§2.1.34Ἀλλʼ ἐπὶ τὸν Ἵππαρχον πρότερον ἐπανιόντες τὰ ἑξῆς ἴδωμεν.
But returning first to Hipparchus, let us see what follows.
πάλιν γὰρ πλάσας ἑαυτῷ λήμματα γεωμετρικῶς ἀνασκευάζει τὰ ὑπʼ ἐκείνου τυπωδῶς λεγόμενα.
For having again fabricated assumptions for himself, he geometrically refutes what was stated in outline by Eratosthenes.
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.
For he says that Eratosthenes says that the distance from Babylon to the Caspian Gates is six thousand seven hundred stadia, and to the borders of Carmania and Persis more than nine thousand, which distance lies on a straight line drawn towards the equinoctial east; and that this line becomes a perpendicular to the common side of the second and third seals, so that according to him there is formed a right-angled triangle having its right angle at the borders of Carmania, and the hypotenuse is smaller than one of the sides about the right angle; therefore Persis must be made part of the second seal.
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.
But against these points it has been said that neither is the line from Babylon to Carmania taken along a parallel, nor has the straight line bounding the seals been said to be a meridian; so that nothing has been said against him.
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.
Nor what follows: for since Eratosthenes has said that from the Caspian Gates to Babylon is the said number of stadia, and to Susa four thousand nine hundred, and from Babylon three thousand four hundred, Hipparchus, starting again from the same assumptions, says that an obtuse-angled triangle is formed at the Caspian Gates, Susa, and Babylon, having the obtuse angle at Susa, and the lengths of the sides being those set out; then he reasons that according to these assumptions, the meridian line through the Caspian Gates will have its point of intersection with the parallel through Babylon and Susa more westerly than the intersection of the same parallel and the straight line coming down from the Caspian Gates to the borders of Carmania and Persis by more than four thousand four hundred stadia; so that indeed the line through the Caspian Gates and the borders of Carmania and Persis makes an angle of almost half a right angle with the meridian line through the Caspian Gates, and inclines towards the midway between south and the equinoctial east; and that the Indus River is parallel to this, so that it too flows from the mountains not towards the south, as Eratosthenes says, but between south and the equinoctial east, just as is depicted in the ancient maps.
τίς οὖν συγχωρήσει τὸ νῦν συσταθὲν τρίγωνον ἀμβλυγώνιον εἶναι, μὴ συγχωρῶν ὀρθογώνιον εἶναι τὸ περιέχον αὐτό;
Who then will grant that the triangle now constructed is obtuse-angled, if he does not grant that the one containing it is right-angled?
τίς δʼ ἐπὶ παραλλήλου κειμένην τὴν ἀπὸ Βαβυλῶνος εἰς Σοῦσα μίαν τῶν τὴν ἀμβλεῖαν περιεχουσῶν, τὴν ὅλην μὴ συγχωρῶν τὴν μέχρι Καρμανίας;
And who will grant that the line from Babylon to Susa, which is one of the sides containing the obtuse angle, lies on a parallel, if he does not grant the whole line as far as Carmania to be so?
τίς δὲ τῷ Ἰνδῷ παράλληλον τὴν ἀπὸ Κασπίων πυλῶν ἐπὶ τοὺς ὅρους τῆς Καρμανίας;
And who will grant that the line from the Caspian Gates to the borders of Carmania is parallel to the Indus?
ὧν χωρὶς κενὸς ἂν εἴη ὁ συλλογισμός.
Without which assumptions the reasoning would be invalid.
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.
And besides these things, Eratosthenes himself has said that the shape of India is rhomboidal; and just as the eastern side is stretched far towards the east, and especially at the easternmost cape, which also projects towards the south more than the rest of the coast, so also is the side along the Indus.
πάντα δὲ ταῦτα λέγει γεωμετρικῶς ἐλέγχων, οὐ πιθανῶς.
But Hipparchus says all these things by way of refuting Eratosthenes geometrically, not persuasively.
§2.1.35ταῦτα δὲ καὶ αὐτὸς ἑαυτῷ ἐπενέγκας ἀπολύεται φήσας, εἰ μὲν παρὰ μικρὰ διαστήματα ὑπῆρχεν ὁ ἔλεγχος, συγγνῶναι ἂν ἦν· ἐπειδὴ δὲ παρὰ χιλιάδας σταδίων φαίνεται διαπίπτων, οὐκ εἶναι συγγνωστά· καίτοι ἐκεῖνόν γε καὶ παρὰ τετρακοσίους σταδίους αἰσθητὰ ἀποφαίνεσθαι τὰ παραλλάγματα, ὡς ἐπὶ τοῦ διʼ Ἀθηνῶν παραλλήλου καὶ τοῦ διὰ Ῥόδου.
And having brought these objections also against himself, he dismisses them by saying that if the refutation were concerned with small distances, it would be pardonable; but since Eratosthenes is shown to err by thousands of stadia, it is not pardonable; and yet Eratosthenes himself declares differences of even four hundred stadia to be perceptible, as in the case of the parallel through Athens and that through Rhodes.
ἔστι δὲ τὸ πρὸς αἴσθησιν οὐχ ἁπλοῦν, ἀλλὰ τὸ μὲν ἐν πλάτει μείζονι τὸ δʼ ἐν ἐλάττονι· μείζονι μέν, ἂν αὐτῷ τῷ ὀφθαλμῷ πιστεύωμεν ἢ καρποῖς ἢ κράσεσιν ἀέρων πρὸς τὴν τῶν κλιμάτων κρίσιν, ἐλάττονι δʼ, ἂν διʼ ὀργάνων γνωμονικῶν ἢ διοπτρικῶν.
But 'perceptible' is not a simple term, but one is in a larger range, and another in a smaller; in a larger range, if we trust our sight itself, or crops, or the temperature of the air for judging climates; in a smaller, if we do so by means of gnomonic or dioptric instruments.
ὁ μὲν οὖν διʼ Ἀθηνῶν παράλληλος γνωμονικῶς ληφθεὶς καὶ ὁ διὰ Ῥόδου καὶ Καρίας, εἰκότως ἐν σταδίοις τοσούτοις αἰσθητὴν ἐποίησε τὴν διαφοράν.
Therefore, the parallel through Athens and that through Rhodes and Caria, being taken by means of a gnomon, reasonably made the difference perceptible in so many stadia.
ὁ δʼ ἐν πλάτει μὲν τρισχιλίων σταδίων, μήκει δὲ καὶ τετρακισμυρίων ὄρους, πελάγους δὲ τρισμυρίων λαμβάνων τὴν ἀπὸ δύσεως ἐπʼ ἰσημερινὰς ἀνατολὰς γραμμήν, καὶ τὰ ἐφʼ ἑκάτερον τὸ μέρος τὰ μὲν νότια ὀνομάζων τὰ δὲ βόρεια, καὶ ταῦτα πλινθία καλῶν καὶ σφραγῖδας, νοείσθω πῶς καὶ ταῦτα λέγει καὶ πλευρὰ τὰ μὲν ἀρκτικὰ τὰ δὲ νότια, καὶ πῶς τὰ μὲν ἑσπέρια τὰ δὲ ἑωθινά· καὶ τὸ μὲν παρὰ πολὺ διαμαρτανόμενον παρορῶν ὑπεχέτω λόγον (δίκαιον γάρ), τὸ δὲ παρὰ μικρὸν οὐδὲ παριδὼν ἐλεγκτέος ἐστίν.
But he who takes a line from west to equinoctial east, with a width of three thousand stadia, and a length of forty thousand in the case of the mountain range, and thirty thousand in the case of the sea, and calls the portions on either side, some southern and others northern, and calls these 'blocks' and 'seals', let it be understood in what sense he also says these things, and calls some sides northern and others southern, and some western and others eastern; and if he overlooks what errs by a great deal, let him render an account (for that is fair), but he should not be refuted for overlooking what is slightly in error.
ἐνταῦθα δʼ οὐδετέρως αὐτῷ προσάγεταί τις ἔλεγχος· οὔτε γὰρ τῶν ἐν τοσούτῳ πλάτει γεωμετρική τις δύναιτʼ ἂν ἀπόδειξις, οὔτʼ ἐν οἷς ἐπιχειρεῖ γεωμετρεῖν ὁμολογουμένοις χρῆται λήμμασιν, ἀλλʼ ἑαυτῷ πλάσας.
But here, in neither way is any refutation brought against him; for neither could there be any geometrical proof of things in such a wide range, nor does Hipparchus, in what he attempts to treat geometrically, use agreed-upon assumptions, but rather ones he fabricated for himself.