Humanitext Reader

Strabo · Geography §2.1.26-2.1.28

Sides of the Third Portion and Hipparchus's Geometry

Passage 54 of 577 · Greek

Summary

Presents Eratosthenes' description of the eastern and western sides of the third portion, and discusses Hipparchus's geometric criticism of it and its inconsistency in assumptions.

§2.1.26τῶν δὲ πλαγίων πλευρῶν τὴν ἑσπερίαν λέγει πρῶτον, ἣν ὁποία τίς ἐστιν, εἴτε μία εἴτε δύο, ἐν μέσῳ πάρεστι σκοπεῖν.
And of the lateral sides he mentions the western first; and what sort of side this is, whether it is one or two, we can consider later.
ἀπὸ γὰρ τῆς κατὰ Θάψακόν φησι διαβάσεως παρὰ τὸν Εὐφράτην εἰς μὲν Βαβυλῶνα σταδίους εἶναι τετρακισχιλίους ὀκτακοσίους, ἐντεῦθεν δʼ ἐπὶ τὰς ἐκβολὰς τοῦ Εὐφράτου καὶ πόλιν Τερηδόνα τρισχιλίους· τὰ δʼ ἀπὸ Θαψάκου πρὸς τὰς ἄρκτους μέχρι μὲν τῶν Ἀρμενίων πυλῶν καταμεμετρῆσθαι καὶ εἶναι ὡς χιλίους ἑκατόν, τοὺς δὲ διὰ Γορδυαίων καὶ Ἀρμενίων μηκέτι· διὸ δὴ παραλείπειν αὐτούς.
For he says that from the crossing at Thapsacus along the Euphrates to Babylon is four thousand eight hundred stadia, and from there to the outlets of the Euphrates and the city of Teredon is three thousand; and that the parts from Thapsacus toward the north as far as the Armenian Gates have been measured and are about one thousand one hundred stadia, but those through the Gordyaeans and Armenians are no longer so, and therefore he leaves them out.
τοῦ δὲ πρὸς ἕω πλευροῦ τὸ μὲν διὰ τῆς Περσικῆς κατὰ μῆκος ἀπὸ τῆς Ἐρυθρᾶς ὡς ἐπὶ Μηδίαν καὶ τὰς ἄρκτους οὐκ ἔλαττον εἶναι δοκεῖ τῶν ὀκτακισχιλίων, ἀπὸ δέ τινων ἀκρωτηρίων καὶ ὑπὲρ τοὺς ἐνακισχιλίους, τὸ δὲ λοιπὸν διὰ τῆς Παραιτακηνῆς καὶ Μηδίας ἐπὶ Κασπίους πύλας ὡς τρισχιλίων·
Of the eastern side, the part through Persis in length from the Red Sea toward Media and the north seems to be not less than eight thousand stadia, and from certain promontories even over nine thousand, and the remainder through Paraitakene and Media to the Caspian Gates about three thousand.
τὸν δὲ Τίγριν ποταμὸν καὶ τὸν Εὐφράτην ῥέοντας ἐκ τῆς Ἀρμενίας πρὸς μεσημβρίαν, ἐπειδὰν παραμείψωνται τὰ τῶν Γορδυαίων ὄρη, κύκλον μέγαν περιβαλομένους καὶ ἐμπεριλαβόντας χώραν πολλὴν τὴν Μεσοποταμίαν ἐπιστρέφειν πρὸς χειμερινὴν ἀνατολὴν καὶ τὴν μεσημβρίαν, πλέον δὲ τὸν Εὐφράτην· γενόμενον δὲ τοῦτον ἔγγιον ἀεὶ τοῦ Τίγριδος κατὰ τὸ Σεμιράμιδος διατείχισμα καὶ κώμην καλουμένην Ὦπιν, διασχόντα ταύτης ὅσον διακοσίους σταδίους καὶ ῥυέντα διὰ Βαβυλῶνος ἐκπίπτειν εἰς τὸν Περσικὸν κόλπον.
And the river Tigris and the Euphrates, flowing from Armenia toward the south, after they pass the mountains of the Gordyaeans, making a great circuit and encompassing a large territory, Mesopotamia, turn toward the winter sunrise and the south, and the Euphrates does so to a greater degree; and this latter, becoming always closer to the Tigris near the wall of Semiramis and the village called Opis, being distant from it by about two hundred stadia and flowing through Babylon, empties into the Persian Gulf.
γίνεται δή φησί τὸ σχῆμα τῆς Μεσοποταμίας καὶ Βαβυλωνίας ὑπηρεσίῳ παραπλήσιον.
Thus, he says, the shape of Mesopotamia and Babylonia becomes similar to a rowing boat.
ὁ μὲν δὴ Ἐρατοσθένης τοιαῦτʼ εἴρηκε.
Eratosthenes indeed has said such things.
§2.1.27περὶ δὲ τῆς τρίτης σφραγῖδος καὶ ἄλλα μέν τινα ἁμαρτήματα ποιεῖ, περὶ ὧν ἐπισκεψόμεθα, ἃ δὲ Ἵππαρχος προφέρει αὐτῷ, οὐ πάνυ.
Now concerning the third seal, he commits certain other errors, which we shall examine later, but as for those which Hipparchus charges against him, he is not altogether in error.
σκοπῶμεν δʼ ἃ λέγει.
But let us look at what Hipparchus says.
βουλόμενος γὰρ βεβαιοῦν τὸ ἐξ ἀρχῆς, ὅτι οὐ μεταθετέον τὴν Ἰνδικὴν ἐπὶ τὰ νοτιώτερα, ὥσπερ Ἐρατοσθένης ἀξιοῖ, σαφὲς ἂν γενέσθαι τοῦτο μάλιστά φησιν ἐξ ὧν αὐτὸς ἐκεῖνος προφέρεται· τὴν γὰρ τρίτην μερίδα κατὰ τὴν βόρειον πλευρὰν εἰπόντα ἀφορίζεσθαι ὑπὸ τῆς ἀπὸ Κασπίων πυλῶν ἐπὶ τὸν Εὐφράτην γραμμῆς σταδίων μυρίων οὔσης, μετὰ ταῦτα ἐπιφέρειν ὅτι τὸ νότιον πλευρὸν τὸ ἀπὸ Βαβυλῶνος εἰς τοὺς ὅρους τῆς Καρμανίας μικρῷ πλειόνων ἐστὶν ἢ ἐνακισχιλίων, τὸ δὲ πρὸς δύσει πλευρὸν ἀπὸ Θαψάκου παρὰ τὸν Εὐφράτην ἐστὶν εἰς Βαβυλῶνα τετρακισχίλιοι ὀκτακόσιοι στάδιοι, καὶ ἑξῆς ἐπὶ τὰς ἐκβολὰς τρισχίλιοι, τὰ δὲ πρὸς ἄρκτον ἀπὸ Θαψάκου τὸ μὲν ἀπομεμέτρηται μέχρι χιλίων ἑκατόν, τὸ λοιπὸν δʼ οὐκέτι.
For wishing to confirm his original claim that India must not be shifted to more southern parts, as Eratosthenes demands, he says that this would become most clear from what that very man brings forward; for after saying that the third portion on its northern side is defined by the line from the Caspian Gates to the Euphrates, which is ten thousand stadia, he then adds that the southern side from Babylon to the boundaries of Carmania is a little more than nine thousand, and the western side from Thapsacus along the Euphrates to Babylon is four thousand eight hundred stadia, and next to the outlets three thousand, and as for the parts toward the north from Thapsacus, one part has been measured as far as one thousand one hundred, but the remainder is no longer so.
ἐπεὶ τοίνυν φησί τὸ μὲν βόρειόν ἐστι πλευρὸν τῆς τρίτης μερίδος ὡς μυρίων, ἡ δὲ τούτῳ παράλληλος ἀπὸ Βαβυλῶνος εὐθεῖα μέχρι ἀνατολικοῦ πλευροῦ συνελογίσθη μικρῷ πλειόνων ἢ ἐνακισχιλίων, δῆλον ὅτι ἡ Βαβυλὼν οὐ πολλῷ πλείοσιν ἢ χιλίοις σταδίοις ἐστὶν ἀνατολικωτέρα τῆς κατὰ Θάψακον διαβάσεως. §2.1.28Ἐροῦμεν δʼ ὅτι, εἰ μὲν ἐπὶ τῆς αὐτῆς μεσημβρινῆς εὐθείας ἐπʼ ἀκριβὲς ἐλαμβάνοντο αἵ τε Κάσπιοι πύλαι καὶ οἱ ὅροι τῶν Καρμανίων καὶ Περσῶν, πρὸς ὀρθάς τε ἤγοντο ἀπὸ τῆς λεχθείσης μεσημβρινῆς εὐθείας ἥ τε ἐπὶ Θάψακον καὶ ἡ ἐπὶ Βαβυλῶνα, συνέβαινεν ἂν τοῦτο.
"Since therefore," he says, "the northern side of the third portion is about ten thousand, and the straight line from Babylon parallel to this as far as the eastern side was calculated to be a little more than nine thousand, it is clear that Babylon is not more than a little over one thousand stadia further east than the crossing at Thapsacus." But we shall say that if the Caspian Gates and the boundaries of the Carmanians and Persians were assumed to be strictly on the same meridian line, and the lines to Thapsacus and Babylon were drawn at right angles from the said meridian line, this would have happened.
ἡ γὰρ προσεκβαλλομένη τῇ διὰ Βαβυλῶνος μέχρι τῆς διὰ Θαψάκου εὐθείας μεσημβρινῆς ἴση ἂν ἦν πρὸς αἴσθησιν ἢ πάρισός γε τῇ ἀπὸ Κασπίων πυλῶν εἰς Θάψακον, ὥστε τῇ ὑπεροχῇ ἐγίνετʼ ἂν ἀνατολικωτέρα ἡ Βαβυλὼν τῆς Θαψάκου, ᾗ ὑπερέχει ἡ ἐκ Κασπίων πυλῶν εἰς Θάψακον τῆς ἐκ τῶν Καρμανίων ὅρων εἰς Βαβυλῶνα.
For the line produced along that through Babylon as far as the meridian line of that through Thapsacus would have been equal to the senses, or at least nearly equal, to that from the Caspian Gates to Thapsacus, so that by the excess Babylon would have been further east than Thapsacus by the amount that the line from the Caspian Gates to Thapsacus exceeds that from the Carmanian boundaries to Babylon.
ἀλλʼ οὔτε τὴν διορίζουσαν γραμμὴν ἑσπέριον πλευρὸν τῆς Ἀριανῆς ἐπὶ μεσημβρινοῦ κειμένην εἴρηκεν Ἐρατοσθένης, οὔτε τὴν ἀπὸ Κασπίων πυλῶν ἐπὶ Θάψακον πρὸς ὀρθὰς τῇ διὰ τῶν Κασπίων πυλῶν μεσημβρινῇ, ἀλλὰ μᾶλλον τὴν τῷ ὄρει γραφομένην, πρὸς ἣν ἡ ἐπὶ Θάψακον γωνίαν ποιεῖ ἀπὸ τοῦ αὐτοῦ σημείου κατηγμένη ἀφʼ οὗ καὶ ἡ τοῦ ὄρους γραμμή· οὔθʼ ἡ ἐπὶ Βαβυλῶνα ἠγμένη ἀπὸ τῆς Καρμανίας παράλληλος εἴρηται τῇ ἐπὶ Θάψακον ἠγμένῃ· οὐδʼ εἰ παράλληλος ἦν, μὴ ὀρθὰς δὲ τῇ διὰ Κασπίων πυλῶν μεσημβρινῇ, οὐδὲν ἂν ἐγίνετο πλέον πρὸς τὸν συλλογισμόν.
But Eratosthenes has neither said that the line bounding the western side of Ariana lies on a meridian, nor that the line from the Caspian Gates to Thapsacus is at right angles to the meridian through the Caspian Gates, but rather that it is drawn along the mountain, with which the line to Thapsacus makes an angle, being drawn down from the same point from which the line of the mountain is also drawn; nor has the line drawn to Babylon from Carmania been said to be parallel to that drawn to Thapsacus; and even if it were parallel, but not at right angles to the meridian through the Caspian Gates, nothing more would have been gained for the calculation.

Notes

  1. 2.1.26ἐν μέσῳ πάρεστι σκοπεῖν — On the interpretation of ἐν μέσῳ. Here it means "in the meantime" or "later," indicating a tentative mention before a full examination of Eratosthenes' theory.
  2. 2.1.27ἃ δὲ Ἵππαρχος προφέρει αὐτῷ, οὐ πάνυ — Ellipsis of the predicate. οὐ πάνυ negates ἁμαρτήματα ποιεῖ, meaning "but as for the charges Hipparchus brings against him, he (Eratosthenes) is not at all (making errors)."
  3. 2.1.28ἡ γὰρ προσεκβαλλομένη τῇ διὰ Βαβυλῶνος — Geometric assumption. εὐθεῖα (straight line) is omitted after ἡ προσεκβαλλομένη, which acts as the subject of the main verb ἂν ἦν. It refers to a line produced in a geometric construction to meet another meridian.

Cite this passage

Strabo, Geography §2.1.26-2.1.28. Humanitext Reader, https://reader.humanitext.ai/en/text/urn:cts:greekLit:tlg0099.tlg001.humanitext-grc2:2.1.26-2.1.28

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