Γεωγραφικά 2.1.34

2.1.34

Ἀλλʼ ἐπὶ τὸν Ἵππαρχον πρότερον ἐπανιόντες τὰ ἑξῆς ἴδωμεν. πάλιν γὰρ πλάσας ἑαυτῷ λήμματα γεωμετρικῶς ἀνασκευάζει τὰ ὑπʼ ἐκείνου τυπωδῶς λεγόμενα. φησὶ γὰρ αὐτὸν λέγειν τὸ ἐκ Βαβυλῶνος εἰς μὲν Κασπίους πύλας διάστημα σταδίων ἑξακισχιλίων ἑπτακοσίων, εἰς δὲ τοὺς ὅρους τῆς Καρμανίας καὶ Περσίδος πλειόνων ἢ ἐνακισχιλίων, ὅπερ ἐπὶ γραμμῆς κεῖται πρὸς ἰσημερινὰς ἀνατολὰς εὐθείας ἀγομένης· γίνεσθαι δὲ ταύτην κάθετον ἐπὶ τὴν κοινὴν πλευρὰν τῆς τε δευτέρας καὶ τῆς τρίτης σφραγῖδος, ὥστε κατʼ αὐτὸν συνίστασθαι τρίγωνον ὀρθογώνιον ὀρθὴν ἔχον τὴν πρὸς τοῖς ὅροις τῆς Καρμανίας, καὶ τὴν ὑποτείνουσαν εἶναι ἐλάττω μιᾶς τῶν περὶ τὴν ὀρθὴν ἐχουσῶν· δεῖν οὖν τὴν Περσίδα τῆς δευτέρας ποιεῖν σφραγῖδος. πρὸς ταῦτα δʼ εἴρηται ὅτι οὔθʼ ἡ ἐκ Βαβυλῶνος εἰς τὴν Καρμανίαν ἐπὶ παραλλήλου λαμβάνεται, οὔθʼ ἡ διορίζουσα εὐθεῖα τὰς σφραγῖδας μεσημβρινὴ εἴρηται· ὥστʼ οὐδὲν εἴρηται πρὸς αὐτόν. οὐδὲ τὸ ἐπιφερόμενον · εἰρηκότος γὰρ ἀπὸ Κασπίων πυλῶν εἰς μὲν Βαβυλῶνα τοὺς λεχθέντας, εἰς δὲ Σοῦσα σταδίους εἶναι τετρακισχιλίους ἐνακοσίους, ἀπὸ δὲ Βαβυλῶνος τρισχιλίους τετρακοσίους, πάλιν ἀπὸ τῶν αὐτῶν ὁρμηθεὶς ὑποθέσεων ἀμβλυγώνιον τρίγωνον συνίστασθαί φησι πρός τε ταῖς Κασπίοις πύλαις καὶ Σούσοις καὶ Βαβυλῶνι, τὴν ἀμβλεῖαν γωνίαν ἔχον πρὸς Σούσοις, τὰ δὲ τῶν πλευρῶν μήκη τὰ ἐκκείμενα· εἶτʼ ἐπιλογίζεται, διότι συμβήσεται κατὰ τὰς ὑποθέσεις ταύτας τὴν διὰ Κασπίων πυλῶν μεσημβρινὴν γραμμὴν ἐπὶ τοῦ διὰ Βαβυλῶνος καὶ Σούσων παραλλήλου δυσμικωτέραν ἔχειν τὴν κοινὴν τομὴν τῆς κοινῆς τομῆς τοῦ αὐτοῦ παραλλήλου καὶ τῆς ἀπὸ Κασπίων πυλῶν καθηκούσης εὐθείας ἐπὶ τοὺς ὅρους τοὺς τῆς Καρμανίας καὶ τῆς Περσίδος πλείοσι τῶν τετρακισχιλίων καὶ τετρακοσίων· σχεδὸν δή τι πρὸς τὴν διὰ Κασπίων πυλῶν μεσημβρινὴν γραμμὴν ἡμίσειαν ὀρθῆς ποιεῖν γωνίαν τὴν διὰ Κασπίων πυλῶν καὶ τῶν ὅρων τῆς τε Καρμανίας καὶ τῆς Περσίδος, καὶ νεύειν αὐτὴν ἐπὶ τὰ μέσα τῆς τε μεσημβρίας καὶ τῆς ἰσημερινῆς ἀνατολῆς· ταύτῃ δʼ εἶναι παράλληλον τὸν Ἰνδὸν ποταμόν, ὥστε καὶ τοῦτον ἀπὸ τῶν ὀρῶν οὐκ ἐπὶ μεσημβρίαν ῥεῖν, ὥς φησιν Ἐρατοσθένης, ἀλλὰ μεταξὺ ταύτης καὶ τῆς ἰσημερινῆς ἀνατολῆς, καθάπερ ἐν τοῖς ἀρχαίοις πίναξι καταγέγραπται. τίς οὖν συγχωρήσει τὸ νῦν συσταθὲν τρίγωνον ἀμβλυγώνιον εἶναι, μὴ συγχωρῶν ὀρθογώνιον εἶναι τὸ περιέχον αὐτό; τίς δʼ ἐπὶ παραλλήλου κειμένην τὴν ἀπὸ Βαβυλῶνος εἰς Σοῦσα μίαν τῶν τὴν ἀμβλεῖαν περιεχουσῶν, τὴν ὅλην μὴ συγχωρῶν τὴν μέχρι Καρμανίας; τίς δὲ τῷ Ἰνδῷ παράλληλον τὴν ἀπὸ Κασπίων πυλῶν ἐπὶ τοὺς ὅρους τῆς Καρμανίας; ὧν χωρὶς κενὸς ἂν εἴη ὁ συλλογισμός. χωρὶς δὲ τούτων κἀκεῖνος εἴρηκεν, ὅτι ῥομβοειδές ἐστι τὸ σχῆμα τῆς Ἰνδικῆς· καὶ καθάπερ ἡ ἑωθινὴ πλευρὰ παρέσπασται πολὺ πρὸς ἕω, καὶ μάλιστα τῷ ἐσχάτῳ ἀκρωτηρίῳ, ὃ καὶ πρὸς μεσημβρίαν προπίπτει πλέον παρὰ τὴν ἄλλην ᾐόνα, οὕτω καὶ ἡ παρὰ τὸν Ἰνδὸν πλευρά. πάντα δὲ ταῦτα λέγει γεωμετρικῶς ἐλέγχων, οὐ πιθανῶς.

We will now return at once to Hipparchus, and see what comes next. Continuing to palm assumptions of his own [upon Eratosthenes], he goes on to refute, with geometrical accuracy, statements which that author had made in a mere general way. Eratosthenes, he says, estimates that there are 6700 stadia between Babylon and the Caspian Gates, and from Babylon to the frontiers of Carmania and Persia above 9000 stadia; this he supposes to lie in a direct line towards the equinoctial rising, and perpendicular to the common side of his second and third sections. Thus, according to his plan, we should have a right-angled triangle, with the right angle next to the frontiers of Carmania, and its hypotenuse less than one of the sides about the right angle! Consequently Persia should be included in the second section.
To this we reply, that the line drawn from Babylon to Carmania was never intended as a parallel, nor yet that which divides the two sections as a meridian, and that therefore nothing has been laid to his charge, at all events with any just foundation. In fact, Eratosthenes having stated the number of stadia from the Caspian Gates to Babylon as above given, [from the Caspian Gates] to Susa 4900 stadia, and from Babylon [to Susa] 3400 stadia, Hipparchus runs away from his former hypothesis, and says that [by drawing lines from] the Caspian Gates, Susa, and Babylon, an obtuse-angled triangle would be the result, whose sides should be of the length laid down, and of which Susa would form the obtuse angle. He then argues, that according to these premises, the meridian drawn from the Gates of the Caspian will intersect the parallel of Babylon and Susa 4400 stadia more to the west, than would a straight line drawn from the Caspian to the confines of Carmania and Persia; and that this last line, forming with the meridian of the Caspian Gates half a right angle, would lie exactly in a direction midway between the south and the equinoctial rising. Now as the course of the Indus is parallel to this line, it cannot flow south on its descent from the mountains, as Eratosthenes asserts, but in a direction lying between the south and the equinoctial rising, as laid down in the ancient charts. But who is there who will admit this to be an obtuse-angled triangle, without also admitting that it contains a right angle? Who will agree that the line from Babylon to Susa, which forms one side of this obtuse-angled triangle, lies parallel, without admitting the same of the whole line as far as Carmania? or that the line drawn from the Caspian Gates to the frontiers of Carmania is parallel to the Indus? Nevertheless, without this the reasoning [of Hipparchus] is worth nothing
Eratosthenes himself also states, [continues Hipparchus,] that the form of India is rhomboidal; and since the whole eastern border of that country has a decided tendency towards the east, but more particularly the extremest cape, which lies more to the south than any other part of the coast, the side next the Indus must be the same.