Nor can it be admitted that the doctrine is true. Thus much indeed is true by accident — that every thing which has no greater obligation to be moved in this direction than in that, must necessarily remain at the centre. But this is true only so long as it remains a compact whole; for, according to the theory which we are discussing, it will not remain stationary, but will be moved: not indeed as a whole, but dispersed into parts (s. 23: ἀλλὰ μὴν οὐδὲ ἀληθές ἐστι τὸ λεγόμενον. κατὰ συμβεβηκὸς μέντοι τοῦτό γε ἀληθές, ὡς ἀναγκαῖον μένειν ἐπὶ τοῦ μέσου πᾶν, ᾧ μηθὲν μᾶλλον δεῦρο ἡ δεῦρο κινεῖσθαι προσήκει. ἀλλὰ διά γε τοῦτον τὸν λόγον οὐ μενεῖ ἀλλὰ κινηθήσεται· οὐ μέντοι ὅλον, ἀλλὰ διεσπασμένον. — I understand κατὰ συμβεβηκός to mean, subject to the condition of its remaining a compact whole). For the same reasoning would apply to Fire as well as to Earth: it would prove that Fire, if placed at the centre, will remain there just as much as Earth, because Fire will have like relation to each point of the extreme periphery. Yet nevertheless it will (not remain at the centre, but will) be carried away, if not impeded, as we observe that it is carried in fact, to the periphery; only not all to one and the same point of the periphery, but corresponding portions of the Fire to corresponding portions of the periphery: I mean, that the fourth part (e.g.) of the Fire will be carried to the fourth part of the periphery; for a point is no real part of bodies (οὐθὲν γὰρ στιγμὴ τῶν σωμάτων ἐστίν). This is the only necessary consequence flowing from the principle of likeness of relation. As, if supposed to be put all together at the centre, it would contract from a larger area into a smaller, so, when carried away from the centre to the different parts of the periphery, it would become rarer and would expand from a smaller area into a larger. In like manner the Earth also would be moved away from the centre, if you reason upon this principle of likeness of relation, and if the centre were not the place belonging to it by nature (s. 24).
CH. 14. — Having thus reported the suppositions of others respecting the figure, place, rest and motion, of the Earth, I shall now deliver my own opinion, first, whether it is in motion or at rest; for some philosophers, as I have said, regard it as one of the stars (and therefore not in the centre, but moving round the centre — the Pythagorean theory); others (as Plato), though they place it in the centre, consider it to be packed and moved round the middle of the axis of the Kosmos (οἱ δὲ ἐπὶ τοῦ μέσου θέντες, εἰλεῖσθαι καὶ κινεῖσθαί φασι περὶ τὸν μέσον πόλον).
That neither of these hypotheses is possible, we shall perceive if we take as our point of departure — That, if the Earth be carried round, whether in the centre or apart from the centre, such motion must necessarily be violent or contra-natural. Such motion does not belong naturally to the Earth itself; for, if such were the fact, it would belong equally to each portion of the Earth, whereas we see that all these portions are carried in a straight line to the centre. Being thus violent or contra-natural, it cannot possibly be eternal. But the order of the Kosmos is eternal. Besides, all the bodies which are carried round in a circular revolution (all except the First or Outermost Sphere — the Aplanês) appear to observation as lagging behind and as being moved in more than one current. The like ought to happen with the Earth, if moved round, whether on the centre or apart from the centre: it ought to be moved in two currents; and, as a consequence thereof, there ought to be side-motions and back-turnings of the stars fastened in their sphere. But we see by observation that this does not happen; and that the same stars always rise and set at the same places of the Earth (s. 1).
Farthermore, the natural current both of the entire Earth and of each of its parts is towards the middle of the universe: this is the reason why it is at the centre, even though it happens to be actually there at present (διὰ τοῦτο γὰρ, κἂν εἰ τυγχάνει κειμένη νῦν ἐπὶ τοῦ κέντρου — he means that though actually there, it remains there not through any force of inertia or other cause, but because it has a natural current towards the centre). You might start a doubt, indeed, since the centre of the Universe coincides with the centre of the Earth, to which of the two it is that the current of heavy bodies naturally tends: whether they tend thereto because it is the centre of the Universe, or because it is the centre of the Earth. We must however necessarily suppose the former; since Fire and light bodies, whose current is the contrary of the current of heavy bodies, are carried to the extreme periphery of the Universe, or of that place which comprehends and surrounds the centre of the Universe (ss. 2, 3). But it happens (συμβέβηκε: it is an accompanying fact) that the same point is centre of the Universe and centre of the Earth; accordingly heavy bodies are carried by accident (κατὰ συμβεβηκός — by virtue of this accompanying fact) to the centre of the Earth; and the proof that they are carried to this same point is, that their lines of direction are not parallel but according to similar angles (s. 4). That the Earth therefore is at the centre, and that it is at rest, we may see by the foregoing reasons, as well as by the fact, that stones thrown upwards to ever so great a height, are carried back in the same line of direction to the same point (s. 5).
We may see farther the cause why the Earth remains at rest. For, if its natural current be from all directions towards the centre, as observation shows, and that of Fire from the centre to the periphery, — no portion of it can possibly be carried away from the centre, except by violence. For to one body belongs one current of motion, and to a simple body a simple current — not the two opposite currents; and the current from the centre is opposite to the current to the centre. If, therefore, it be impossible for any portion of the Earth to be carried in a direction away from the centre, it is yet more impossible for the whole Earth to be so; for the natural current of each part is the same as that of the whole. Accordingly, since the Earth cannot be moved except by a superior force or violence, it must necessarily remain stationary at the centre (s. 6). The same conclusion is confirmed by what we learn from geometers respecting astronomy; for all the phenomena of the Heavens — the changes in figure, order, and arrangement of the stars — take place as if the Earth were in the centre (s. 7).
The figure of the Earth is necessarily spherical. For each of its parts has gravity, until it reaches the centre; and the lesser part, pushed forward by the greater, cannot escape laterally, but must become more and more squeezed together, one part giving place to the other, until the centre itself is reached. We must conceive what is here affirmed as occurring in a manner like what some of the ancient physical philosophers tell us, except that they ascribe the downward current to an extraneous force; whereas we think it better to state the truth, and to say that it occurs because by nature all heavy bodies are carried towards the centre. Since, therefore, the preliminary Chaos or hotchpotch existed in power (or with its inherent powers existing though not exercised), the elements (those which had gravity), were carried from all sides equally towards the centre (ἐν δυνάμει οὖν ὄντος τοῦ μίγματος, τὰ διακρινόμενα ἐφέρετο ὁμοίως πάντοθεν πρὸς τὸ μέσον — this is an allusion to the doctrine of Anaxagoras); indeed, whether brought together at the centre equally from all the periphery or in any other manner, the result will be the same. If we suppose particles to be brought together at the centre equally from all sides, it is plain that the mass so formed will be regular and spherical; and, even if not equally from all sides, this will make no difference in the reasoning; for, since all portions of the mass have weight or tend to the centre, the larger portions will necessarily push the lesser before them as far as the centre (ss. 8, 9).
A difficulty here presents itself, which may be solved upon the same principles. The Earth being spherical, and at the centre, suppose that a vast additional weight were applied to either of its hemispheres. In that case, the centre of the Universe, and the centre of the Earth, would cease to coincide: either, therefore, the Earth will not remain at the centre; or, if it would still remain at rest, while not occupying the centre, it is in its nature to be moved even now (s. 10: ὥστε ἢ οὐ μενεῖ ἐπὶ τοῦ μέσου, ἢ εἴπερ ἠρεμήσει γε καὶ μὴ τὸ μέσον ἔχουσα ᾖ, πέφυκε κινεῖσθαι καὶ νῦν) — i.e., if the Earth can be at rest when not at the centre, we must infer that the centre is not its natural place, and therefore that its nature will be to be moved from the centre towards that natural place wherever situated).
Such is a statement of the difficulty; but we shall see that it may be cleared up with a little attention. We must distinguish what we mean when we affirm that every particle having weight is carried towards the centre. We clearly do not mean that it will be so carried until the particles farthest from the centre shall touch the centre. We mean that the greater mass must press with preponderating force (δεῖ κρατεῖν τὸ πλεῖον ἕως ἂν λάβῃ τῷ αὑτοῦ μέσῳ τὸ μέσον) until its centre grasps the centre of the universe; up to this point its gravity will last; and this is equally true about any clod of earth as about the whole earth: large or small size makes no difference. Whether the whole Earth were carried in a mass from any given position, or whether it were carried in separate particles, in either case it would be carried onward until it embraced the centre equally on all sides; the smaller parts being equalized to the greater in gravitating tendency because they are pushed forward by the greater (ἀνισαζομένων τῶν ἐλαττόνων ὑπὸ τῶν μειζόνων τῇ προώσει — s. 11). If, therefore, the Earth was ever generated, it must have been generated in this manner, and must thus acquire a spherical figure; and, even if it be ungenerable and stationary from everlasting, we must conceive its figure to be that which it would have acquired, if it had been generable and generated from the first (εἴτε ἀγέννητος ἀεὶ μένουσα, τὸν αὐτὸν τρόπον ἔχειν, ὅνπερ κἂν εἰ γιγνομένη τὸ πρῶτον ἐγένετο). That it must be spherical, we see not only from this reasoning, but also because all heavy bodies are carried towards it, not in parallel lines but, in equal angles. This is what naturally happens with what is either actually spherical, or by nature spherical. Now we ought to call every thing such as it by nature wishes to become and to be: we ought not to call it such as it is by force and contrary to nature (s. 12).
The same conclusion is established by the sensible facts within our observation. If the Earth had been of any other than spherical figure, the eclipses of the Moon would not have projected on the Sun the outlines which we now see. The moon in her configurations throughout the month takes on every variety of outline — rectilinear, double convex, and hollow. But in her eclipses the distinguishing line is always convex. Now this must necessarily be occasioned by the circumference of the Earth being spherical, since the eclipses of the Moon arise from the interposition of the Earth (s. 13).
Farthermore, we see from the visible phenomena of the stars not only that the Earth is spherical, but also that its magnitude is not great. For, when we change our position a little as observers, either to the north or to the south, we find the celestial horizon to be manifestly different. The stars at the zenith are greatly changed, and the same stars do not appear: some stars are visible in Egypt and Cyprus, but become invisible when we proceed farther north; and those which are constantly visible in the northern regions, are found to be not constantly visible, but to set, when the observer is in Egypt or Cyprus. The bulk of the Earth must therefore be small, when a small change of position is made so soon manifest to us (s. 14). Hence those who hold that the regions near the pillars of Herakles join on with India and that the ocean eastward and westward is one and the same, must not be supposed to talk extravagantly (μὴ λίαν ὑπολαμβάνειν ἄπιστα δοκεῖν): they infer this from the presence of elephants alike at both extremities. Geometers who try to calculate the magnitude of the Earth, affirm that its circumference is 400,000 stadia.