καὶ ἐν τοῖς ἑξῆς δὲ περὶ τῶν αὐτῶν ἐπιχειρῶν ἢ ταὐτὰ λέγει τοῖς ἐξελεγχθεῖσιν ὑφʼ ἡμῶν, ἢ λήμμασι προσχρῆται ψευδέσιν, ἢ ἐπιφέρει τὸ μὴ ἀκολουθοῦν. οὔτε γὰρ τῷ ἀπὸ Βαβυλῶνος εἰς Θάψακον εἶναι σταδίους τετρακισχιλίους ὀκτακοσίους, ἐντεῦθεν δὲ πρὸς τὴν ἄρκτον ἐπὶ τὰ Ἀρμένια ὄρη χιλίους ἑκατόν, ἀκολουθεῖ τὸ ἀπὸ Βαβυλῶνος ἐπὶ τοῦ διʼ αὐτῆς μεσημβρινοῦ ἐπὶ τὰ ἀρκτικὰ ὄρη πλείους εἶναι τῶν ἑξακισχιλίων· οὔτε τὸ ἀπὸ Θαψάκου ἐπὶ τὰ ὄρη χιλίων καὶ ἑκατόν φησιν Ἐρατοσθένης, ἀλλʼ εἶναί τι λοιπὸν ἀκαταμέτρητον, ὥσθʼ ἡ ἑξῆς ἔφοδος ἐκ μὴ διδομένου λήμματος οὐκ ἂν ἐπεραίνετο· οὔτʼ ἀπεφήνατο οὐδαμοῦ Ἐρατοσθένης τὴν Θάψακον τῆς Βαβυλῶνος πρὸς ἄρκτους κεῖσθαι πλείοσιν ἢ τετρακισχιλίοις καὶ πεντακοσίοις σταδίοις.
In the instances which follow, Hipparchus, treating of these subjects, either asserts things similar to those which we have already refuted, or takes for granted matters which are not so, or draws improper sequences. For instance, from the computation [of Eratosthenes] that the distance from Babylon to Thapsacus is 4800 stadia, and thence northward to the mountains of Armenia 2100 stadia more, it does not follow that, starting from the meridian of that city, the distance to the northern mountains is above 6000 stadia. Besides, Eratosthenes never says that the distance from Thapsacus to these mountains is 2100 stadia, but that a part thereof has never yet been measured; so that this argument [of Hipparchus], founded on a false hypothesis, amounts to nothing. Nor (lid Eratosthenes ever assert that Thapsacus lies more than 4500 stadia north of Babylon.
̔εξῆς δὲ συνηγορῶν ἔτι τοῖς ἀρχαίοις πίναξιν οὐ τὰ λεγόμενα ὑπὸ τοῦ Ἐρατοσθένους προφέρεται περὶ τῆς τρίτης σφραγῖδος, ἀλλʼ ἑαυτῷ κεχαρισμένως πλάττει τὴν ἀπόφασιν πρὸς ἀνατροπὴν εὐφυῆ. ὁ μὲν γὰρ ἀκολουθῶν τῇ θέσει τῇ προειρημένῃ τοῦ τε Ταύρου καὶ τῆς ἀπὸ στηλῶν θαλάττης, διελὼν τῇ γραμμῇ ταύτῃ τὴν οἰκουμένην δίχα καὶ καλέσας τὸ μὲν βόρειον μέρος τὸ δὲ νότιον, πειρᾶται τούτων ἑκάτερον τέμνειν πάλιν εἰς τὰ δυνατὰ μέρη· καλεῖ δὲ ταῦτα σφραγῖδας. καὶ δὴ τοῦ νοτίου μέρους πρώτην εἰπὼν σφραγῖδα τὴν Ἰνδικήν, δευτέραν δὲ τὴν Ἀριανήν, ἐχούσας τι εὐπερίγραφον, ἴσχυσεν ἀμφοτέρων ἀποδοῦναι καὶ μῆκος καὶ πλάτος, τρόπον δέ τινα καὶ σχῆμα, ὡς ἂν γεωμετρικός. τὴν μὲν γὰρ Ἰνδικὴν ῥομβοειδῆ φησι διὰ τὸ τῶν πλευρῶν τὰς μὲν θαλάττῃ κλύζεσθαι τῇ τε νοτίῳ καὶ τῇ ἑῴᾳ, μὴ πάνυ κολπώδεις ᾐόνας ποιούσαις, τὰς δὲ λοιπὰς τὴν μὲν τῷ ὄρει τὴν δὲ τῷ ποταμῷ, κἀνταῦθα τοῦ εὐθυγράμμου σχήματος ὑπό τι σωζομένου· τὴν δʼ Ἀριανὴν ὁρῶν τάς γε τρεῖς πλευρὰς ἔχουσαν εὐφυεῖς πρὸς τὸ ἀποτελέσαι παραλληλόγραμμον σχῆμα, τὴν δʼ ἑσπέριον οὐκ ἔχων σημείοις ἀφορίσαι διὰ τὸ ἐπαλλάττειν ἀλλήλοις τὰ ἔθνη, γραμμῇ τινι ὅμως δηλοῖ τῇ ἀπὸ Κασπίων πυλῶν ἐπὶ τὰ ἄκρα τῆς Καρμανίας τελευτώσῃ τὰ συνάπτοντα πρὸς τὸν Περσικὸν κόλπον. ἑσπέριον μὲν οὖν καλεῖ τοῦτο τὸ πλευρόν, ἑῷον δὲ τὸ παρὰ τὸν Ἰνδόν, παράλληλα δʼ οὐ λέγει· οὐδὲ τὰ λοιπά, τό τε τῷ ὄρει γραφόμενον καὶ τὸ τῇ θαλάττῃ, ἀλλὰ μόνον τὸ μὲν βόρειον τὸ δὲ νότιον.
Again, Hipparchus, ever anxious to defend the [accuracy of the] ancient charts, instead of fairly stating the words of Eratosthenes concerning his third section of the habitable earth, wilfully makes him the author of an assertion easy of disproof. For Eratosthenes, following the opinion we before mentioned, that a line drawn from the Pillars of Hercules across the Mediterranean, and the length of the Taurus, would run due west and east, divides, by means of this line, the habitable earth into two portions, which he calls the northern and southern divisions; each of these he again essays to subdivide into as many smaller partitions as practicable, which he denominates sections. He makes India the first section of the southern part, and Ariana the second; these two countries possessing a good outline, he has been able not only to give us an accurate statement of their length and breadth, but an almost geometrically exact description of their figure. He tells us that the form of India is rhomboidal, being washed on two of its sides by the southern and eastern oceans [respectively], which do not deeply indent its shores, The two remaining sides are contained by its mountains and the river [Indus], so that it presents a kind of rectilinear figure. As to Ariana, he considered three of its sides well fitted to form a parallelogram; but of the western side he could give no regular definition, as it was inhabited by various nations; nevertheless he attempts an idea of it by a line drawn from the Caspian Gates to the limits of Carmania, which border on the Persian Gulf. This side he calls western, and that next the Indus eastern, but he does not tell us they are parallel to each other; neither does he say this of the other sides, one bounded by the mountains, and the other by the sea; he simply calls them north and south.
οὕτω δʼ ὁλοσχερεῖ τινι τύπῳ τὴν δευτέραν ἀποδιδοὺς σφραγῖδα πολὺ ταύτης ὁλοσχερέστερον ἀποδίδωσι τὴν τρίτην σφραγῖδα κατὰ πλείους αἰτίας. πρώτην μὲν τὴν λεχθεῖσαν, ὅτι οὐκ εὐκρινῶς ἀφώρισται ἡ ἀπὸ Κασπίων πυλῶν ἐπὶ Καρμανίαν, ἥτις κοινή ἐστι τῇ τρίτῃ πρὸς τὴν δευτέραν σφραγῖδα πλευρά· ἔπειθʼ ὅτι εἰς τὴν νότιον πλευρὰν ὁ Περσικὸς ἐμπίπτει κόλπος, ὅπερ καὶ αὐτός φησιν, ὥστʼ ἠνάγκασται τὴν ἐκ Βαβυλῶνος λαβεῖν γραμμὴν ὡς ἂν εὐθεῖάν τινα διὰ Σούσων καὶ Περσεπόλεως μέχρι τῶν ὅρων τῆς Καρμανίας καὶ τῆς Περσίδος, ᾗ δυνατὸς ἦν εὑρεῖν μεμετρημένην ὁδόν, σταδίων οὖσαν τὴν ὅλην μικρῷ πλειόνων ἢ ἐνακισχιλίων· ἣν νότιον μὲν καλεῖ πλευράν, παράλληλον δʼ οὐ λέγει τῇ βορείῳ. δῆλον δʼ ὅτι οὐδʼ ὁ Εὐφράτης, ᾧ τὸ ἑσπέριον ἀφορίζει πλευρόν, σύνεγγύς ἐστιν εὐθείᾳ γραμμῇ, ἀλλʼ ἀπὸ τῶν ὀρῶν ἐπὶ τὴν μεσημβρίαν ῥυεὶς εἶτʼ ἐπιστρέφει πρὸς ἕω καὶ πάλιν πρὸς νότον μέχρι τῆς εἰς θάλατταν ἐκβολῆς. δηλοῖ δὲ τὸ μὴ εὐθύπορον τοῦ ποταμοῦ, φράζων τὸ σχῆμα τῆς Μεσοποταμίας, ὃ ποιοῦσι συμπίπτοντες εἰς ἓν ὅ τε Τίγρις καὶ ὁ Εὐφράτης, ὑπηρεσίῳ παραπλήσιον, ὥς φησι. καὶ μὴν οὐδὲ πᾶν μεμετρημένον ἔχει τὸ ἑσπέριον πλευρὸν τὸ ἀφοριζόμενον ὑπὸ τοῦ Εὐφράτου, ἀλλὰ φησὶ τὸ πρὸς τῇ Ἀρμενίᾳ μέρος καὶ τοῖς ἀρκτικοῖς ὄρεσι μὴ ἔχειν πόσον ἐστὶ διὰ τὸ ἀμέτρητον εἶναι. διὰ δὴ ταῦτα πάντα τυπωδῶς φησιν ἀποδιδόναι τὴν τρίτην μερίδα· καὶ γὰρ καὶ τὰ διαστήματά φησιν ἐκ πολλῶν συναγαγεῖν τῶν τοὺς σταθμοὺς πραγματευσαμένων, τινὰς καὶ ἀνεπιγράφους καλεῖ. ἀγνωμονεῖν δὴ δόξειεν ἂν ὁ Ἵππαρχος πρὸς τὴν τοιαύτην ὁλοσχέρειαν γεωμετρικῶς ἀντιλέγων, ἐν ᾗ χάριν εἰδέναι δεῖ τοῖς καὶ ὁπωσοῦν ἀπαγγείλασιν ἡμῖν τὴν τῶν τόπων φύσιν. ὅταν δὲ δὴ μηδʼ ἐξ ὧν ἐκεῖνος λέγει λαμβάνῃ τὰς γεωμετρικὰς ὑποθέσεις ἀλλʼ ἑαυτῷ πλάσας, ἐκφανέστερον ἂν τὸ φιλότιμον καταμηνύοιτο.
Having in this manner but imperfectly traced the outlines of his second section, the third section, for various reasons, is still less exact. The first cause has been already explained, viz. that the line from the Caspian Gates to Carmania is not clearly defined, as the side of the section is common both to the third and second sections. Secondly, on account of the Persian Gulf interrupting the continuity of the southern side, as he himself tells us, he has been obliged to take the measured road running through Susa and Persepolis to the boundaries of Carmania and Persia, and suppose it straight. This road, which he calls the southern side, is a little more than 9000 stadia. He does not, however, tell us, that it runs parallel to the northern side. It is also clear that the Euphrates, which he makes the western boundary, is any thing but a straight line. On leaving the mountains it flows south, but soon shifts its course to the east; it then again pursues a southerly direction till it reaches the sea. In fact, Eratosthenes himself acknowledges the indirect course of this river, when he compares the shape of Mesopotamia, which is formed by the junction of the Tigris and Euphrates, to the cushion on a rower’s bench. The western side bounded by the Euphrates is not entirely measured; for he tells us that he does not know the extent of the portion between Armenia and the northern mountains, as it has not been measured. By reason of these hinderances he states that he has been only able to give a very superficial view of the third section, and that his estimate of the distances is borrowed from various Itineraries, some of them, according to his own description, anonymous. Hipparchus therefore must be considered guilty of unfairness, for criticising with geometrical precision a work of this general nature. We ought rather to be grateful to a person who gives us any description at all of the character of such [unknown] places. But when he urges his geometrical objections not against any real statement of Eratosthenes, but merely against imaginary hypotheses of his own creation, he shows too plainly the contradictory bent of his mind.
̔ο μὲν δὴ οὕτως φησὶ τὴν τρίτην μερίδα τυπωδῶς ἀποδίδοσθαι μυρίων σταδίων ἀπὸ Κασπίων πυλῶν ἐπὶ τὸν Εὐφράτην, κατὰ μέρος δὲ διαιρῶν, ὡς ἀναγεγραμμένην εὗρε τὴν μέτρησιν οὕτω τίθησιν, ἔμπαλιν τὴν ἀρχὴν ἀπὸ τοῦ Εὐφράτου ποιησάμενος καὶ τῆς κατὰ Θάψακον διαβάσεως αὐτοῦ. μέχρι μὲν δὴ τοῦ Τίγριδος, ὅπου Ἀλέξανδρος διέβη, σταδίους χιλίους καὶ τετρακοσίους γράφει· ἐντεῦθεν δʼ ἐπὶ τοὺς ἑξῆς τύπους διὰ Γαυγαμήλων καὶ τοῦ Λύκου καὶ Ἀρβήλων καὶ Ἐκβατάνων, ᾗ Δαρεῖος ἐκ τῶν Γαυγαμήλων ἔφυγε μέχρι Κασπίων πυλῶν, τοὺς μυρίους ἐκπληροῖ, τριακοσίοις μόνον πλεονάσας. τὸ μὲν δὴ βόρειον πλευρὸν οὕτω καταμετρεῖ, οὐ παράλληλον τοῖς ὄρεσι θεὶς οὐδὲ τῇ διὰ στηλῶν καὶ Ἀθηνῶν καὶ Ῥόδου γραμμῇ· ἡ γὰρ Θάψακος πολὺ τῶν ὀρῶν ἀφέστηκε, συμπίπτει δὲ καὶ τὸ ὄρος καὶ ἡ ἀπὸ Θαψάκου ὁδὸς ἐπὶ τὰς Κασπίους πύλας. καὶ τά γε προσάρκτια μέρη τοῦ ὅρου ταῦτʼ ἐστίν.
It is in this general kind of description of the third section that Eratosthenes supposes 10,000 stadia from the Caspian Gates to the Euphrates. This he again divides according to former admeasurements which he found preserved. Starting from the point where the Euphrates passes near to Thapsacus, he computes from thence to the place where Alexander crossed the Tigris 2400 stadia. The route thence through Gaugamela, the Lycus, Arbela, and Ecbatana, whither Darius fled from Gaugamela to the Caspian Gates, makes up the 10,000 stadia, which is only 300 stadia too much. Such is the measure of the northern side given by Eratosthenes, which he could not have supposed to be parallel to the mountains, nor yet to the line drawn from the Pillars of Hercules through Athens and Rhodes. For Thapsacus is far removed from the mountains, and the route from Thapsacus to the Caspian Gates only falls in with the mountains at that point. Such is the boundary on the northern side.
Ἀποδοὺς δὲ τὸ βόρειον οὕτω πλευρόν τὸ δὲ νότιον φησί παρὰ μὲν τὴν θάλατταν οὐκ ἔστι λαβεῖν διὰ τὸ τὸν Περσικὸν ἐμπίπτειν κόλπον, ἀπὸ Βαβυλῶνος δὲ διὰ Σούσων καὶ Περσεπόλεως μέχρι τῶν ὁρίων τῆς τε Περσίδος καὶ τῆς Καρμανίας σταδίους εἶναι ἐνακισχιλίους καὶ διακοσίους, νότιον μὲν λέγων, παράλληλον δʼ οὐ λέγων τῷ βορείῳ τὸ νότιον. τὴν δὲ διαφωνίαν τοῦ μήκους φησὶ συμβαίνειν, τοῦ τε βορείου τεθέντος πλευροῦ καὶ τοῦ νοτίου, διὰ τὸ τὸν Εὐφράτην μέχρι τινὸς πρὸς μεσημβρίαν ῥυέντα πρὸς τὴν ἕω πολὺ ἐγκλίνειν.
Thus, says Eratosthenes, we have given you a description of the northern side; as for the southern, we cannot take its measure along the sea, on account of the Persian Gulf, which intercepts [its continuity], but from Babylon through Susa and Persepolis to the confines of Persia and Carmania there are 9200 stadia. This he calls the southern side, but he does not say it is parallel to the northern. The difference of length between the northern and southern sides is caused, he tells us, by the Euphrates, which after running south some distance shifts its course almost due east.
τῶν δὲ πλαγίων πλευρῶν τὴν ἑσπερίαν λέγει πρῶτον, ἣν ὁποία τίς ἐστιν, εἴτε μία εἴτε δύο, ἐν μέσῳ πάρεστι σκοπεῖν. 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. 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· 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. γίνεται δή φησί τὸ σχῆμα τῆς Μεσοποταμίας καὶ Βαβυλωνίας ὑπηρεσίῳ παραπλήσιον. ὁ μὲν δὴ Ἐρατοσθένης τοιαῦτʼ εἴρηκε.
Of the two remaining sides, he describes the western first, but whether we are to regard it as one single straight line, or two, seems to be undecided. He says,—From Thapsacus to Babylon, following the course of the Euphrates, there are 4800 stadia; from thence to the mouth of the Euphrates and the city of Teredon, 3000 more; from Thapsacus northward to the Gates of Armenia, having been measured, is stated to be 1100 stadia, but the distance through Gordyaea and Armenia, not having yet been measured, is not given. The eastern side, which stretches lengthwise through Persia from the Red Sea towards Media and the north, does not appear to be less than 8000 stadia, and measured from certain headlands above 9000, the rest of the distance through Paraetacena and Media to the Caspian Gates being 3000 stadia. The rivers Tigris and Euphrates flowing from Armenia towards the south, after having passed the Gordytaean mountains, and having formed a great circle which embraces the vast country of Mesopotamia, turn towards the rising of the sun in winter and the south, particularly the Euphrates, which, continually approaching nearer and nearer to the Tigris, passes by the rampart of Semiramis, and at about 200 stadia from the village of Opis, thence it flows through Babylon, and so discharges itself into the Persian Gulf. Thus the figure of Mesopotamia and Babylon resembles the cushion of a rower’s bench.—Such are the words of Eratosthenes.
περὶ δὲ τῆς τρίτης σφραγῖδος καὶ ἄλλα μέν τινα ἁμαρτήματα ποιεῖ, περὶ ὧν ἐπισκεψόμεθα, ἃ δὲ Ἵππαρχος προφέρει αὐτῷ, οὐ πάνυ. σκοπῶμεν δʼ ἃ λέγει. 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. 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.
In the Third Section it is true he does make some mistakes, which we shall take into consideration; but they are nothing like the amount which Hipparchus attributes to him. However, we will examine his objections. [In the first place,] he would have the ancient charts left just as they are, and by no means India brought more to the south, as Eratosthenes thinks proper. Indeed, he asserts that the very arguments adduced by that writer only confirm him the more in his opinion. He says, According to Eratosthenes, the northern side of the third section is bounded by a line of 10,000 stadia drawn from the Caspian Gates to the Euphrates, the southern side from Babylon to the confines of Carmania is a little more than 9000 stadia. On the western side, following the course of the Euphrates, from Thapsacus to Babylon there are 4800 stadia, and thence to the outlets of the river 3000 stadia more. Northward from Thapsacus [to the Gates of Armenia] is reckoned 1100 stadia; the rest has not been measured. Now since Eratosthenes says that the northern side of this Third Section is about 10,000 stadia, and that the right line parallel thereto drawn from Babylon to the eastern side is computed at just above 9000 stadia, it follows that Babylon is not much more than 1000 stadia east of the passage of [the Euphrates] near Thapsacus.
Ἐροῦμεν 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. 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. 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.
We answer, that if the Caspian Gates and the boundary line of Carmania and Persia were exactly under the same meridian, and if right lines drawn in the direction of Thapsacus and Babylon would intersect such meridian at right angles, the inference would be just. For then the line [from the common frontier of Carmania and Persia] to Babylon if produced to the meridian of Thapsacus, would appear to the eye equal, or nearly equal, to that from the Caspian Gates to Thapsacus. Consequently, Babylon would only be east of Thapsacus in the same proportion as the line drawn from the Caspian Gates to Thapsacus exceeds the line drawn from the frontier of Carmania to Babylon. Eratosthenes, however, does not tell us that the line which bounds the western coast of Ariana follows the direction of the meridian; nor yet that a line drawn from the Caspian Gates to Thapsacus would form right angles with the meridian of the Caspian Gates. But rather, that the line which would form right angles with the meridian, would be one which should follow the course of the Taurus, and with which the line drawn from the Caspian Gates to Thapsacus would form an acute angle. Nor, again, does he ever say that a line drawn from Carmania to Babylon would be parallel to that drawn [from the Caspian Gates] to Thapsacus; and even if it were parallel, this would prove nothing for the argument of Hipparchus, since it does not form right angles with the meridian of the Caspian Gates.
ὁ δὲ ταῦτα λαβὼν ἐξ ἑτοίμου καὶ δείξας, ὡς οἴεται, διότι ἡ Βαβυλὼν κατὰ Ἐρατοσθένη Θαψάκου ἀνατολικωτέρα ἐστὶ μικρῷ πλείοσιν ἢ χιλίοις σταδίοις, πάλιν ἄλλως πλάττει λῆμμα ἑαυτῷ πρὸς τὴν ἑξῆς ἀπόδειξιν καί φησιν, ἐὰν ἐννοηθῇ ἀπὸ Θαψάκου ἐπὶ μεσημβρίαν εὐθεῖα ἀγομένη καὶ ἀπὸ Βαβυλῶνος ἐπὶ ταύτην κάθετος, τρίγωνον ὀρθογώνιον ἔσεσθαι, συνεστηκὸς ἔκ τε τῆς ἀπὸ Θαψάκου ἐπὶ Βαβυλῶνα τεινούσης πλευρᾶς καὶ τῆς ἀπὸ Βαβυλῶνος καθέτου ἐπὶ τὴν διὰ Θαψάκου μεσημβρινὴν γραμμὴν ἠγμένης καὶ αὐτῆς τῆς διὰ Θαψάκου μεσημβρινῆς. τούτου δὲ τοῦ τριγώνου τὴν μὲν ὑποτείνουσαν τῇ ὀρθῇ τὴν ἀπὸ Θαψάκου εἰς Βαβυλῶνα τίθησιν, ἥν φησι τετρακισχιλίων ὀκτακοσίων εἶναι, τὴν δʼ ἐκ Βαβυλῶνος εἰς τὴν διὰ Θαψάκου μεσημβρινὴν γραμμὴν κάθετον μικρῷ πλειόνων ἢ χιλίων, ὅσων ἦν ἡ ὑπεροχὴ τῆς ἐπὶ Θάψακον πρὸς τὴν μέχρι Βαβυλῶνος· ἐκ δὲ τούτων καὶ τὴν λοιπὴν τῶν περὶ τὴν ὀρθὴν συλλογίζεται πολλαπλάσιον οὖσαν τῆς λεχθείσης καθέτου· προστίθησι δὲ ταύτῃ τὴν ἀπὸ Θαψάκου πρὸς ἄρκτον ἐκβαλλομένην μέχρι τῶν Ἀρμενίων ὀρῶν, ἧς τὸ μὲν ἔφη μεμετρῆσθαι Ἐρατοσθένης καὶ εἶναι χιλίων ἑκατόν, τὸ δʼ ἀμέτρητον ἐᾷ. οὗτος δʼ ἐπὶ τοὐλάχιστον ὑποτίθεται χιλίων, ὥστε τὸ συνάμφω δισχιλίων καὶ ἑκατὸν γίγνεσθαι, ὃ προσθεὶς τῇ ἐπʼ εὐθείας πλευρᾷ τοῦ τριγώνου μέχρι τῆς καθέτου τῆς ἐκ Βαβυλῶνος πολλῶν χιλιάδων λογίζεται διάστημα τὸ ἀπὸ τῶν Ἀρμενίων ὀρῶν καὶ τοῦ διʼ Ἀθηνῶν παραλλήλου μέχρι τῆς ἐκ Βαβυλῶνος καθέτου, ἥτις ἐπὶ τοῦ διὰ Βαβυλῶνος παραλλήλου ἵδρυται. τὸ δέ γε ἀπὸ τοῦ διʼ Ἀθηνῶν παραλλήλου ἐπὶ τὸν διὰ Βαβυλῶνος δείκνυσιν οὐ μεῖζον ὂν σταδίων δισχιλίων τετρακοσίων, ὑποτεθέντος τοῦ μεσημβρινοῦ παντὸς τοσούτων σταδίων, ὅσων Ἐρατοσθένης φησίν. εἰ δὲ τοῦτο, οὐκ ἂν ἦν τὰ ὄρη τὰ Ἀρμένια καὶ τὰ τοῦ Ταύρου ἐπὶ τοῦ διʼ Ἀθηνῶν παραλλήλου, ὡς Ἐρατοσθένης, ἀλλὰ πολλαῖς χιλιάσι σταδίων ἀρκτικώτερα κατʼ αὐτὸν ἐκεῖνον. ἐνταῦθα δὴ πρὸς τῷ τοῖς ἀνεσκευασμένοις λήμμασι προσχρῆσθαι πρὸς τὴν τοῦ ὀρθογωνίου τριγώνου τάξιν καὶ τοῦτο λαμβάνει τὸ μὴ διδόμενον, τὸ τὴν ὑποτείνουσαν τῇ ὀρθῇ γωνίᾳ τὴν ἀπὸ Θαψάκου γραμμὴν εὐθεῖαν εἶναι μέχρι Βαβυλῶνος ἐν σταδίοις τετρακισχιλίοις ὀκτακοσίοις. παρά τε γὰρ τὸν Εὐφράτην φησὶν εἶναι τὴν ὁδὸν ταύτην ὁ Ἐρατοσθένης, καὶ τὴν Μεσοποταμίαν σὺν τῇ Βαβυλωνίᾳ μεγάλῳ κύκλῳ περιέχεσθαι λέγων ὑπό τε τοῦ Εὐφράτου καὶ τοῦ Τίγριδος, τὸ πλέον δὲ τῆς περιοχῆς ὑπὸ τοῦ Εὐφράτου συμβαίνειν φησίν· ὥσθʼ ἡ ἀπὸ Θαψάκου εἰς Βαβυλῶνα εὐθεῖα οὔτʼ ἂν παρὰ τὸν Εὐφράτην εἴη οὔτʼ ἂν τοσούτων σταδίων οὐδʼ ἐγγύς. ἀνατέτραπται οὖν ὁ συλλογισμός· καὶ μὴν εἴρηταί γε, ὅτι οὐχ οἷόν τε δυεῖν δεδομένων γραμμῶν ἀπὸ τῶν Κασπίων πυλῶν κατάγεσθαι τὴν μὲν ἐπὶ Θάψακον τὴν δʼ ἐπὶ τὰ τῶν Ἀρμενίων ὄρη τὰ κατάλληλα τῇ Θαψάκῳ, ἀπέχοντα τῆς Θαψάκου τοὐλάχιστον κατʼ αὐτὸν τὸν Ἵππαρχον δισχιλίους καὶ ἑκατὸν σταδίους, ἀμφοτέρας παραλλήλους εἶναι καὶ ἀλλήλαις καὶ τῇ διὰ Βαβυλῶνος, ἣν νότιον πλευρὰν Ἐρατοσθένης ἐκάλεσεν. ἐκεῖνος μὲν οὖν οὐκ ἔχων καταμεμετρημένην εἰπεῖν τὴν παρὰ τὰ ὄρη ὁδόν, τὴν δʼ ἀπὸ Θαψάκου ἐπὶ Κασπίους πύλας, ταύτην εἶπε καὶ προσέθηκε τὸ ὡς τυπωδῶς εἰπεῖν· ἄλλως τε τῷ βουλομένῳ τὸ μῆκος εἰπεῖν τῆς μετὰ τὴν Ἀριανὴν μέχρι Εὐφράτου χώρας οὐ πολὺ διέφερε ταύτην ἢ ἐκείνην καταμετρεῖν. ὁ δʼ ὡς παραλλήλους ὑπακούων λέγεσθαι τελέως ἂν δόξειε καταγινώσκειν παιδικὴν ἀμαθίαν τἀνθρώπου.
But taking this for granted, and proving, as he imagines, that, according to Eratosthenes, Babylon is east of Thapsacus rather more than 1000 stadia, he draws from this false hypothesis a new argument, which he uses to the following purpose; and says, If we suppose a right line drawn from Thapsacus towards the south, and another from Babylon perpendicular thereto, a right-angled triangle would be the result; whose sides should be, 1. A line drawn from Thapsacus to Babylon; 2. A perpendicular drawn from Babylon to the meridian of Thapsacus; 3. The meridian line of Thapsacus. The hypotenuse of this triangle would be a right line drawn from Thapsacus to Babylon, which he estimates at 4800 stadia. The perpendicular drawn from Babylon to the meridian of Thapsacus is scarcely more than 1000 stadia; the same amount by which the line drawn [from the Caspian Gates] to Thapsacus exceeds that [from the common frontier of Carmania and Persia] to Babylon. The two sides [of the triangle] being given, Hipparchus proceeds to find the third, which is much greater than the perpendicular aforesaid. To this he adds the line drawn from Thapsacus northwards to the mountains of Armenia, one part of which, according to Eratosthenes, was measured, and found to be 1100 stadia; the other, or part unmeasured by Eratosthenes, Hipparchus estimates to be 1000 stadia at the least: so that the two together amount to 2100 stadia. Adding this to the [length of the] side upon which falls the perpendicular drawn from Babylon, Hipparchus estimated a distance of many thousand stadia from the mountains of Armenia and the parallel of Athens to this perpendicular, which falls on the parallel of Babylon. From the parallel of Athens to that of Babylon he shows that there cannot be a greater distance than 2400 stadia, even admitting the estimate supplied by Eratosthenes himself of the number of stadia which the entire meridian contains; and that if this be so, the mountains of Armenia and the Taurus cannot be under the same parallel of latitude as Athens, (which is the opinion of Eratosthenes,) but many thousand stadia to the north, as the data supplied by that writer himself prove.
But here, for the formation of his right-angled triangle, Hipparchus not only makes use of propositions already overturned, but assumes what was never granted, namely, that the hypotenuse subtending his right angle, which is the straight line from Thapsacus to Babylon, is 4800 stadia in length. What Eratosthenes says is, that this route follows the course of the Euphrates, and adds, that Mesopotamia and Babylon are encompassed as it were by a great circle formed by the Euphrates and Tigris, but principally by the former of these rivers. So that a straight line from Thapsacus to Babylon would neither follow the course of the Euphrates, nor yet be near so many stadia in length. Thus the argument [of Hipparchus] is overturned. We have stated before, that supposing two lines drawn from the Caspian Gates, one to Thapsacus, and the other to the mountains of Armenia opposite Thapsacus, and distant therefrom, according to Hipparchus’s own estimate, 2100 stadia at the very least, neither of them would be parallel to each other, nor yet to that line which, passing through Babylon, is styled by Eratosthenes the southern side [of the third section]. As he could not inform us of the exact length of the route by the mountains, Eratosthenes tells us the distance between Thapsacus and the Caspian Gates; in fact, to speak in a general way, he puts this distance in place of the other; besides, as he merely wanted to give the length of the territory between Ariana and the Euphrates, he was not particular to have the exact measure of either route. To pretend that he considered the lines to be parallel to each other, is evidently to accuse the man of more than childish ignorance, and we dismiss the insinuation as nonsense forthwith.
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