CH. 2. — Since the Pythagoreans and others recognize a Right and Left in the Heaven, let us enquire whether such ἀρχαί can properly be ascribed to the body of the Universe; for, if these can be ascribed, much more may the other ἀρχαί prior to them be ascribed to it. Of ἀρχαί κινήσεως (termini a quibus), there are three couples: (1) Upwards and Downwards; (2) Forward and Backward; (3) Right and Left. All the three exist in animals; but the first alone is found in plants. All the three are in all perfect bodies, and in all animated bodies which have in themselves a beginning of motion; but not in inanimate bodies, which have not in themselves a beginning. Each of these three ἀρχαί or διαστάσεις is true and appropriate as an attribute; but among the three, Upwards and Downwards comes first in the order of nature, Right and Left, last. The Pythagoreans are to be blamed for dwelling on Right and Left, and not noticing the other two pairs which are prior in the order of nature and more appropriate, and for supposing that Right and Left are to be found in every thing. Upward is the principle of length; Right, of breadth; Forward, of depth. Again, from upward movement comes growth; movement from the right is local movement; movement from before is movement of sense (ἡ κατὰ τὴν αἴσθησιν), or the line in which sensible impressions are propagated (ἐφ’ ᾧ αἰσθήσεις). Up is the source from whence motion originates (τὸ ὅθεν ἡ κίνησις — s. 6); Right, the point from which the direction of the motion starts; Forward, the point towards which it goes (τὸ ἐφ’ ὅ). In inanimate bodies (which are either not moved at all, or only moved in one manner and direction, as fire only upwards, earth only downwards), we speak of above and below, right and left, only with reference to ourselves, and not as attributes really belonging to these objects; for by inverting the objects these attributes will be inverted also, right will become left, and left will become right. But in animated objects, which have in themselves an ἀρχὴ κινήσεως, a real right and left, a real upward and downward, are to be recognized: of course therefore in the Heaven, which is an animated object of this character (ἔμψυχος). For we must not make any difficulty in consequence of the spherical figure of the universe, or suppose that such a figure excludes real right and left, the parts being all alike and all in perpetual motion. We must conceive the case as like that of a person having a real right and left, distinct in attributes, but who has been enclosed in a hollow sphere: he will still have the real distinct right and left, yet to a spectator outside he will appear not to have it. In like manner, we must speak of the Heaven as having a beginning of motion; for, though its motion never did begin, yet there must be some point from which it would have taken its departure, if it ever had begun, and from which it would recommence, if it ever came to a standstill. I call the length of the Heaven, the distance between the poles — one of the poles above, the other below. Now the pole which is above us, is the lower pole; that which is invisible to us, is the upper pole. For that is called right, in each object, from whence local movement takes its departure, or where local movement begins. But the revolution of the Heaven begins on the side where the stars rise; this, therefore, is the true right, and the side on which they set, is left. If, therefore, it begins from the right, and revolves round to the right (ἐπὶ τὰ δέξια περιφέρεται), the invisible pole must be the upper pole; for, if the visible pole were the upper, the movement of the Heaven would be to the left, which we deny to be the fact. The invisible pole is therefore the upper, and those who live near it are in the upper hemisphere, and to the right (πρὸς τοῖς δεξίοις); we on the contrary are in the lower hemisphere, and to the left. The Pythagoreans are in error when they say that we are in the upper hemisphere, and to the right, and that inhabitants of the southern hemisphere are in the lower hemisphere and to the left. But, speaking with reference to the second revolution (τῆς δευτέρας περιφορᾶς) or that of the planets, which is in the contrary direction to the first revolution or that of the First Heaven, it is we who are in the upper hemisphere and on the right side; it is the inhabitants of the southern hemisphere, who are in the lower hemisphere and on the left side: that is, it is we who are on the side of the beginning of motion, they who are on the side of the end (ss. 1-10).
CH. 3. — I have previously laid it down, that circular movement is not opposite to circular. But, if this be the case, what is the reason that there are many different revolutions in the Heaven? This is what I shall now enquire, fully aware of the great distance from which the enquiry must be conducted (πόῤῥωθεν) — not so much a distance in place, as owing to the small number of accompanying facts which can be observed by the senses respecting them.
The cause must be looked for in this direction. Every thing which performs a work, exists for the sake of that work. Now the work of Deity is immortality, or eternal life; so that the divine substance must of necessity be in eternal motion. The Heaven is a divine body and has for that reason the encyclical body, whose nature it is to be moved for ever in a circle. But why is not the whole body of the Heaven thus constituted (i.e., encyclical)? Because it is necessary that some portion of its body should remain stationary in the centre; and no portion of the encyclical body can possibly remain stationary, either in the centre or elsewhere. For, if it could, its natural motion (i.e., the motion of that supposed portion) would be towards the centre; whereas its natural motion is circular; and it cannot move towards the centre contrary to its nature, because on that supposition its motion would not be eternal: no motion contrary to nature can be eternal. Moreover that which is contrary to nature is posterior to that which is natural; it is a deviation therefrom arising in the course of generation (s. 1).
Hence it is necessary that earth should exist, the nature of which it is to rest in the centre (i.e., the divine encyclical body will not suffice alone, without adjuncts of different nature). I assume this for the present; more will be said about it anon.
But, if earth exists, fire must exist also; for of two contraries, if the one exist by nature, the other must exist by nature also. For the matter of contraries is the same, and Form (positive and affirmable) is prior by nature to Privation (for example, hot is prior to cold); now rest and gravity denote the privation of motion and lightness (s. 2 — i.e., fire is prior in nature to earth, as having the positive essences motion and levity, while earth has for its essence the privation thereof).
Again, if fire and earth exist, the two other elements intermediate between them must also exist; for each of the four elements has its peculiar mode of contrariety with reference to each. At least let this be assumed now: I shall show it at length presently.
Now, these points being established, we see that generation must necessarily come to pass, because no one of the four elements can be eternal: they act upon each other, and suffer from each other, with contrary effects; they are destructive of each other. Besides, each of them has a mode of motion natural and appropriate to it, but this mode of motion is not eternal (because it is either to the centre or to the circumference and therefore has a natural terminus). It is not reasonable to suppose that any Mobile can be eternal, whose natural mode of motion cannot be eternal (s. 3).
Thus the four elements are not eternal, but require to be renewed by generation; therefore generation must come to pass. But, if generation be necessary, more than one revolution of the celestial body is indispensably required: two at least, if not more. For, if there were no other revolution except that of the First Heaven, that is consistent only with a perfectly uniform condition of the four elements in relation to each other (s. 4).
When the question is asked, therefore, Why there are (not one only but) several encyclical bodies? I answer: Because generation must come to pass. There must be generation, if there be fire; there must be fire and the other elements, if there be earth; there must be earth, because something must remain stationary eternally in the centre, if there is to be eternal revolution (s. 5).
CH. 4. — The Heaven is by necessity spherical: this figure is at once both most akin to its essence and first in its own nature. I shall begin with some observations respecting figures generally — plane and solid, as to which among them is the first. Every plane figure is either rectilinear or curvilinear; the former is comprehended by many lines, the latter only by one. Now, since in every department one is prior to many and simple to compound, the first of all plane figures must be the circle. Moreover, since that is perfect which can receive nothing additional from without, and since addition can be made to every straight line, but none whatever to the line circumscribing a circle, it is plain that this latter is perfect; and therefore the circle is the first of all plane figures, and the sphere of all solid figures (ss. 1, 2). This doctrine appears most reasonable when we set out the different figures, each with a number belonging to it in numerical order. The circle corresponds to One, the triangle to Two, since its three angles are equal to two right angles; whereas, if we assign number One to the triangle and place that first, we can find no number fit for the circle: the circle will be no longer recognized as a figure (s. 4).