§2.5.9εἰ δὲ προστεθείη τῷ ἀπὸ τῆς Ῥοδίας μέχρι Βορυσθένους διαστήματι τὸ ἀπὸ Βορυσθένους ἐπὶ τὰς ἄρκτους τῶν τετρακισχιλίων σταδίων διάστημα, γίνεται τὸ πᾶν μύριοι δισχίλιοι ἑπτακόσιοι στάδιοι, τὸ δʼ ἀπὸ τῆς Ῥοδίας ἐπὶ τὸ νότιον πέρας ἐστὶ τῆς οἰκουμένης μύριοι ἑξακισχίλιοι ἑξακόσιοι, ὥστε τὸ σύμπαν πλάτος τῆς οἰκουμένης εἴη ἂν ἔλαττον τῶν τρισμυρίων ἀπὸ νότου πρὸς ἄρκτον·
If to the distance from Rhodes to the Borysthenes there be added the distance of four thousand stadia from the Borysthenes to the north, the total becomes twelve thousand seven hundred stadia; and the distance from Rhodes to the southern limit of the inhabited world is sixteen thousand six hundred, so that the entire width of the inhabited world from south to north would be less than thirty thousand.
τὸ δέ γε μῆκος περὶ ἑπτὰ μυριάδας λέγεται, τοῦτο δʼ ἐστὶν ἀπὸ δύσεως ἐπὶ τὰς ἀνατολὰς τὸ ἀπὸ τῶν ἄκρων τῆς Ἰβηρίας ἐπὶ τὰ ἄκρα τῆς Ἰνδικῆς, τὸ μὲν ὁδοῖς τὸ δὲ ταῖς ναυτιλίαις ἀναμεμετρημένον.
On the other hand, its length is said to be about seventy thousand, and this is from west to east, the distance from the extremities of Iberia to the extremities of India, measured partly by journeys on land and partly by voyages.
ὅτι δʼ ἐντὸς τοῦ λεχθέντος τετραπλεύρου τὸ μῆκός ἐστι τοῦτο, ἐκ τοῦ λόγου τῶν παραλλήλων πρὸς τὸν ἰσημερινὸν δῆλον, ὥστε πλέον ἢ διπλάσιόν ἐστι τοῦ πλάτους τὸ μῆκος.
And that this length is within the said quadrilateral is clear from the ratio of the parallel circles to the equator, so that the length is more than double the width.
λέγεται δὲ καὶ χλαμυδοειδές πως τὸ σχῆμα· πολλὴ γὰρ συναγωγὴ τοῦ πλάτους πρὸς τοῖς ἄκροις εὑρίσκεται καὶ μάλιστα τοῖς ἑσπερίοις, τὰ καθʼ ἕκαστα ἐπιόντων ἡμῶν.
And its shape is also said to be somehow like a chlamys; for a great contraction of the width is found at the extremities, and especially at the western ones, as we proceed to the individual details.
§2.5.10νυνὶ μὲν οὖν ἐπιγεγράφαμεν ἐπὶ σφαιρικῆς ἐπιφανείας τὸ χωρίον, ἐν ᾧ φαμεν ἱδρῦσθαι τὴν οἰκουμένην· καὶ δεῖ τὸν ἐγγυτάτω διὰ τῶν χειροκμήτων σχημάτων μιμούμενον τὴν ἀλήθειαν ποιήσαντα σφαῖραν τὴν γῆν, καθάπερ τὴν Κρατήτειον, ἐπὶ ταύτης ἀπολαβόντα τὸ τετράπλευρον ἐντὸς τούτου τιθέναι τὸν πίνακα τῆς γεωγραφίας.
Now we have previously outlined on a spherical surface the region in which we say the inhabited world is situated; and he who would mimic the truth as closely as possible by means of man-made shapes, having made the earth a sphere like that of Crates, and having marked off the quadrilateral upon it, ought to place the map of geography within this.
ἀλλʼ ἐπειδὴ μεγάλης δεῖ σφαίρας, ὥστε πολλοστημόριον αὐτῆς ὑπάρχον τὸ λεχθὲν τμῆμα ἱκανὸν γενέσθαι δέξασθαι σαφῶς τὰ προσήκοντα μέρη τῆς οἰκουμένης, καὶ τὴν οἰκείαν παρασχεῖν ὄψιν τοῖς ἐπιβλέπουσι, τῷ μὲν δυναμένῳ κατασκευάσασθαι τηλικαύτην οὕτω ποιεῖν βέλτιον· ἔστω δὲ μὴ μείω δέκα ποδῶν ἔχουσα τὴν διάμετρον· τῷ δὲ μὴ δυναμένῳ τηλικαύτην ἢ μὴ πολλῷ ταύτης ἐνδεεστέραν ἐν ἐπιπέδῳ καταγραπτέον πίνακι τοὐλάχιστον ἑπτὰ ποδῶν.
But since a large sphere is required, so that the said segment, being only a tiny fraction of it, may be sufficient to receive clearly the appropriate parts of the inhabited world and to afford the proper view to those who look upon it, for him who is able to construct one of such a size it is better to do so—and let it have a diameter of not less than ten feet—but for him who is not able to make one of such a size or only slightly smaller than this, it must be drawn on a flat map of at least seven feet.
διοίσει γὰρ μικρόν, ἐὰν ἀντὶ τῶν κύκλων τῶν τε παραλλήλων καὶ τῶν μεσημβρινῶν, οἷς τά τε κλίματα καὶ τοὺς ἀνέμους διασαφοῦμεν καὶ τὰς ἄλλας διαφορὰς καὶ τὰς σχέσεις τῶν τῆς γῆς μερῶν πρὸς ἄλληλά τε καὶ τὰ οὐράνια, εὐθείας γράφωμεν, τῶν μὲν παραλλήλων παραλλήλους, τῶν δὲ ὀρθῶν πρὸς ἐκείνους ὀρθάς, τῆς διανοίας ῥᾳδίως μεταφέρειν δυναμένης τὸ ὑπὸ τῆς ὄψεως ἐν ἐπιπέδῳ θεωρούμενον ἐπιφανείᾳ σχῆμα καὶ μέγεθος ἐπὶ τὴν περιφερῆ τε καὶ σφαιρικήν.
For it will make little difference if, instead of the circles, both the parallels and the meridians, by which we make clear the latitudes, the winds, and the other differences and relations of the parts of the earth to one another and to the heavenly bodies, we draw straight lines, namely parallels for the parallels, and perpendiculars for those perpendicular to them, since the mind is easily able to transfer the shape and size seen by the eye on a flat surface to the curved and spherical one.
ἀνάλογον δὲ καὶ περὶ τῶν λοξῶν κύκλων καὶ εὐθειῶν φαμεν.
And we say the same analogously concerning the oblique circles and straight lines.
εἰ δʼ οἱ μεσημβρινοὶ οἱ παρʼ ἑκάστοις τοῦ πόλου γραφόμενοι πάντες συννεύουσιν ἐν τῇ σφαίρᾳ πρὸς ἓν σημεῖον, ἀλλʼ ἐν τῷ ἐπιπέδῳ γε οὐ διοίσει πίνακι τὰς εὐθείας μικρὰς συννευούσας ποιεῖν μόνον τὰς μεσημβρινάς· οὐδὲ γὰρ πολλαχοῦ τοῦτʼ ἀναγκαῖον, οὐδʼ ἐκφανής ἐστιν ὥσπερ ἡ περιφέρεια οὕτω καὶ ἡ σύννευσις, μεταφερομένων τῶν γραμμῶν εἰς τὸν πίνακα τὸν ἐπίπεδον καὶ γραφομένων εὐθειῶν.
And even if the meridians drawn for each place all converge on the sphere to one point at the pole, yet on a flat map it will make no difference to make the straight meridian lines converge only slightly; for this is not necessary in many places, nor is the convergence, just like the curvature, conspicuous when the lines are transferred to the flat map and drawn as straight lines.