§2.14#2εἴτʼ οὖν ὁμοίως ἀπὸ τῶν ἐσχάτων διῃρημένα τὰ μόρια συνήχθη πρὸς τὸ μέσον, εἴτʼ ἄλλως ἔχοντα, ποιήσει ταὐτόν.
Whether, then, the parts were gathered to the center from the extremes, having been divided in a like manner, or in some other state, they will produce the same result.
ὅτι μὲν οὖν ὁμοίως γε πανταχόθεν ἀπὸ τῶν ἐσχάτων φερομένων πρὸς ἓν τὸ μέσον ἀναγκαῖον ὅμοιον γίγνεσθαι πάντη τὸν ὄγκον, φανερόν· ἴσου γὰρ πάντῃ προστιθεμένου ἴσον ἀνάγκη ἀπέχειν τοῦ μέσου τὸ ἔσχατον· τοῦτο δὲ τὸ σχῆμα σφαίρας ἐστίν.
Now, that the mass must necessarily become similar in every direction if they are carried in a like manner from all sides from the extremes to a single center, is clear; for if an equal amount is added in every direction, the extreme must necessarily be at an equal distance from the center; and this is the shape of a sphere.
οὐδὲν δὲ διοίσει πρὸς τὸν λόγον, οὐδʼ εἰ μὴ πανταχόθεν ὁμοίως συνέθει πρὸς τὸ μέσον τὰ μόρια αὐτῆς.
But it will make no difference to the argument, even if the parts of the earth did not run together to the center in a like manner from all sides.
τὸ γὰρ πλεῖον ἀεὶ τὸ πρὸ αὐτοῦ ἔλαττον προωθεῖν ἀναγκαῖον μέχρι τοῦ μέσου τὴν ῥοπὴν ἐχόντων ἀμφοῖν, καὶ τοῦ βαρυτέρου προωθοῦντος μέχρι τούτου τὸ ἔλαττον βάρος.
For the larger part must always push forward the smaller part that is in front of it, since both have their inclination towards the center, and the heavier pushes the lighter weight to this point.
ὁ γὰρ ἄν τις ἀπορήσειε, τὴν αὐτὴν ἔχει τούτοις λύσιν·
For the difficulty which one might raise has the same solution as these.
εἰ γὰρ οὕσης ἐπὶ τοῦ μέσου καὶ σφαιροειδοῦς τῆς γῆς πολλαπλάσιον βάρος ἐπιγένοιτο πρὸς θάτερον ἡμισφαίριον, οὐκ ἔσται τὸ αὐτὸ μέσον τοῦ ὅλου καὶ τὸ τῆς γῆς·
If, when the earth is at the center and is spherical, a weight many times greater were added to one hemisphere, the center of the whole and that of the earth would no longer be the same.
ὥστε ἢ οὐ μενεῖ ἐπὶ τοῦ μέσου, ἢ εἴπερ, ἠρεμήσει γε καὶ μὴ τὸ μέσον ἔχουσα, ᾗ πέφυκε κινεῖσθαι καὶ νῦν.
Consequently, either it will not remain at the center, or, if it does, it will remain at rest even without holding the center, in the way in which it is of its nature to be moved even now.
τὸ μὲν οὖν 297 b ἀπορούμενον τοῦτʼ ἐστίν·
This, then, is the difficulty.
ἰδεῖν δʼ οὐ χαλεπὸν μικρὸν ἐπιτείναντας, καὶ διελόντας πῶς ἀξιοῦμεν ὁποσονοῦν μέγεθος φέρεσθαι πρὸς τὸ μέσον, βάρος ἔχον.
But it is not difficult to see, if we strain our minds a little and distinguish in what way we deem any magnitude whatever having weight to be carried towards the center.
δῆλον γὰρ ὡς οὐχὶ μέχρι τοῦ ἅψασθαι τοῦ κέντρου τὸ ἔσχατον, ἀλλὰ δεῖ κρατεῖν τὸ πλέον ἕως ἂν λάβη τῷ αὑτοῦ μέσῳ τὸ μέσον· μέχρι τούτου γὰρ ἔχει τὴν ῥοπήν.
For it is clear that it is not carried only until its extreme touches the center, but the larger part must prevail until it takes the center with its own center; for it has its inclination up to this point.
οὐδὲν τοίνυν διαφέρει τοῦτο λέγειν ἐπὶ βώλου καὶ μορίου τοῦ τυχόντος ἢ ἐπὶ ὅλης τῆς γῆς· οὐ γὰρ διὰ μικρότητα ἢ μέγεθος εἴρηται τὸ συμβαῖνον, ἀλλὰ κατὰ παντὸς τοῦ ῥοπὴν ἔχοντος ἐπὶ τὸ μέσον·
Now there is no difference in saying this of a clod of earth or of any chance part, or of the whole earth; for what happens has not been said because of smallness or greatness, but concerning everything that has an inclination towards the center.
ὥστε εἴτε ὅλη πόθεν ἐφέρετο εἴτε κατὰ μέρος, ἀναγκαῖον μέχρι τούτου φέρεσθαι ἕως ἂν πανταχόθεν ὁμοίως λάβῃ τὸ μέσον, ἀνιδιαφέρει σαζομένων τῶν ἐλαττόνων ὑπὸ τῶν μειζόνων τῇ προώσει τῆς ῥοπῆς.
So that whether the whole was carried from somewhere, or part by part, it must necessarily be carried until it takes the center in a like manner from all sides, and it makes no difference that the smaller parts are equalized by the larger ones through the pushing forward of their inclination.
εἴτʼ οὖν ἐγένετο, τοῦτονἀναγκαῖον γενέσθαι τὸν τρόπον, ὥστε φανερὸν ὅτι σφαιροειδὴς ἡ γένεσις αὐτῆς, εἴτʼ ἀγένητος ἀεὶ μένουσα, τὸν αὐτὸν τρόπον ἔχειν ὅνπερ κἂν εἰ γιγνομένη τὸ πρῶτον ἐγένετο.
Whether, then, the earth came to be, it must necessarily have come to be in this manner, so that it is clear that its coming to be was spherical; or if it is ungenerated and always remains, it must have the same manner as it would have had if it had come to be at first.
κατὰ τοῦτόν τε δὴ τὸν λόγον ἀναγκαῖον εἶναι τὸ σχῆμα σφαιροειδὲς αὐτῆς, καὶ ὅτι πάντα φέρεται τὰ βαρέα πρὸς τὰς ὁμοίας γωνίας, ἀλλʼ οὐ παρʼ ἄλληλα· τοῦτο δὲ πέφυκε πρὸς τὸ φύσει σφαιροειδές.
According to this argument, then, it is necessary that its shape is spherical, and also because all heavy things are carried at like angles, and not parallel to one another; and this is the natural way of moving towards that which is naturally spherical.
ἢ οὖν ἐστὶ σφαιροειδής, ἢ φύσει γε σφαιροειδής.
Therefore, it is either spherical, or at least naturally spherical.
δεῖ δʼ ἕκαστον λέγειν τοιοῦτον εἶναι ὃ φύσει βούλεται εἶναι καὶ ὃ ὑπάρχει, ἀλλὰ μὴ ὃ βίᾳ καὶ παρὰ φύσιν.
But one must say that each thing is of such a kind as it wishes to be by nature and as it is, but not what it is by force and contrary to nature.
ἔτι δὲ καὶ διὰ τῶν φαινομένων κατὰ τὴν αἴσθησιν·
Moreover, this is also clear through the phenomena apparent to perception.
οὕτε γὰρ ἂν αἱ τῆς σελήνης ἐκλείψεις τοιαύτας ἄν εἶχον τὰς ἀποτομάς·
For otherwise the eclipses of the moon would not have such cut-offs.
νῦν γὰρ ἐν μὲν τοῖς κατὰ μῆνα σχηματισμοῖς πάσας λαμβάνει τὰς διαιρέσεις (καὶ γὰρ εὐθεῖα γίνεται καὶ ἀμφίκυρτος καὶ κοίλη), περὶ δὲ τὰς ἐκλείψεις ἀεὶ κυρτὴν ἔχει τὴν ὁρίζουσαν γραμμήν, ὥστʼ ἐπείπερ ἐκλείπει διὰ τὴν τῆς γῆς ἐπιπρόσθησιν, ἡ τῆς γῆς ἂν εἴη περιφέρεια τοῦ σχήματος αἰτία σφαιροειδὴς οὖσα.
For now, in its monthly phases, it takes all divisions (for it becomes straight, gibbous, and concave), but during eclipses it always has its defining line curved. Therefore, since it suffers eclipse because of the interposition of the earth, the circumference of the earth, being spherical, must be the cause of this shape.
ἔτι δὲ διὰ τῆς τῶν ἄστρων φαντασίας οὐ μόνον φανερὸν ὅτι περιφερής, ἀλλὰ καὶ τὸ μέγεθος οὐκ οὖσα μεγάλη·
Furthermore, through the appearance of the stars, it is clear not only that the earth is circular, but also that its size is not large.
μικρὰς γὰρ γιγνομένης μεταστάσεως ἡμῖν πρὸς μεσημβρίαν καὶ ἄρκτον ἐπιδήλως ἕτερος γίγνεται ὁ ὁρίζων κύκλος, ὥστε τὰ ὑπὲρ κεφαλῆς ἄστρα μεγάλην ἔχειν τὴν μεταβολήν, καὶ μὴ ταὐτὰ φαίνεσθαι πρὸς ἄρκτον τε καὶ μεσημβρίαν μεταβαίνουσιν·
For if we make a small change of place to the south or the north, the horizon circle clearly becomes different, so that the stars above our heads undergo a great change, and the same stars do not appear to those who move to the north and the south.
ἔνιοι γὰρ ἐν Αἰγύπτῳ μὲν ἀστέρες ὁρῶνται καὶ περὶ Κύπρον, ἐν τοῖς πρὸς ἄρκτον δὲ χωρίοις οὐχ ὁρῶνται, καὶ τὰ διὰ παντὸς ἐν τοῖς πρὸς ἄρκτον φαινόμενα τῶν ἄστρων ἐν ἐκείνοις τοῖς τόποις ποιεῖταιδύσιν.
For some stars are seen in Egypt and near Cyprus, but are not seen in the regions to the north, and the stars that are always visible in the northern regions set in those places.
ὥστʼ οὐ μόνον ἐκ τούτων δῆλον περιφερὲς ὂν τὸ σχῆμα τῆς γῆς, ἀλλὰ καὶ σφαίρας οὐ μεγάλης· οὐ γὰρ ἂν οὕτω ταχύ ἐπίδηλον ἐποίει μεθισταμένοις οὕτω βραχύ.
So that from these facts it is clear not only that the shape of the earth is circular, but also that it is a sphere of no great size; for otherwise it would not have made this clear so quickly to those who change their place by so short a distance.
διὸ τοὺς ὑπολαμβάνοντας συνάπτειν τὸν περὶ τὰς Ἡρακλείους στήλας τόπον τῷ περὶ τὴν Ἰνδικήν, καὶ τοῦτον τὸν τρόπον εἶναι τὴν θάλατταν μίαν, μἤ λίαν ὑπολαμβάνειν ἄπιστα δοκεῖν·
For this reason, those who suppose that the region around the Pillars of Hercules connects with the region around India, and that in this way the sea is one, do not seem to suppose things that are too incredible.
λέγουσι δὲ τεκμαιρόμενοι καὶ τοῖς ἐλέφασιν, ὅτι περὶ ἀμφοτέρους τοὺς τόπους τοὺς ἐσχάτους ὄντας τὸ γένος αὐτῶν ἐστίν, ὡς τῶν ἐσχάτων διὰ τὸ συνάπτειν ἀλλήλοις τοῦτο πεπονθότων.
And they also speak of elephants as evidence, because their species exists in both of these extreme regions, on the ground that the extremes suffer this because they connect with one another.
καὶ τῶν μαθηματικῶν ὅσοι τὸ μέγεθος ἀναλογίζεσθαι πειρῶνται τῆς περιφερείας, εἰς τετταράκοντα λέγουσιν εἶναι μυριάδας σταδίων·
And those of the mathematicians who attempt to calculate the size of the circumference say that it is about forty ten-thousands of stadia.
ἐξ ὧν τεκμαιρομένοις οὐ μόνον σφαιροειδῇ τὸν ὄγκον ἀναγκαῖον εἶναι τῆς γῆς, ἀλλὰ καὶ μὴ μέγαν πρὸς τὸ τῶν ἄλλων ἄστρων μέγεθος.
From these arguments, as they infer, it is necessary not only that the mass of the earth is spherical, but also that it is not large in comparison with the size of the other stars.