§2.5.5̔υποκείσθω δὴ σφαιροειδὴς ἡ γῆ σὺν τῇ θαλάττῃ, μίαν καὶ τὴν αὐτὴν ἐπιφάνειαν ἴσχουσα τοῖς πελάγεσι.
Let it be assumed, then, that the earth together with the sea is spherical, having one and the same surface with the high seas.
συγκρύπτοιτο γὰρ ἂν τὸ ἐξέχον τῆς γῆς ἐν τῷ τοσούτῳ μεγέθει μικρὸν ὂν καὶ λανθάνειν δυνάμενον, ὥστε τὸ σφαιροειδὲς ἐπὶ τούτων οὐχ ὡς ἂν ἐκ τόρνου φαμέν, οὐδʼ ὡς ὁ γεωμέτρης πρὸς λόγον, ἀλλὰ πρὸς αἴσθησιν καὶ ταύτην παχυτέραν.
For the projecting part of the earth, being small and capable of escaping notice in such a great magnitude, would be concealed, so that we do not speak of the spherical shape in these matters as if it were turned on a lathe, nor as the geometer does in strict theory, but with reference to perception, and that rather rough.
νοείσθω δὴ πεντάζωνος καὶ ὁ ἰσημερινὸς τεταγμένος ἐν αὐτῇ κύκλος, καὶ ἄλλος τούτῳ παράλληλος, ὁρίζων τὴν κατεψυγμένην ἐν τῷ βορείῳ ἡμισφαιρίῳ, καὶ διὰ τῶν πόλων τις τέμνων τούτους πρὸς ὀρθάς.
Let it then be conceived as having five zones, and the equator as a circle positioned in it, and another circle parallel to this, defining the frigid zone in the northern hemisphere, and some circle passing through the poles cutting these at right angles.
τοῦ δὴ βορείου ἡμισφαιρίου δύο περιέχοντος τεταρτημόρια τῆς γῆς, ἃ ποιεῖ ὁ ἰσημερινὸς πρὸς τὸν διὰ τῶν πόλων, ἐν ἑκατέρῳ τούτων ἀπολαμβάνεται τετράπλευρον χωρίον, οὗ ἡ μὲν βόρειος πλευρὰ ἥμισυ τοῦ πρὸς τῷ πόλῳ παραλλήλου ἐστίν, ἡ δὲ νότιος τοῦ ἰσημερινοῦ ἥμισυ, αἱ δὲ λοιπαὶ πλευραὶ τμήματά εἰσι τοῦ διὰ τῶν πόλων ἀντικείμενα ἀλλήλοις, ἴσα τὸ μῆκος.
Since the northern hemisphere contains two quadrants of the earth, which the equator makes with the circle through the poles, in each of these a quadrilateral region is cut off, of which the northern side is half of the parallel circle near the pole, and the southern side is half of the equator, while the remaining sides are segments of the circle through the poles, opposite to each other and equal in length.
ἐν θατέρῳ δὴ τῶν τετραπλεύρων τούτων (ὁποτέρῳ δʼ οὐδὲν ἂν διαφέρειν δόξειεν) ἱδρῦσθαί φαμεν τὴν καθʼ ἡμᾶς οἰκουμένην περίκλυστον θαλάττῃ καὶ ἐοικυῖαν νήσῳ· εἴρηται γὰρ ὅτι καὶ τῇ αἰσθήσει καὶ τῷ λόγῳ δείκνυται τοῦτο.
In one of these two quadrilaterals (and it would seem to make no difference in which of the two) we say that our inhabited world is situated, washed all around by the sea and resembling an island; for it has been said that this is demonstrated both by perception and by reason.
εἰ δʼ ἀπιστεῖ τις τῷ λόγῳ τούτῳ, διαφέροι ἂν πρὸς τὴν γεωγραφίαν οὐδὲν νῆσον ποιεῖν, ἢ ὅπερ ἐκ τῆς πείρας ἐλάβομεν τούτῳ συγχωρεῖν, ὅτι καὶ ἀπὸ τῆς ἠοῦς ἑκατέρωθεν περίπλους ἐστὶ καὶ ἀπὸ τῆς ἑσπέρας πλὴν ὀλίγων τῶν μέσων χωρίων.
But if anyone disbelieves this argument, it would make no difference for geography to make it an island, or to concede to this which we have received from experience, namely, that from the east on both sides there is a circumnavigation, and also from the west, except for a few of the middle regions.
ταῦτα δʼ οὐ διαφέρει θαλάττῃ περατοῦσθαι ἢ γῇ ἀοικήτῳ· ὁ γὰρ γεωγραφῶν ζητεῖ τὰ γνώριμα μέρη τῆς οἰκουμένης εἰπεῖν, τὰ δʼ ἄγνωστα ἐᾷ καθάπερ καὶ τὰ ἔξω αὐτῆς.
And it makes no difference whether these are bounded by sea or by uninhabitable land; for the geographer seeks to describe the known parts of the inhabited world, and leaves the unknown parts alone, just like those outside of it.
ἀρκέσει δʼ ἐπιζεύξασιν εὐθεῖαν γραμμὴν ἐπὶ τὰ ὕστατα σημεῖα τοῦ ἑκατέρωθεν παράπλου τὸ πᾶν ἐκπληρῶσαι σχῆμα τῆς λεγομένης νήσου.
And it will be sufficient to complete the whole shape of the so-called island by connecting a straight line between the furthest points of the coastal voyage on either side.
§2.5.6προκείσθω δὴ ἡ μὲν νῆσος ἐν τῷ λεχθέντι τετραπλεύρῳ.
Let the island, then, be assumed to lie in the said quadrilateral.
δεῖ δὲ λαβεῖν τὸ μέγεθος αὐτῆς τὸ φαινόμενον, ἀφελόντας ἀπὸ μὲν τοῦ ὅλου μεγέθους τῆς γῆς τὸ ἡμισφαίριον τὸ καθʼ ἡμᾶς, ἀπὸ δὲ τούτου τὸ ἥμισυ, ἀπὸ δʼ αὖ τούτου πάλιν τὸ τετράπλευρον, ἐν ᾧ δὴ τὴν οἰκουμένην κεῖσθαί φαμεν.
And we must grasp its apparent size, by taking away from the whole size of the earth our hemisphere, and from this its half, and from this again the quadrilateral in which we say the inhabited world lies.
ἀνάλογον δὲ καὶ περὶ τοῦ σχήματος ὑπολαβεῖν δεῖ τὸ φαινόμενον τοῖς ὑποκειμένοις ἐφαρμόττοντας.
And similarly concerning its shape, we must conceive its appearance, adapting it to our hypotheses.
ἀλλʼ ἐπειδὴ τὸ μεταξὺ τοῦ ἰσημερινοῦ καὶ τοῦ ληφθέντος παραλλήλου τούτῳ πρὸς τῷ πόλῳ τμῆμα τοῦ βορείου ἡμισφαιρίου σπόνδυλός ἐστι τὸ σχῆμα, ὁ δὲ διὰ τοῦ πόλου δίχα τέμνων τὸ ἡμισφαίριον δίχα τέμνει καὶ τὸν σπόνδυλον καὶ ποιεῖ τὸ τετράπλευρον, ἔσται δῆλον ὅτι σπονδύλου ἐπιφανείας ἥμισυ τὸ τετράπλευρον, ᾧ ἐπίκειται τὸ Ἀτλαντικὸν πέλαγος, ἡ δʼ οἰκουμένη χλαμυδοειδὴς ἐν τούτῳ νῆσος, ἔλαττον ἢ ἥμισυ τοῦ τετραπλεύρου μέρος οὖσα.
But since the segment of the northern hemisphere between the equator and the parallel circle near the pole taken parallel to it is a spondylos in shape, and the circle cutting the hemisphere in half through the pole also cuts the spondylos in half and makes the quadrilateral, it will be clear that the quadrilateral is half of the surface of the spondylos, upon which lies the Atlantic Ocean, and the inhabited world is a chlamys-shaped island in this, being a part less than half of the quadrilateral.
φανερὸν δὲ τοῦτο ἔκ τε γεωμετρίας καὶ τοῦ πλήθους τῆς περικεχυμένης θαλάττης, καλυπτούσης τὰ ἄκρα τῶν ἠπείρων ἑκατέρωθεν καὶ συναγούσης εἰς μύουρον σχῆμα, καὶ τρίτου τοῦ μήκους καὶ πλάτους τοῦ μεγίστου, ὧν τὸ μὲν ἑπτὰ μυριάδων σταδίων ἐστίν, ὡς ἐπὶ τὸ πολὺ περατούμενον θαλάττῃ μηκέτι πλεῖσθαι δυναμένῃ διὰ τὸ μέγεθος καὶ τὴν ἐρημίαν, τὸ * δʼ ἔλαττον τριῶν μυριάδων ὁριζόμενον τῷ ἀοικήτῳ διὰ θάλπος ἢ ψῦχος.
And this is evident both from geometry and from the abundance of the surrounding sea, which covers the extremities of the continents on both sides and draws them together into a tapered shape, and thirdly, from its maximum length and width; of which, the length is seventy thousand stadia, for the most part bounded by a sea no longer navigable because of its magnitude and emptiness, while the other, being less than thirty thousand stadia, is defined by the region uninhabitable on account of heat or cold.
αὐτὸ γὰρ τὸ διὰ θάλπος ἀοίκητον τοῦ τετραπλεύρου, πλάτος μὲν ἔχον ὀκτακισχιλίων καὶ ὀκτακοσίων σταδίων, μῆκος δὲ τὸ μέγιστον μυριάδων δώδεκα καὶ ἑξακισχιλίων, ὅσον ἐστὶν ἥμισυ τοῦ ἰσημερινοῦ πλέον ἂν εἴη τὸ λοιπόν.
For that part of the quadrilateral which is uninhabitable on account of heat itself, having a width of eight thousand eight hundred stadia, and a maximum length of one hundred and twenty-six thousand stadia, which is half of the equator, the remaining part would be greater.