- Source
- Polybius. Vols. 1-4. Büttner-Wobst, Theodor, editor. Leipzig: Teubner, 1893.
- Translation
- AI-generated (gemini-3.5-flash) — machine translation; may contain errors
- Languages
- 日本語 · English · 简体中文 · 한국어
- CTS URN
- urn:cts:greekLit:tlg0543.tlg001.humanitext-grc2:34.6.1-34.6.15
- Generated
- Humanitext Reader · reader.humanitext.ai · 2026-11-12
Polybius attempts to refute Dicaearchus' Mediterranean distance measurements using a geometric model of an obtuse triangle with Narbo as its vertex. Strabo, however, uses Polybius' own data on Greek and Illyrian distances to expose Polybius' own logical inconsistencies and errors.
οἷς1 ἐκείνους ἐλέγχει καθαρεύων. τοῦ γοῦν Δικαιάρχου2 μυρίους μὲν εἰπόντος τοὺς ἐπὶ στήλας ἀπὸ τῆς Πελοποννήσου σταδίους, πλείους δὲ τούτων τοὺς ἐπὶ τὸν Ἀδρίαν μέχρι τοῦ μυχοῦ, τοῦ δʼ ἐπὶ στήλας τὸ μέχρι τοῦ πορθμοῦ τρισχιλίους ἀποδόντος, ὡς γίνεσθαι τὸ λοιπὸν ἑπτακισχιλίους τὸ ἀπὸ πορθμοῦ μέχρι στηλῶν, τοὺς μὲν τρισχιλίους ἐᾶν φησιν εἴτʼ εὖ λαμβάνονται εἴτε μή, τοὺς δʼ ἑπτακισχιλίους οὐδετέρως, οὔτε τὴν παραλίαν ἐκμετροῦντι οὔτε τὴν διὰ μέσου τοῦ πελάγους.
...[but not even in] those very things in which he refutes them is he himself free [from error]. At any rate, Dicaearchus having said that it is ten thousand stades from the Peloponnese to the Pillars, and more than this to the recess of the Adriatic, and having estimated the distance as far as the Strait at three thousand of those to the Pillars, so that the remainder from the Strait to the Pillars becomes seven thousand, Polybius says that he lets the three thousand stades be, whether they are well taken or not, but by no means the seven thousand, whether one measures the coastline or the line through the open sea.
τὴν μὲν γὰρ παραλίαν ἐοικέναι μάλιστʼ ἀμβλείᾳ γωνίᾳ, βεβηκυίᾳ3 ἐπί τε τοῦ πορθμοῦ καὶ τῶν στηλῶν, κορυφὴν δʼ ἐχούσῃ Νάρβωνα, ὥστε συνίστασθαι τρίγωνον, βάσιν ἔχον τὴν διὰ τοῦ πελάγους εὐθεῖαν, πλευρὰς δὲ τὰς τὴν γωνίαν ποιούσας τὴν λεχθεῖσαν·
For he says that the coastline resembles most of all an obtuse angle, resting upon the Strait and the Pillars, and having its vertex at Narbo, so that there is formed a triangle which has for its base the straight line through the sea, and for its sides those which make the said angle;
ὧν ἡ μὲν ἀπὸ τοῦ πορθμοῦ μέχρι Νάρβωνος μυρίων ἐστὶ καὶ πλειόνων ἢ διακοσίων ἐπὶ τοῖς χιλίοις, ἡ δὲ λοιπὴ μικρῷ λεῖπον [ἐλαττόνων ἢ] ὀκτακισχιλίων.
of which sides, the one from the Strait to Narbo is ten thousand and more than twelve hundred stades, and the remaining side is a little less than eight thousand.
καὶ μὴν πλεῖστον μὲν διάστημα ἀπὸ τῆς Εὐρώπης ἐπὶ τὴν Λιβύην ὁμολογεῖσθαι κατὰ τὸ Τυρρηνικὸν πέλαγος σταδίων οὐ πλειόνων ἢ τρισχιλίων, κατὰ τὸ Σαρδόνιον δὲ λαμβάνειν συναγωγήν.
Moreover, it is agreed that the greatest distance from Europe to Libya at the Tyrrhenian Sea is no more than three thousand stades, and that at the Sardinian Sea it becomes narrower.
ἀλλʼ ἔστω, φησί, καὶ ἐκεῖνο τρισχιλίων, προειλήφθω δʼ ἐπὶ τούτοις δισχιλίων σταδίων τὸ τοῦ κόλπου βάθος τοῦ κατὰ Νάρβωνα, ὡς ἂν κάθετος ἀπὸ τῆς κορυφῆς ἐπὶ τὴν βάσιν τοῦ ἀμβλυγωνίου.
”But,” he says, “let that distance also be three thousand, and let there be assumed, in addition to these, the depth of the gulf at Narbo as two thousand stades, serving as a perpendicular from the vertex to the base of the obtuse-angled triangle.”
δῆλον οὖν, φησίν, ἐκ τῆς παιδικῆς μετρήσεως ὅτι ἡ σύμπασα παραλία ἡ ἀπὸ τοῦ πορθμοῦ ἐπὶ στήλας ἔγγιστα ὑπερέχει τῆς διὰ τοῦ πελάγους εὐθείας πεντακοσίοις σταδίοις.
”It is clear, then,” he says, “from elementary measurement, that the entire coastline from the Strait to the Pillars exceeds the straight line through the sea by approximately five hundred stades.”
προστεθέντων δὲ τῶν ἀπὸ τῆς Πελοποννήσου ἐπὶ τὸν πορθμὸν τρισχιλίων, οἱ σύμπαντες ἔσονται στάδιοι, αὐτοὶ οἱ ἐπʼ εὐθείας, πλείους ἢ διπλάσιοι ὧν Δικαίαρχος εἶπε.
”And if the three thousand stades from the Peloponnese to the Strait are added, the total number of stades, along the straight line itself, will be more than double what Dicaearchus stated.”
πλείους δὲ τούτων τοὺς ἐπὶ τὸν μυχὸν τὸν Ἀδριατικὸν δεήσει, φησί, τιθέναι κατʼ ἐκεῖνον. ἀλλʼ, ὦ φίλε Πολύβιε, φαίη τις ἄν, ὥσπερ τούτου τοῦ ψεύσματος ἐναργῆ παρίστησι τὸν ἔλεγχον ἡ πεῖρα ἐξ αὐτῶν ὧν εἴρηκας αὐτός, εἰς μὲν Λευκάδα ἐκ Πελοποννήσου ἑπτακοσίους, ἐντεῦθεν δὲ τοὺς ἴσους εἰς Κόρκυραν, καὶ πάλιν ἐντεῦθεν εἰς τὰ Κεραύνια τοὺς ἴσους καὶ ἐν δεξιᾷ εἰς τὴν Ἰαπυδίαν ἀπὸ τῶν Κεραυνίων τὴν Ἰλλυρικὴν παραλίαν σταδίων ἑξακισχιλίων ἑκατὸν πεντήκοντα, οὕτως4 κἀκεῖνα ψεύσματά ἐστιν ἀμφότερα, καὶ ὃ Δικαίαρχος εἶπε, τὸ ἀπὸ πορθμοῦ ἐπὶ στήλας εἶναι σταδίων ἑπτακισχιλίων, καὶ ὃ σὺ δοκεῖς ἀποδεῖξαι·
”And according to him,” he says, “it will be necessary to make the distance to the recess of the Adriatic even greater than this.” But, my dear Polybius, one might say, just as experience presents a clear refutation of this falsehood from the very things which you yourself have stated— namely, seven hundred stades from the Peloponnese to Leucas, and an equal number thence to Corcyra, and again an equal number thence to the Ceraunian Mountains, and from the Ceraunian Mountains, on the right, along the Illyrian coast to Iapydia, six thousand one hundred and fifty stades— so also both of those statements are falsehoods, both the one Dicaearchus made, that the distance from the Strait to the Pillars is seven thousand stades, and the one you think you have demonstrated;
ὁμολογοῦσι γὰρ οἱ πλεῖστοι λέγοντες τὸ διὰ πελάγους μυρίων εἶναι καὶ δισχιλίων. —
for the majority agree in saying that the distance through the open sea is twelve thousand stades.
πῶς οὐκ ἂν εἰκότως δόξειεν5 ὑπερβεβηκέναι καὶ ἀπολεληρηκέναι τὸν Βεργαῖον Ἀντιφάνην καὶ καθόλου μηδενὶ καταλιπεῖν ὑπερβολὴν ἀνοίας τῶν ἐπιγινομένων; —
—how could he not with good reason be thought to have surpassed and out-babble Antiphanes the Bergaean, and to have left absolutely no excess of folly to any of his successors? —
- 34.6.1οἷς
A relative pronoun in the neuter plural, acting as the object of an omitted preposition (like ἐν) from the preceding incomplete clause, meaning 'in the very things in which [he refutes them]'. The participle καθαρεύων is nominative singular, agreeing with the subject Polybius, carrying over the negative force from the preceding οὐδʼ.
- 34.6.1τοῦ γοῦν Δικαιάρχου
The series of genitive elements starting with τοῦ γοῦν Δικαιάρχου, including the participles εἰπόντος and ἀποδόντος, forms a genitive absolute construction, setting up the background premise for Polybius' mathematical refutation of Dicaearchus' estimates.
- 34.6.3βεβηκυίᾳ
Perfect active participle of βαίνω in the dative feminine singular, used in a geometrical sense meaning 'resting upon' or 'fixed at', describing how the base angles of the hypothetical obtuse triangle are situated at the Strait and the Pillars.
- 34.6.11ὥσπερ... οὕτως
The conjunction ὥσπερ in §34.6.11 and the adverb οὕτως in §34.6.13 correlate to form the structural backbone of Strabo's direct refutation, drawing an analogy between the obvious local errors and the larger Mediterranean ones. This whole structure is framed by the potential optative clause φαίη τις ἄν ('one might say').
- 34.6.15δόξειεν
The third-person singular aorist active optative of δοκέω, which, combined with the particle ἄν, expresses potentiality in a rhetorical question. It has Polybius as its subject and governs the perfect infinitives ὑπερβεβηκέναι and ἀπολεληρηκέναι, forming the climax of Strabo's sarcastic criticism.