§2.5.3πεντάζωνον μὲν γὰρ ὑποθέσθαι δεῖ τὸν οὐρανόν, πεντάζωνον δὲ καὶ τὴν γῆν, ὁμωνύμους δὲ καὶ τὰς ζώνας τὰς κάτω ταῖς ἄνω· τὰς δʼ αἰτίας εἰρήκαμεν τῆς εἰς τὰς ζώνας διαιρέσεως.
For one must assume that the heaven is divided into five zones, and the earth likewise into five zones, and that the zones below are homonymous with those above; and we have already stated the reasons for the division into zones.
διορίζοιντο δʼ ἂν αἱ ζῶναι κύκλοις παραλλήλοις τῷ ἰσημερινῷ γραφομένοις ἑκατέρωθεν αὐτοῦ, δυσὶ μὲν τοῖς ἀπολαμβάνουσι τὴν διακεκαυμένην, δυσὶ δὲ τοῖς μετὰ τούτους, οἳ πρὸς μὲν τῇ διακεκαυμένῃ τὰς εὐκράτους δύο ποιοῦσι, πρὸς δὲ ταῖς εὐκράτοις τὰς κατεψυγμένας.
These zones would be defined by circles drawn parallel to the equator on either side of it, two of them enclosing the scorched zone, and two following after these, which create the two temperate zones adjacent to the scorched zone, and the frigid zones adjacent to the temperate zones.
ὑποπίπτει δʼ ἑκάστῳ τῶν οὐρανίων κύκλων ὁ ἐπὶ γῆς ὁμώνυμος αὐτῷ, καὶ ἡ ζώνη δὲ ὡσαύτως τῇ ζώνῃ.
Under each of the heavenly circles lies the circle on earth homonymous with it, and the zone likewise under the zone.
εὐκράτους μὲν οὖν φασι τὰς οἰκεῖσθαι δυναμένας, ἀοικήτους δὲ τὰς ἄλλας, τὴν μὲν διὰ καῦμα τὰς δὲ διὰ ψῦχος.
Now they say that the temperate zones are capable of being inhabited, but the others are uninhabitable, one because of heat and the others because of cold.
τὸν δʼ αὐτὸν τρόπον καὶ περὶ τῶν τροπικῶν καὶ τῶν ἀρκτικῶν, παρʼ οἷς εἰσιν ἀρκτικοί, διορίζουσιν ὁμωνύμως τοῖς ἄνω τοὺς ἐπὶ γῆς ποιοῦντες, καὶ τοὺς ἑκάστοις ὑποπίπτοντας.
In the same manner also concerning the tropics and the polar circles, among those for whom polar circles exist, they define them by making those on earth homonymous with those above, and also those lying under each of them.
τοῦ δʼ ἰσημερινοῦ δίχα τέμνοντος τὸν ὅλον οὐρανόν, καὶ τὴν γῆν ἀνάγκη διαιρεῖσθαι ὑπὸ τοῦ ἐν αὐτῇ ἰσημερινοῦ.
Since the equator cuts the whole heaven in half, the earth also must necessarily be divided by the equator upon it.
καλεῖται δὲ τῶν ἡμισφαιρίων ἑκάτερον τῶν τε οὐρανίων καὶ τῶν ἐπὶ γῆς τὸ μὲν βόρειον τὸ δὲ νότιον· οὕτως δὲ καὶ τῆς διακεκαυμένης ὑπὸ τοῦ αὐτοῦ κύκλου δίχα διαιρουμένης τὸ μὲν ἔσται βόρειον αὐτῆς μέρος τὸ δὲ νότιον· δῆλον δʼ ὅτι καὶ τῶν εὐκράτων ζωνῶν ἡ μὲν ἔσται βόρειος ἡ δὲ νότιος ὁμωνύμως τῷ ἡμισφαιρίῳ ἐν ᾧ ἐστι.
And each of the hemispheres both of the heaven and of the earth is called, the one northern, the other southern; and so, with the scorched zone also being cut in half by the same circle, one part of it will be northern, the other southern; and it is clear that also of the temperate zones, the one will be northern and the other southern, homonymously with the hemisphere in which it lies.
καλεῖται δὲ βόρειον μὲν ἡμισφαίριον τὸ τὴν εὔκρατον ἐκείνην περιέχον, ἐν ᾗ ἀπὸ τῆς ἀνατολῆς βλέποντι ἐπὶ τὴν δύσιν ἐν δεξιᾷ μέν ἐστιν ὁ πόλος, ἐν ἀριστερᾷ δʼ ὁ ἰσημερινός, ἢ ἐν ᾧ πρὸς μεσημβρίαν βλέπουσιν ἐν δεξιᾷ μέν ἐστι δύσις ἐν ἀριστερᾷ δʼ ἀνατολή, νότιον δὲ τὸ ἐναντίως ἔχον· ὥστε δῆλον ὅτι ἡμεῖς ἐσμεν ἐν θατέρῳ τῶν ἡμισφαιρίων, καὶ τῷ βορείῳ γε, ἐν ἀμφοτέροις δʼ οὐχ οἷόν τε· μέσσῳ γὰρ μεγάλοι ποταμοί, ὠκεανὸς μὲν πρῶτα,
ἔπειτα ἡ διακεκαυμένη.
And the northern hemisphere is called that which contains that temperate zone in which, to one looking from the east toward the west, the pole is on the right and the equator on the left, or in which, to those looking toward the south, the west is on the right and the east on the left, while the southern is that which is in the opposite state; so that it is clear that we are in one of the two hemispheres, and indeed in the northern one, and it is not possible to be in both; for in the middle are great rivers, first Oceanus, then the scorched zone.
οὔτε δὲ ὠκεανὸς ἐν μέσῳ τῆς καθʼ ἡμᾶς οἰκουμένης ἐστὶ τέμνων ὅλην, οὔτʼ οὖν διακεκαυμένον χωρίον· οὐδὲ δὴ μέρος αὐτῆς εὑρίσκεται τοῖς κλίμασιν ὑπεναντίως ἔχον τοῖς λεχθεῖσιν ἐν τῇ βορείῳ εὐκράτῳ.
And neither is there Oceanus in the middle of our inhabited world cutting it as a whole, nor indeed a scorched region; nor indeed is any part of it found to have climates opposite to those described in the northern temperate zone.
§2.5.4λαβὼν οὖν ταῦθʼ ὁ γεωμέτρης, προσχρησάμενος τοῖς ὑπὸ τοῦ ἀστρονομικοῦ δεικνυμένοις, ἐν οἷς οἵ τε παράλληλοι τῷ ἰσημερινῷ εὑρίσκονται οἱ καθʼ ἑκάστην τὴν οἴκησιν καὶ οἱ πρὸς ὀρθὰς τέμνοντες τούτους, γραφόμενοι δὲ διὰ τῶν πόλων, καταμετρεῖ τὴν μὲν οἰκήσιμον ἐμβατεύων, τὴν δʼ ἄλλην ἐκ τοῦ λόγου τῶν ἀποστάσεων.
The geometer, then, taking these things and further employing the things demonstrated by the astronomer—among which are found both the circles parallel to the equator for each habitation and those cutting these at right angles, being drawn through the poles—measures the habitable earth by traveling through it, and the rest from the ratio of distances.
οὕτω δʼ ἂν εὑρίσκοι πόσον ἂν εἴη τὸ ἀπὸ τοῦ ἰσημερινοῦ μέχρι πόλου, ὅπερ ἐστὶ τεταρτημόριον τοῦ μεγίστου κύκλου τῆς γῆς· ἔχων δὲ τοῦτο ἔχει καὶ τὸ τετραπλάσιον αὐτοῦ, τοῦτο δʼ ἐστὶν ἡ περίμετρος τῆς γῆς.
In this way he would find how great the distance is from the equator to the pole, which is a quadrant of the greatest circle of the earth; and having this, he also has its fourfold, which is the circumference of the earth.
ὥσπερ οὖν ὁ μὲν τὴν γῆν ἀναμετρῶν παρὰ τοῦ ἀστρονομοῦντος ἔλαβε τὰς ἀρχάς, ὁ δὲ ἀστρονόμος παρὰ τοῦ φυσικοῦ, τὸν αὐτὸν τρόπον χρὴ καὶ τὸν γεωγράφον παρὰ τοῦ ἀναμεμετρηκότος ὅλην τὴν γῆν ὁρμηθέντα, πιστεύσαντα τούτῳ καὶ οἷς ἐπίστευσεν οὗτος, πρῶτον μὲν ἐκθέσθαι τὴν οἰκουμένην καθʼ ἡμᾶς πόση τις καὶ ποία τὸ σχῆμα καὶ τὴν φύσιν οἵα ἐστὶ καὶ πῶς ἔχουσα πρὸς τὴν ὅλην γῆν (ἴδιον γὰρ τοῦ γεωγράφου τοῦτο), ἔπειτα περὶ τῶν καθʼ ἕκαστα τῶν τε κατὰ γῆν καὶ τῶν κατὰ θάλατταν ποιήσασθαι τὸν προσήκοντα λόγον, παρασημαινόμενον ὅσα μὴ ἱκανῶς εἴρηται τοῖς πρὸ ἡμῶν τοῖς μάλιστα πεπιστευμένοις ἀρίστοις γεγονέναι περὶ ταῦτα.
Just as, therefore, the one who measured the earth received his principles from the astronomer, and the astronomer from the physicist, in the same way the geographer also must start from the one who has measured the whole earth, believing him and those whom he believed, and first set forth how large our inhabited world is, what its shape is, and what its nature is and how it stands in relation to the whole earth (for this is peculiar to the geographer), and then make the fitting account concerning the particulars both on land and on sea, pointing out whatever has not been adequately stated by our predecessors who are believed to have been the best in these matters.