§2.1.18φησὶ δὲ ὁ Ἵππαρχος κατὰ τὸν Βορυσθένη καὶ τὴν Κελτικὴν ἐν ὅλαις ταῖς θεριναῖς νυξὶ παραυγάζεσθαι τὸ φῶς τοῦ ἡλίου περιιστάμενον ἀπὸ τῆς δύσεως ἐπὶ τὴν ἀνατολήν, ταῖς δὲ χειμεριναῖς τροπαῖς πλεῖστον μετεωρίζεσθαι τὸν ἥλιον ἐπὶ πήχεις ἐννέα, ἐν δὲ τοῖς ἀπέχουσι τῆς Μασσαλίας ἑξακισχιλίοις καὶ τριακοσίοις (οὓς ἐκεῖνος μὲν ἔτι Κελτοὺς ὑπολαμβάνει, ἐγὼ δʼ οἶμαι Βρεττανοὺς εἶναι, βορειοτέρους τῆς Κελτικῆς σταδίοις δισχιλίοις πεντακοσίοις) πολὺ μᾶλλον τοῦτο συμβαίνειν.
Hipparchus says that around the Borysthenes and Celtica, during the whole of the summer nights, the light of the sun shines all around, passing from west to east, and at the winter solstice the sun rises to a maximum height of nine cubits; and that in the regions distant six thousand three hundred stadia from Massalia (which he indeed still supposes to be Celtica, but I think to be Britannia, which is two thousand five hundred stadia further north than Celtica) this occurs much more.
ἐν δὲ ταῖς χειμεριναῖς ἡμέραις ὁ ἥλιος μετεωρίζεται πήχεις ἕξ, τέτταρας δʼ ἐν τοῖς ἀπέχουσι Μασσαλίας ἐνακισχιλίους σταδίους καὶ ἑκατόν, ἐλάττους δὲ τῶν τριῶν ἐν τοῖς ἐπέκεινα, οἳ κατὰ τὸν ἡμέτερον λόγον πολὺ ἂν εἶεν ἀρκτικώτεροι τῆς Ἰέρνης.
And on winter days, the sun rises to six cubits, and to four cubits in the regions distant nine thousand one hundred stadia from Massalia, and less than three cubits in the regions beyond, which according to our argument would be much further north than Ierne.
οὗτος δὲ Πυθέᾳ πιστεύων κατὰ τὰ ἀρκτικώτερα τῆς Βρεττανικῆς τὴν οἴκησιν ταύτην τίθησι, καί φησιν εἶναι τὴν μακροτάτην ἐνταῦθα ἡμέραν ὡρῶν ἰσημερινῶν δέκα ἐννέα, ὀκτωκαίδεκα δὲ ὅπου τέτταρας ὁ ἥλιος μετεωρίζεται πήχεις· οὕς φησιν ἀπέχειν τῆς Μασσαλίας ἐνακισχιλίους καὶ ἑκατὸν σταδίους, ὥσθʼ οἱ νοτιώτατοι τῶν Βρεττανῶν βορειότεροι τούτων εἰσίν.
But he, trusting Pytheas, places this habitation in the northern parts of Britannia, and says that the longest day there is nineteen equinoctial hours, and eighteen hours where the sun rises to four cubits; which he says is nine thousand one hundred stadia distant from Massalia, so that the southernmost of the Britons are further north than these.
ἤτοι οὖν ἐπὶ τοῦ αὐτοῦ παραλλήλου εἰσὶ τοῖς πρὸς τῷ Καυκάσῳ Βακτρίοις ἢ ἐπί τινος πλησιάζοντος· εἴρηται γὰρ ὅτι κατὰ τοὺς περὶ Δηίμαχον συμβήσεται βορειοτέρους εἶναι τῆς Ἰέρνης τοὺς πρὸς τῷ Καυκάσῳ Βακτρίους σταδίοις τρισχιλίοις ὀκτακοσίοις· προστεθέντων δὲ τούτων τοῖς ἀπὸ Μασσαλίας εἰς Ἰέρνην, γίνονται μύριοι δισχίλιοι πεντακόσιοι.
Therefore they are either on the same parallel as the Bactrians near the Caucasus, or on one very close to it; for it has been said that according to Deïmachus and his followers, the Bactrians near the Caucasus will turn out to be three thousand eight hundred stadia further north than Ierne; and if these are added to the distance from Massalia to Ierne, the total becomes twelve thousand five hundred stadia.
τίς οὖν ἱστόρηκεν ἐν τοῖς ἐκεῖ τόποις (λέγω δὲ τοῖς περὶ Βάκτρα) τοῦτο τὸ μῆκος τῶν μεγίστων ἡμερῶν ἢ τὸ ἔξαρμα τοῦ ἡλίου τὸ κατὰ τὰς μεσουρανήσεις ἐν ταῖς χειμεριναῖς τροπαῖς;
Who, then, has recorded in those parts (I mean around Bactra) this length of the longest days or the elevation of the sun at meridian during the winter solstice?
ὀφθαλμοφανῆ γὰρ πάντα ταῦτα ἰδιώτῃ καὶ οὐ δεόμενα μαθηματικῆς σημειώσεως, ὥστε συνέγραψαν ἂν πολλοὶ καὶ τῶν παλαιῶν τῶν τὰ Περσικὰ ἱστορούντων καὶ τῶν ὕστερον μέχρι καὶ εἰς ἡμᾶς.
For all these things are obvious to any layman and do not require mathematical observation, so that many of the ancient historians who wrote Persian history, as well as later ones down to our own time, would have recorded them.
πῶς δʼ ἂν ἡ λεχθεῖσα εὐδαιμονία τῶν τόπων ὡμολόγητο τοῖς τοιούτοις ἐν τῷ οὐρανῷ φαινομένοις;
And how could the alleged prosperity of those regions have been agreed upon with such celestial phenomena?
ἐκ δὲ τῶν εἰρημένων δῆλον ὡς καὶ σοφῶς ἀντιλέγει πρὸς τὴν ἀπόδειξιν, ὡς ἰσοδυναμούντων τῶν ζητουμένων λαμβάνοντος πρὸς τὸ ἀποδεῖξαι τὸ ζητούμενον.
From what has been said, it is clear that he (Hipparchus) also cleverly argues against the proof, taking the very points in question as equivalent to prove the point in question.
§2.1.19πάλιν δʼ ἐκείνου τὸν Δηίμαχον ἰδιώτην ἐνδείξασθαι βουλομένου καὶ ἄπειρον τῶν τοιούτων· οἴεσθαι γὰρ τὴν Ἰνδικὴν μεταξὺ κεῖσθαι τῆς τε φθινοπωρινῆς ἰσημερίας καὶ τῶν τροπῶν τῶν χειμερινῶν, Μεγασθένει τε ἀντιλέγειν φήσαντι ἐν τοῖς νοτίοις μέρεσι τῆς Ἰνδικῆς τάς τε ἄρκτους ἀποκρύπτεσθαι καὶ τὰς σκιὰς ἀντιπίπτειν· μηδέτερον γὰρ τούτων μηδαμοῦ τῆς Ἰνδικῆς συμβαίνειν· ταῦτα δὴ φάσκοντος ἀμαθῶς λέγεσθαι·
¦p.100 And again, when he (Eratosthenes) wishes to show that Deïmachus is a layman and inexperienced in such matters; for he says that he (Deïmachus) thinks India lies between the autumnal equinox and the winter solstice, and contradicts Megasthenes, who said that in the southern parts of India the Bears hide and the shadows fall in the opposite direction; for neither of these, he says, occurs anywhere in India; and he asserts that these things are said ignorantly.
τό τε γὰρ τὴν φθινοπωρινὴν τῆς ἐαρινῆς διαφέρειν οἴεσθαι κατὰ τὴν διάστασιν τὴν πρὸς τὰς τροπὰς ἀμαθές, τοῦ τε κύκλου τοῦ αὐτοῦ ὄντος καὶ τῆς ἀνατολῆς· τοῦ τε διαστήματος τοῦ ἐπὶ τῆς γῆς τροπικοῦ ἀπὸ τοῦ ἰσημερινοῦ, ὧν μεταξὺ τίθησι τὴν Ἰνδικὴν ἐκεῖνος, δειχθέντος ἐν τῇ ἀναμετρήσει πολὺ ἐλάττονος τῶν δισμυρίων σταδίων, συμβῆναι ἂν καὶ κατʼ αὐτὸν ἐκεῖνον, ὅπερ αὐτὸς νομίζει, οὐχ ὃ ἐκεῖνος· δυεῖν μὲν γὰρ ἢ καὶ τριῶν μυριάδων οὖσαν τὴν Ἰνδικὴν οὐδὲ πεσεῖν μεταξὺ τοσούτου διαστήματος, ὅσων δʼ αὐτὸς εἴρηκε, πεσεῖν ἄν·
For to think that the autumnal equinox differs from the vernal equinox in its distance from the solstices is ignorant, since the circle and the rising are the same; and since the terrestrial distance of the tropic from the equator, between which he places India, has been shown in the measurement to be much less than twenty thousand stadia, it would happen even according to him what he himself thinks, and not what Megasthenes thinks; for if India were twenty or thirty thousand stadia, it would not even fall within such a distance, but if it were as much as he himself says, it would fall within it.
τῆς δʼ αὐτῆς ἀγνοίας εἶναι καὶ τὸ μηδαμοῦ τῆς Ἰνδικῆς ἀποκρύπτεσθαι φάσκειν τὰς ἄρκτους μηδὲ τὰς σκιὰς ἀντιπίπτειν, ὅτε γε καὶ πεντακισχιλίους προελθόντι ἀπʼ Ἀλεξανδρείας εὐθὺς συμβαίνειν ἄρχεται·
And it belongs to the same ignorance to say that nowhere in India do the Bears hide nor the shadows fall in the opposite direction, since to one who has gone forward only five thousand stadia from Alexandria, this immediately begins to happen.
ταῦτα δὴ εἰπόντος, εὐθύνει πάλιν οὐκ εὖ ὁ Ἵππαρχος, πρῶτον ἀντὶ τοῦ χειμερινοῦ τροπικοῦ τὸν θερινὸν δεξάμενος, εἶτʼ οὐκ οἰόμενος δεῖν μάρτυρι χρῆσθαι τῶν μαθηματικῶν ἀναστρολογήτῳ ἀνθρώπῳ, ὥσπερ τοῦ Ἐρατοσθένους προηγουμένως τὴν ἐκείνου μαρτυρίαν ἐγκρίνοντος, ἀλλʼ οὐ κοινῷ τινι ἔθει χρωμένου πρὸς τοὺς ματαιολογοῦντας.
When he (Eratosthenes) had said these things, Hipparchus again corrects him, but not well, first receiving the summer tropic instead of the winter tropic, and then not thinking it right to use as a witness a man unversed in astronomy, as if Eratosthenes were primarily accepting his testimony, and not rather using a common practice against those who talk idly.
εἷς γάρ τις τῶν πρὸς τοὺς ματαίως ἀντιλέγοντας ἐλέγχων ἐστίν, ὅταν αὐτὴν τὴν ἐκείνων ἀπόφασιν, ὁποία ποτέ ἐστι, δείξωμεν ἡμῖν συνηγοροῦσαν.
For one of the refutations against those who argue idly is when we show their very assertion, whatever it may be, advocating for us.