Γεωγραφικά 2.1.36

2.1.36

βέλτιον δὲ περὶ τῆς τετάρτης λέγει μερίδος, προστίθησι δὲ καὶ τοῦ φιλαιτίου καὶ τοῦ μένοντος ἐπὶ τῶν αὐτῶν ὑποθέσεων ἢ τῶν παραπλησίων. τοῦτο μὲν γὰρ ὀρθῶς ἐπιτιμᾷ διότι μῆκος ὀνομάζει τῆς μερίδος ταύτης τὴν ἀπὸ Θαψάκου μέχρι Αἰγύπτου γραμμήν, ὥσπερ εἴ τις παραλληλογράμμου τὴν διάμετρον μῆκος αὐτοῦ φαίη· οὐ γὰρ ἐπὶ τοῦ αὐτοῦ παραλλήλου κεῖται ἥ τε Θάψακος καὶ ἡ τῆς Αἰγύπτου παραλία, ἀλλʼ ἐπὶ διεστώτων πολὺ ἀλλήλων, ἐν δὲ τῷ μεταξὺ διαγώνιός πως ἄγεται καὶ λοξὴ ἡ ἀπὸ Θαψάκου εἰς Αἴγυπτον. τὸ δὲ θαυμάζειν, πῶς ἐθάρρησεν εἰπεῖν ἑξακισχιλίων σταδίων τὸ ἀπὸ Πηλουσίου εἰς Θάψακον, πλειόνων ὄντων ἢ ὀκτακισχιλίων, οὐκ ὀρθῶς. λαβὼν γὰρ διʼ ἀποδείξεως μέν, ὅτι ὁ διὰ Πηλουσίου παράλληλος τοῦ διὰ Βαβυλῶνος πλείοσιν ἢ δισχιλίοις καὶ πεντακοσίοις σταδίοις νοτιώτερός ἐστι, κατʼ Ἐρατοσθένη δὲ (ὡς οἴεται), διότι τοῦ διὰ Βαβυλῶνος ὁ διὰ τῆς Θαψάκου ἀρκτικώτερος τετρακισχιλίοις ὀκτακοσίοις, συμπίπτειν φησὶ πλείους τῶν ὀκτακισχιλίων. πῶς οὖν κατʼ Ἐρατοσθένη δείκνυται ἡ τοσαύτη ἀπόστασις τοῦ διὰ Βαβυλῶνος παραλλήλου ἀπὸ τοῦ διὰ Θαψάκου, ζητῶ. ὅτι μὲν γὰρ ἀπὸ Θαψάκου ἐπὶ Βαβυλῶνα τοσοῦτόν ἐστιν, εἴρηκεν ἐκεῖνος· ὅτι δὲ καὶ ἀπὸ τοῦ διʼ ἑκατέρου παραλλήλου ἐπὶ τὸν διὰ θατέρου, οὐκ εἴρηκεν· οὐδὲ γάρ, ὅτι ἐπὶ ταὐτοῦ μεσημβρινοῦ ἐστιν ἡ Θάψακος καὶ ἡ Βαβυλών. τἀναντία γὰρ αὐτὸς ὁ Ἵππαρχος ἔδειξε κατʼ Ἐρατοσθένη πλείοσιν ἢ χιλίοις σταδίοις συμβαίνειν ἀνατολικωτέραν εἶναι τὴν Βαβυλῶνα τῆς Θαψάκου. ἡμεῖς τε παρετίθεμεν τὰς Ἐρατοσθένους ἀποφάσεις, ἐν αἷς τὸν Τίγριν καὶ τὸν Εὐφράτην ἐγκυκλοῦσθαι τήν τε Μεσοποταμίαν καὶ τὴν Βαβυλωνίαν, καὶ τὸ πλέον γε τῆς ἐγκυκλώσεως τὸν Εὐφράτην ποιεῖν· ἀπὸ γὰρ τῶν ἄρκτων ἐπὶ μεσημβρίαν ῥυέντα ἐπιστρέφειν πρὸς τὰς ἀνατολάς, ἐκπίπτειν δὲ ἐπὶ μεσημβρίαν. ἡ μὲν οὖν ἐπὶ μεσημβρίαν ἀπὸ τῶν ἄρκτων ὁδὸς ὡς ἂν μεσημβρινοῦ τινός ἐστιν, ἡ δʼ ἐπὶ τὰς ἀνατολὰς ἐπιστροφὴ καὶ ἐπὶ τὴν Βαβυλῶνα ἔκνευσίς τέ ἐστιν ἀπὸ τοῦ μεσημβρινοῦ καὶ οὐκ ἐπʼ εὐθείας διὰ τὴν ῥηθεῖσαν ἐγκύκλωσιν. τὴν δέ γε ὁδὸν εἴρηκε τετρακισχιλίων καὶ ὀκτακοσίων σταδίων τὴν ἐπὶ Βαβυλῶνα ἀπὸ Θαψάκου παρὰ τὸν Εὐφράτην προσθείς, καθάπερ ἐπίτηδες, τοῦ μή τινα εὐθεῖαν αὐτὴν δέξασθαι καὶ μέτρον τοῦ μεταξὺ δυεῖν παραλλήλων διαστήματος. μὴ διδομένου δὲ τούτου, κενόν ἐστι καὶ τὸ ἐφεξῆς δείκνυσθαι δοκοῦν, ὅτι συνισταμένου ὀρθογωνίου τριγώνου πρός τε Πηλουσίῳ καὶ Θαψάκῳ καὶ τῇ τομῇ τοῦ τε διὰ Πηλουσίου παραλλήλου καὶ τοῦ διὰ Θαψάκου μεσημβρινοῦ, μία τῶν περὶ τὴν ὀρθήν, ἡ ἐπὶ τοῦ μεσημβρινοῦ, μείζων ἔσται τῆς ὑπὸ τὴν ὀρθήν, τῆς ἀπὸ Θαψάκου εἰς Πηλούσιον. κενὸν δὲ καὶ τὸ συνάπτον τούτῳ, ἀπὸ μὴ συγχωρουμένου λήμματος κατασκευαζόμενον. οὐ γὰρ δὴ δίδοται τὸ ἀπὸ Βαβυλῶνος ἐπὶ τὸν διὰ Κασπίων πυλῶν μεσημβρινὸν εἶναι διάστημα τετρακισχιλίων ὀκτακοσίων. ἐλήλεγκται γὰρ ὑφʼ ἡμῶν ἐκ τῶν μὴ συγχωρουμένων ὑπʼ Ἐρατοσθένους κατεσκευακότα τοῦτο τὸν Ἵππαρχον· ἵνα δʼ ἀνίσχυρον ᾖ τὸ ὑπὸ ἐκείνου διδόμενον, λαβὼν τὸ εἶναι πλείους ἢ ἐννακισχιλίους ἐκ Βαβυλῶνος ἐπὶ τὴν ἐκ Κασπίων πυλῶν οὕτως ἀγομένην γραμμήν, ὡς ἐκεῖνος εἴρηκεν, ἐπὶ τοὺς ὅρους τῆς Καρμανίας, ἐδείκνυε τὸ αὐτό.

The fourth section Hipparchus certainly manages better, though he still maintains the same censorious tone, and obstinacy in sticking to his first hypotheses, or others similar. He properly objects to Eratosthenes giving as the length of this section a line drawn from Thapsacus to Egypt, as being similar to the case of a man who should tell us that the diagonal of a parallelogram was its length. For Thapsacus and the coasts of Egypt are by no means under the same parallel of latitude, but under parallels considerably distant from each other, and a line drawn from Thapsacus to Egypt would lie in a kind of diagonal or oblique direction between them. But he is wrong when he expresses his surprise that Eratosthenes should dare to state the distance between Pelusium and Thapsacus at 6000 stadia, when he says there are above 8000. In proof of this he advances that the parallel of Pelusium is south of that of Babylon by more than 2500 stadia, and that according to Eratosthenes (as he supposes) the latitude of Thapsacus is above 4800 stadia north of that of Babylon; from which Hipparchus tells us it results that [between Thapsacus and Pelusium] there are more than 8000 stadia. But I would inquire how he can prove that Eratosthenes supposed so great a distance between the parallels of Babylon and Thapsacus? He says, indeed, that such is the distance from Thapsacus to Babylon, but not that there is this distance between their parallels, nor yet that Thapsacus and Babylon are under the same meridian. So much the contrary, that Hipparchus has himself pointed out, that, according to Eratosthenes, Babylon ought to be east of Thapsacus more than 2000 stadia. We have before cited the statement of Eratosthenes, that Mesopotamia and Babylon are encircled by the Tigris and Euphrates, and that the greater portion of the Circle is formed by this latter river, which flowing north and south takes a turn to the east, and then, returning to a southerly direction, discharges itself [into the sea]. So long as it flows from north to south, it may be said to follow a southerly direction; but the turning towards the east and Babylon is a decided deviation from the southerly direction, and it never recovers a straight course, but forms the circuit we have mentioned above. When he tells us that the journey from Babylon to Thapsacus is 4800 stadia, he adds, following the course of the Euphrates, as if on purpose lest any one should understand such to be the distance in a direct line, or between the two parallels. If this be not granted, it is altogether a vain attempt to show that if a right-angled triangle were constructed by lines drawn from Pelusium and Thapsacus to the point where the parallel of Thapsacus intercepts the meridian of Pelusium, that one of the lines which form the right angle, and is in the direction of the meridian, would be longer than that forming the hypotenuse drawn from Thapsacus to Pelusium. Worthless, too, is the argument in connexion with this, being the inference from a proposition not admitted; for Eratosthenes never asserts that from Babylon to the meridian of the Caspian Gates is a distance of 4800 stadia. We have shown that Hipparchus deduces this from data not admitted by Eratosthenes; but desirous to controvert every thing advanced by that writer, he assumes that from Babylon to the line drawn from the Caspian Gates to the mountains of Carmania, according to Eratosthenes’ description, there are above 9000 stadia, and from thence draws his conclusions.