 +2ab. φυσικά· βαναυσικὴ γὰρ ἕξις αὕτη τῆς τῶν Αγγλων διανοίας. Καὶ σὺ ὡσαύτως μὴ κακολόγει τὴν μάθησιν. Ατὰρ ὕστερον περιτυχών σοι ἐλπίζω οὐ πάνυ ἄπειρον εὑρήσειν σε τοῦ πῶς διαφέρει τὰ 9 + 2 καὶ τὰ 9 - 2, καὶ μὴν καὶ ἴσως εἰς τοσοῦτον προαχθέντα σοφίας ὥστε καταλαβεῖν τὸ μυστικὸν τόδε (α + β)2 = α2 + β2 + 2αβ. ADDITIONAL WORDS AND PHRASES. Angle-γωνία, -ας, ἡ, Circumference-περιφέρεια, -ας, ἡ. Circle-κύκλος, -ου, ὁ. A complement—παραπλήρωμα, -ατος, τό. Distance or interval—διάστημα, ατος, τό. Figure σχῆμα, ατος, τό. Line-γραμμή, ης, ή. Magnitude-μέγε θος, -ους, τό. A perpendicular-κάθετος, -ου, ἡ. A plane ἐπίπεδον, -ου, τό A point-σημεῖον, -ου, τό. A ratio-λόγος, -ου, ὁ. Segment—τμῆμα, ατος, τό. A straight lineεὐθεῖα, -ας, ἡ. A surface-ἐπιφάνεια, -ας, ἡ. A triangle τρίγωνον, -ου, τό. DIALOGUE FIFTEENTH. LOGIC AND METAPHYSICS. Well, my good friend, in Η ΔΙΑΛΕΚΤΙΚΗ ΚΑΙ ΤΑ Λέγοις ἂν, ἀντιβολῶ σε, ὦ δαι- Ἐγὼ, εἰ Γερμανὸς ἔφυν, εἰκότως ἂν εἰς ὑπερνεφέλους τόπους |