CH. 1. — The science of Nature has for its principal object — Bodies, Magnitudes, and the various affections and movements of Bodies and Magnitudes; also the beginnings or principles of this sort of Essence. The Continuous is that which is divisible into parts perpetually divisible: and Body is that which is divisible in every direction. Of magnitudes, some (lines) are divisible only in one direction; others (planes) only in two directions; others again (bodies) in three directions. This is the maximum: there is no other magnitude beyond; for three are all, and to say “in three directionsâ€� is the same as to say “in all directions.â€� As the Pythagoreans say, The Universe and All Things are determined by Three: in End, Middle, and Beginning, lies the number of the Universe, or the Triad. We have received these as laws from nature, and we accordingly employ this number (Three) for solemnities in honour of the Gods. Moreover, we apply our predicates on the same principle; for we call Two, and The Two — Both, but we do not call them all. Three is the first number to which we apply the predicate All. Herein (as was observed before) we follow the lead of Nature herself. Since therefore these three phrases — All Things, The Universe, The Perfect or Complete — do not specifically differ from each other, but are distinguished only in respect of the matter or occasions on which they are applied. Body is the only kind of magnitude which can be declared Perfect or Complete, that is, All; for it is the only magnitude determined or defined by the Three. Being divisible in three directions, it is divisible every way; other magnitudes are divisible either only in one way or only in two. Magnitudes are both divisible and continuous according to the number by which they are designated — continuous in one direction, in two, in three, or all. All divisible magnitudes are also continuous: whether all continuous magnitudes are divisible, is not yet clear. But whatisclear is — that there is no upward transition to a higher genus beyond Body, as there is from line to surface, and from surface to Body. If there were, Body would not be perfect or complete as a magnitude; for the transition would be made at the point of deficiency; but the perfect or complete can have no deficiency: it stretches every way. Such is each body included as a part in the universe: it has dimensions in every direction. Yet each is distinguished from its neighbour by contact, and each therefore in a certain sense is many. But the Universe (τὸ πᾶν) including all these parts is of necessity perfect and complete; extending not merely in one way, and in another way not, but πάντῃ, as the word literally means (ss. 1-4).
CH. 2. — Respecting the nature of the Universe, we shall enquire presently whether in the aggregate it be infinite or of finite magnitude. But first let us speak about its different constituent species, proceeding on the following basis. I affirm that all natural bodies and magnitudes areper selocally moveable; and that Nature is to them a beginning or principle of motion. Now all Local Motion (known by the name of φορά) is either Rectilinear or Circular, or compounded of the two; for these two are the only simple motions, by reason that the only two simple magnitudes are the rectilinear and the circular. The circular is motion round the Centre; the rectilinear is motion either downwards towards the centre or upwards from the centre. These three are the only simple modes of motion or currents: as I said in the last chapter that body was made complete in the number three, so also the motion of body is made complete in the number three. Now, as there are some bodies (such as fire, earth, and their cognates) which are simple (i.e.which have in themselves a natural beginning or principle of motion), and others which are compounds of these, so also there must be simple motions belonging to the former and compound motions belonging to the latter; such compound motions being determined by the preponderant element therein. Since, therefore, circular motion is a simple mode of motion, and since simple modes of motionbelong only to simple bodies, there must of necessity be a particular variety of simple body, whose especial nature it is to be carried round in circular motion. By violence, indeed, one body might be moved in a mode belonging to another; but not by nature. Moreover, since motion against nature is opposite to motion conformable to nature, and since each mode has one single opposite, simple circular motion, if it be not conformable to the nature of this body, must be against its nature. If then the body rotating in a circle be fire or any of the other elements, its natural mode of motion must be opposite to circular motion. But each thing has only one opposite; and up and down are each other’s opposites. If then the body which rotates in a circle rotates thus against nature, it must have some other mode of motion conformable to nature. But this is impossible: for, if the motion conformable to its nature be motion upwards, the body must be fire or air; if motion downwards, the body must be earth or water (and there is no other simple mode of motion that it can have). Moreover, its rotatory motion must be a first motion; for the perfect is prior in nature to the imperfect. Now the circle is perfect; but no straight line is perfect: neither an infinite straight line, for in order to be perfect, it must have an end and a boundary; nor any finite straight line, for each has something without it and may be prolonged at pleasure. So that, if motion first by nature belong to a body first by nature, if circular motion (as being perfect) be prior to rectilinear motion, and if rectilinear motion belong to a first or a simple body, as we see both in fire and in earth, — we may be sureà fortiorithat circular motion belongs to a simple body, and that there is, besides the four elements here, prior to them and more divine than them, a different body cf special nature and essence. Indeed, since circular motion is against the nature of these four elements, there must be some other different body to whose nature it is conformable. There must thus be some simple and primary body, whose nature it is to be carried round in a circle, as earth is carried downwards and fire upwards. On the assumption that the revolving bodies revolved against their own nature, it would be wonderful and even unreasonable that this one single mode of motion, being thus contrary to nature, should be continuous and eternal; for in all other things we see that what is contrary to nature dies away most speedily. Now, if the revolving body were fire, as some affirm, the revolving motion would be just as much contrary to its nature as motion downwards; for the natural motion of fire is upwards or away from the centre. Reasoning from all these premisses, we may safely conclude that, distinct from all these bodies which are here around us, there exists a body whose nature is more honourable in proportion to its greater distance from us here (ss. 1-13).
CH. 3. — We plainly cannot affirm that every body is either heavy or light: meaning by heavy, that which is carried by its nature downwards or towards the centre; by light, that which is carried by its nature upwards or away from the centre. Heaviest (or earth) is that which underlies all other downward moving bodies, lightest (fire) is that which floats above all upward moving bodies. Air and water are both light and heavy, relatively, but relatively to different terms of comparison; thus, water is heavy as compared to air and fire, light as compared to earth. But that body whose nature it is to revolve in a circle, cannot possibly have either heaviness or levity; for it cannot move in a right line, either upwards or downwards, nor either by nature or against nature. Not by nature, for, in that case, it must be identical with some one of the four elements; not against nature, because, if it moved upwards against nature, this would prove that motion downwards was conformable to its nature, and it would thus be identical with earth: we have already seen that, if a body moves upwards against nature, it must move downwards according to nature, andvice versâ. Now the same natural motion which belongs to any body as a whole, belongs also to its minute fragments (to the whole earth and to any of its constituent clods). Accordingly the revolving body in its local movement of revolution cannot possibly be dragged in any other direction, either upward or downward, — neither the whole nor any portion thereof. It is alike reasonable to conceive it as ungenerable, indestructible, incapable both of increase and of qualitative change (ἀναυξὲς καὶ ἀναλλοίωτον). It cannot be generated, because every thing generated comes out of a substratum and an opposite, into which it relapses on being destroyed. Now the revolving body has no opposite; for we have already seen that opposite bodies have their currents of motion opposite, and there is no current of motion opposite to that of circular rotation. Nature has rightly excepted this ungenerable and indestructible substance from the action of contraries, in which generation and destruction occur. It is also incapable ofincrease or diminution, because these processes take place through the accession of new cognate materials; and in this case there are none such. It is farther incapable of qualitative change, because this always implies the being affected favourably or unfavourably (πάθος); and this last never takes place, in plants or in animals, without some increase or diminution in quantity (ss. 1-5).
This Celestial Substance is thus eternal, ungenerable, indestructible, noway increased nor diminished, neither growing old nor capable of disturbing affections nor changeable in quality. Herein the evidence of reason and that of phenomena concur. For all men, Hellenes and Barbarians, have some belief respecting the Gods, and all who believe Gods to exist assign to the divine nature the uppermost place in the Kosmos; an immortal place going naturally along with immortal persons. Our perceptions confirm this sufficiently, at least when we speak with reference to human belief. For not the smallest change has ever been observed in the celestial substance, throughout all past time. Under these impressions, the ancients gave to it the name which it now bears; for the same opinions suggest themselves to us not once, nor twice, but an infinite number of times.Hence the ancients, regarding the First Body as something distinct from Fire, Earth, Air, or Water, called the uppermost place Æther, from its being always running (ἀπὸ τοῦ θεῖν ἀεί), the adverbial designation being derived from eternal duration. Anaxagoras employs this name improperly: he calls Fire by the name of Æther (s. 6).
It is plain, from all we have said, that the simple bodies cannot be more in number than those just indicated; for a simple body must of necessity have a simple mode of motion, and there are only three simple modes of motion — one circular and two rectilinear, one of these being from the centre, the other towards the centre (s. 7).
CH. 4. — That Circular Rotation has no motion opposed to it, may be shown by several different arguments. If there were any, it would certainly be rectilinear motion; for convex and concave, though each respectively opposed to the other, are, when both put together, opposed as a couple to rectilinear motion. But each variety of rectilinear motion has another variety of rectilinear motion opposed to it; and each thing has but one opposite. Moreover the oppositions between one motion (or one current — φορά) and another are founded upon oppositions of place, which are three in number: (1) Above and Below; (2) Before and Behind; (3) Right and Left. Now the motion in circular rotationfromA to B is not opposite to that from B to A: the opposition of motion is along the straight line which joins the two; for an infinite number of different circles may be drawn, not interfering with each other but all passing through the same two points A and B. In the same circle, the opposition between the current from A to B and that from B to A, is along the line of diameter — not along the line of circumference. If one circular current were really opposed to any other circular current, one or other of the two would have existed to no purpose; for both have the same object. That is to say: what is carried round in a circle, let it begin from any point whatever, must necessarily come round equally to all the opposite places, above, below, before, behind, right, left. If the two (presumed) opposite circular currents were equal, they would neutralize each other, and there would be no motion at all of either of them. If one of the two were the more powerful, it would extinguish the other; so that to suppose the existence of both is to suppose that one or both exists in vain (i.e., can never be realized). We say that a sandal exists in vain (μάτην), when it cannot be fastened on. But God and nature do nothing in vain (ss. 1-8).
CH. 5. — Most of the ancient philosophers admitted an infinite body; but this may be shown to be impossible. The question is very important; for the consequences which follow from admitting the Infinite as principium, affect our speculations concerning the whole of Nature (s. 1).
Every body is of necessity either simple or compound. The infinite body therefore, if it exists, must of necessity be either one or the other. But there can be no infinite compound composed of simple bodies finite in magnitude and in number: so that, if an infinite body exist, it must be simple. We shall first enquire whether the First Body, whose nature it is to move in a circle, can be infinite in magnitude. Now, if it were infinite, the radii thrown out from the centre would be infinite, and the distance between them would also be infinite; that is, no finite peripheral line can be found touching all the extremities of the radii without: if any such line be assumed, you may always assume a greater. We call Number infinite, because the greatest number cannot be given; and the like may be said about this distance. Now, as an infinite distance cannot be passed over, no circular motion passing over it is possible, so as to come round to thepoint of departure. But we see plainly that the First Body or the Heaven does come round in a circle; and it has been shown by reasoningà priorithat thereisa variety of body whose nature it is to move in a circle. Such a body therefore as the First (revolving) Body cannot be infinite (ss. 2, 3).
Four other arguments are added, proving the same conclusion (s. 4, seq.). One of them is: That an infinite square, circle, or sphere, is an impossibility; each of these figures being defined or determined. As there can be no infinite circle, so neither can an infinite body be moved round in a circle (s. 7).
CH. 6. — As the First Body cannot be infinite, so neither can those bodies be infinite whose nature it is to move to the centre and from the centre — neither the centripetal nor the centrifugal body. For these two currents are opposite in nature; opposite currents being characterized by the opposite places to which they tend. But of two opposites, if the one be fixed and determinate, the other must be fixed and determinate also. Now the centre is determined; for the centripetal body, let it fall from what height it will, can never fall lower than the centre; and, since the centre is determined, the upper region or extremity must also be determined. The places at each extreme being thus determined, the intermediate space must be determined also; otherwise there would exist motion undetermined or infinite, which has been shown in a former treatise to be impossible (Physica, VIII. viii.); and therefore that body which either is therein, or may possibly be therein, must be determined. But it is a fact that the centripetal body and the centrifugal body can be therein; for centripetality and centrifugality are of the nature of each respectively (ss. 1, 2).
Hence we see that there can be no infinite body. There are other reasons also. As the centripetal body is heavy, if it be infinite, its gravity must also be infinite; and, if gravity cannot be infinite, neither can any heavy body be infinite. The like about any light body, such as the centrifugal (s. 3).
He then shows (by a long process of reasoning, not easy to follow) first, that there cannot be an infinite body with finite gravity; next, that there can be no infinite gravity. Accordingly there can be no infinite body at all, having gravity. At the end, he considers that this is established, (1) by the partial arguments (διὰ τῶν κατὰ μέρος) immediately preceding; (2) by the general reasonings in his other treatises respecting first principles, in which he explained the Infinite — in what sense it existed and did not exist; (3) by an argument about the Infinite, upon which he touches in the next chapter (ss. 4-13).
CH. 7. — Every body is of necessity either infinite or finite. If infinite, it is as a whole either of like constituents or of unlike. If the latter, either of a finite number of species, or of an infinite number. The last is impossible, if our fundamental assumptions are allowed to stand. For since the simple modes of motion are limited in number, the simple bodies must be alike limited; each simple mode of notion belonging to its own special simple body, and each natural body having always its own natural motion. But, if the Infinite be composed of a finite number of species, each of these constituent parts must be infinite; that is, water and fire must be infinite. Yet this too, is impossible; for we have seen that there cannot be either infinite levity or infinite gravity (the attributes of fire and water). Moreover, if these bodies be infinite, the places which they occupy, and the motions which they make, must also be infinite; but this also we have shown to be inadmissible, if our fundamental assumptions are admitted. The centripetal body cannot be carried to an infinite distance downward, nor the centrifugal body to an infinite distance upward. That which cannot come to pass, cannot be in course of coming to pass; thus, if a thing cannot come to be white, or a cubit long, or domiciled in Egypt, it cannot be in course of becoming white, or a cubit long, &c. It cannot be in course of being carried to a terminus which cannot be reached. It might be argued that fire, though discontinuous and dispersed, might still be infinite, in the sum total of its different masses. But body is that which is extended in every direction: how can there be many bodies unlike to each other, yet each of them infinite? Each of them, if infinite at all, ought to be infinite in every direction (ss. 1-5).
We thus see that the Infinite cannot consist of unlike constituents. But neither can it consist of constituents all similar. For, first, there are only three simple motions, and one of the three it must have; but we have shown that it cannot have either centripetal or centrifugal motion (i.e., that it cannot have either infinite gravity or infinite levity); nor can it again have circular motion, for the Infinite cannot be carried in a circle: this would amount to saying that the Heaven is infinite, which we have shown to be impossible. The Infinite indeed cannot be moved in any way at all; for, if moved, it must be moved either according to nature, or contraryto nature (violently), and, if its present motion be violent, it must have some other mode of motion which is natural to it. But, if it have any such, this assumes that there exists some other place belonging to it, into which it may be conveyed — an obvious impossibility (ss. 6, 7).
Farthermore, the Infinite cannot act in any way upon the Finite, nor be acted upon thereby (ss. 8-10). Nor can the Infinite be acted upon in any way by the Infinite (ss. 11-12).
If then every perceptible body possesses powers, as agent or patient or both, there can be no perceptible body which is infinite. But all bodies which are in any place are perceptible; therefore no body which is in any place can be infinite. There is no infinite body, indeed there can be no body at all, outside of the Heaven; for that which is outside of the Heaven is in a place. Even if perceivable only up to a certain point (μέχρι τινός), even if merely intelligible, it would still be in a place, and would therefore come under the foregoing argument — that there is no body outside of the Heaven (ss. 13, 14).
The foregoing reasoning may be summed up, in more general language (λογικώτερον), as follows:— The Infinite assumed as homogeneous cannot be moved in a circle, since the Infinite has no centre; nor in a straight line, since this would imply a second infinite place into which it must be moved according to nature, and a third infinite place into which it must be moved against nature, and since in either case the force which causes it to be moved must be infinite. But we have already argued, in treating of Motion (Phys. VIII. x.) that nothing finite can have infinite power, nothing infinite can have finite power; and, if that which is moved according to nature can also be moved contrary to nature, there must of necessity be two Infinites — Movens and Motum. Yet what can that be which causes the Infinite to move? If it cause itself to move, it must be animated (ἔμψυχον): but how can an infinite animated being (ζῷον) exist? And, if there be anything else which causes it to move, there must exist two Infinites, each distinguished from the other in form and power (ss. 15-17).
Again, even if we admit the doctrine of Leukippus and Demokritus — That the whole is not continuous, but discontinuous, atoms divided by intervening spaces — still the Infinite is inadmissible. For the nature and essence of these atoms is all the same, though they are different from each other in figure and arrangement; accordingly the motion of all must be the same: if one is heavy or centripetal, all must be so alike; if one is light or centrifugal, all must be so alike. But either of these motions would imply the existence of centre and periphery; which does not consist with an infinite whole. In the Infinite, there is neither centre nor periphery; no terminus prefixed either for upward or downward motion; noown placeeither for centripetal or centrifugal matter. Therefore in an infinite universe, there can be no motion at all (ss. 18, 19).
CH. 8. — There cannot be more than one Kosmos. All things both rest and are moved, either by violence, or according to nature. In that place to which it is carried by nature, it also rests by nature: in that place to which it is carried by violence, it rests by violence. If the current which we see towards the centre is by violence, the opposite current must be natural; if earth is carried by violence from thence hitherward, its natural current must be from hence thitherward; and, if being here it rests without violence, its current towards here must be a natural one. For there is one only which is natural. Now, if there be many Kosmi, they must be alike in their nature, and must be composed of the same bodies, having the same nature and powers — fire, earth, and the two intermediate elements: for, if the bodies here are not the same as those in other Kosmi — if the same names are given in an equivocal sense and do not connote the same specific attributes — the name Kosmos must be equivocal also, and there cannot be many true or real Kosmi, in the same sense. To the parts or elements of each Kosmos, therefore, the centripetal andcentrifugalcurrents are natural; for the simple currents are limited in number, and each element is so named as to connote one of them specially; and, if the currents are the same, the elements must also be the same everywhere. If there were another Kosmos, the earth in that would tend towards the centre of our Kosmos, and the fire in that would tend towards the periphery of our Kosmos. But this is impossible; since in that case the earth in that Kosmos would run away from the centre of its own Kosmos, and the fire therein would run away from its own periphery. Either we must not admit the same nature in the simple elements of the numerous Kosmi; or, if we do admit it, we must recognize only one centre and one periphery. This difficulty prevents our recognizing more than one Kosmos (ss. 1-6).
It is unphilosophical to affirm that the nature of these simple elements becomes changed according as they are more orless distant from their own places. The difference is at best one of degree, not one of kind. That theyaremoved, we see plainly; there must therefore be some one current of motion natural to them. Accordingly every portion of the same element (or of elements the same in kind) must tend towards the same numerical place — towards this actual centre (πρὸς τόδε τι μέσον), or that actual periphery; and, if the tendency be towards one centrespecie, but towards many centresnumero, because particulars differnumeroalone, and notspecie, still the attribute will be alike in all, and will not be present in some portions, absent in others: I mean that, if the portions of this Kosmos are relative to each other, those in another Kosmos are in the like condition, and what is taken from this Kosmos will not be different from what is taken from the corresponding elements of any other Kosmos. Unless these assumptions can be overthrown, it is indisputably certain that there can be only one centre and one periphery; by consequence therefore, only one Kosmos and not more (ss. 7-10).
There are other reasons to show that there is a given terminus for the natural current both of fire and of earth. A thing moved, speaking generally, changes from something definite into something else definite; but there are different species of such change: the change called getting-well is from sickness to health; that called growth is from the little to great; that called local movement is from a terminus to another terminus, and local movements are specifically different from each other, according as the terminusa quoand the terminusad quemis defined in each. The terminus is always a known and definite point: it is not accidental, nor dependent upon the arbitrium of the mover. Fire and earth therefore do not move on to infinity, but to definite points in opposite directions; and the local antithesis is between above and below: these are the two termini of the respective currents. Earth is carried with greater velocity, the nearer it approaches to the centre; fire is carried with greater velocity, the nearer it approaches to the periphery. This shows that its current does not stretch to infinity; for its velocity would then increase infinitely. Earth is not carried downward by the force of any thing else, nor fire upwards: not by any violence, nor by squeezing out (ἐκθλίψει), as some say. If this were so, a larger quantity of earth would move downward, and a larger quantity of fire upward, more slowly than a smaller. But the reverse is what occurs: the larger quantity of earth moves downward more rapidly than the smaller; if its motion had been caused by violence or by squeezing out, such motion would have slackened as it became more widely distant from the moving force (ss. 11-14).
We may deduce the same conclusion from the reasonings of the First Philosophy, also from the fact of circular motion which of necessity is constant both here and everywhere. Further, it is clear that there can be only one Kosmos; for, as there are three bodily elements, so there are three special places of such elements: one the undermost, at the centre; another the uppermost, at the periphery, revolving in a circular orbit; the third, in the intermediate place between the two, being the light or floating element (τὸ ἐπιπόλαζον); for, if not there, it must be outside of the Kosmos, which is impossible (ss. 15, 16).
CH. 9. — We must however now examine some reasons, which have been alleged to prove the contrary; and which seem to show, not only that there are many Kosmi, but even that theremustbe many, and that the hypothesis of one single Kosmos is inadmissible. It is urged that in all aggregates, natural as well as artificial, the Form by itself is one thing, and the Form implicated with Matter is another. When we declare the definition of a sphere or a circle, we do not include therein gold or brass, for this makes no part of the essence: if we mention these metals, it is when we cannot conceive or grasp anything beyond the particular case; for example, if we have one particular circle before us. Nevertheless, even here the circle in the abstract is one thing, and this particular circle is another: the first is the Form by itself, the last is the Form along with Matter, one among particular objects. Now, since the Heaven is perceivable by sense, it must be one among particular objects; for every thing perceivable is implicated with Matter. As such, it isthisHeaven: to bethisHeaven (Form along with Matter) is one thing; to be the Heaven simply and absolutely (Form without Matter) is another. Now, wherever there is Form, there either are or may be many distinct particulars; whether we admit (with Plato) that the Forms exist separately, or not. In all things where the Essence is implicated with Matter, we see that the particular manifestations are many and of indefinite number. Upon this reasoning therefore, there are or at least may be many Heavens: the supposition that there can be no more than one, is inadmissible (ss. 1-2).
But we must see how far this reasoning will hold. That the Form without Matter differs from the Form with Matter, is perfectly true. But this does not show that there must be many Kosmi; nor can there be many, if this one Kosmos exhausts all the matter that exists. If the matter of man were flesh and bone, and if a single man were formed, including all flesh and all bone indissolubly united; there could not possibly exist any other man; and the like is true about other objects; for, where the essence is implicated with an underlying matter, no object can come into existence unless some matter be furnished. The Kosmos, or Heaven, is a particular object, composed partly out of appropriate matter: but if it absorbs all the appropriate matter, no second Kosmos can come to pass. We shall now show that it does include all the appropriate matter (ss. 3-5).
The word Heaven has three different senses. 1. It means the essence of the extreme periphery of the universe, or the natural body which is there situated: we call this highest and farthest place Heaven, where we suppose all the divine agency to be situated (ἐν ᾧ τὸ θεῖον πᾶν ἱδρῦσθαί φαμεν). 2. It means the body continuous (τὸ συνεχὲς σῶμα) with the extreme periphery of the universe, wherein are contained Sun, Moon, and some of the Stars (Planets); for these we affirm to be in the Heaven. 3. In a third sense, it means the body circumscribed (περιεχόμενον) by this extreme periphery: for we usually call the Whole and the Universe, Heaven. — These being the three senses of Heaven, the Whole circumscribed by the extreme periphery must by necessity consist of all the natural and perceivable body existing, since there neither is nor can be any such outside of the Heaven. For, if there were any such outside of the Heaven, it must be either one of the elements or a compound thereof — either by nature or contrary to nature. For we have shown that each of the three elements — the circular, the centrifugal, and the centripetal — has its own special place by nature; and that, even if the place in which it now is were not its natural place, that place would be the natural place of another one among the three; for, if a place be contrary to nature in reference to one, it must be conformable to nature in reference to another. Neither of these three elements therefore can be outside of the Heaven, nor, of course, any of their compounds. And there exists no other body besides these; nor canthereexist any other (ss. 6, 7).
We see therefore plainly that there neither is nor can be any mass of body (σῶματος ὄγκον) outside of the Heaven; and that the Heaven comprehends all matter — all body natural and perceptible. So that there neither are, nor ever have been, nor ever can be, many Heavens: this one is unique as well as perfect. Nor is there either place, or vacuum, or time, outside of the Heaven. There is no place or vacuum; because, if there were, body might be placed therein; which we have shown to be impossible. There is no time; because time is the number of motion, and there can be no motion without some natural body; but there cannot exist any extra-celestial body. Neither, therefore, are the things outside of the Heaven in place, nor is there time to affect them with old age, nor do they undergo change of any kind. They are without any change of quality and without susceptibility of suffering; they remain, throughout the entire Æon, in possession of the best and most self-sufficing life. The word Æon is a divine expression proposed (θείως ἔφθεγκται) by the ancient philosophers: they call the Æon of each creature that end which circumscribes the natural duration of the creature’s life. Pursuant to this same explanation, the end of the whole Heaven — the end comprising all time and the infinity of all things — is Æon, so denominated ἀπὸ τοῦἀεὶεἶναι, immortal and divine. From this is suspended existence and life for all other things; for some closely and strictly, for others faintly and feebly. For it is a doctrine often repeated to us in ordinary philosophical discourse (ἐν τοῖς ἐγκυκλίοις φιλοσοφήμασι) respecting divine matters — that the Divine, every thing primary and supreme, is by necessity unchangeable; and this confirms what has been just affirmed. For there exists nothing more powerful than itself which can cause it to be moved (if there were,thatwould be more divine); nor has it any mean attribute; nor is it deficient in any of the perfections belonging to its nature. Its unceasing motion too is easily explained. For all things cease to be moved, when they come into their own place; but with the circular or revolving body the place in which it begins and in which it ends is the same (ss. 8-10).
CH. 10. — We shall next discuss whether the Kosmos be generable or ungenerable, and perishable or imperishable; noticing what others have said on the subject before. All of them consider the Kosmos to be generated: but some think it (although generated) to be eternal; others look upon it as perishable, like other natural compounds; others again — Empedokles and Herakleitus — declareit to be generated and destroyed in perpetual alternation. Now to affirm that it is generated and yet that it is eternal, is an impossibility: we cannot reasonably affirm any thing, except what we see to happen with all things or with most things; and, in the case before us, what happens is the very reverse of the foregoing affirmation, for all things generated are seen to be destroyed. Again that which has no beginning of being as it is now — that which cannot possibly have been otherwise previously throughout the whole Æon — can never by any possibility change; for, if it could ever change, there must exist some cause, which, if it had existed before, would have compelled what is assumed to be incapable of being otherwise, to be otherwise. To those who say that the Kosmos has come together from materials previously existing in another condition, we may reply:If these materials were always in this prior condition and incapable of any other, the Kosmos would never have been generated at all; and, if ithasbeen generated, we may be sure that the antecedent materials must have been capable of coming into another condition, and were not under a necessity to remain always in the same condition; so that aggregations once existing were dissolved, and disgregations brought into combination, many times over before the present Kosmos; at least they possibly may have been so: and this is enough to prove that the Kosmos is not indestructible (ss. 1-3).
Among those who maintain the Kosmos to have been generated yet to be indestructible, there are some who defend themselves in the following manner. They tell us that the generation of which they speak is not meant to be affirmed as a real past fact, but is a mere explanatory or illustrative fiction, like the generation of a geometrical figure, introduced to facilitate the understanding by pupils. But such an analogy cannot be admitted. For in geometry the conclusions are just the same, if we suppose all the figures existing simultaneously; but it is not so with the demonstrations which they tender about the generation of the Cosmos, where the antecedent condition and the consequent condition are the reverse of each other. Out of disorder (they tell us) things came into order: these two conditions cannot be simultaneous; generation must be a real fact, and distinction of time comparing the one condition with the other; whereas in geometrical figures no distinction of time is required (ss. 4-6).
To assume alternate generation and dissolution, over and over again, is in fact to represent the Kosmos as eternal, but as changing its form; as if you should suppose the same person to pass from boyhood to manhood and then back again from manhood to boyhood — calling that by the name of generation and destruction. For, if the elements come together, the aggregation resulting will not be accidental and variable but always the same, especially upon the assumptions of these philosophers. So that, if the whole Kosmos, remaining continuous, is sometimes arranged in one way, sometimes in another, it is these arrangements which are generated and destroyed, not the Kosmos itself (ss. 7, 8).
Total generation, and total destruction without any renovation, of Kosmos might be possible, if there were an infinity of Kosmi, but cannot be possible with only one; for anterior to the moment of generation there existed the antecedent condition, which, never having been generated, could not be destroyed (s. 9).
There are some who think (with Plato in Timæus) that the non-generable may yet be destroyed, and that the generated may be indestructible. We have combated this opinion on physical grounds, respecting the Heaven specially. We shall now treat the subject upon universal reasonings (i.e., belonging to Logic or Metaphysics — πρὸς οὓς φυσικῶς μὲν περὶ τοῦ οὐράνου μόνον εἴρηται· καθόλου δὲ περὶ ἅπαντος σκεψαμένοις, ἔσται καὶ περὶ τούτου δῆλον — s. 10).
CH. 11. — In this reasoning, the first step is to point out that Generable and Non-Generable, Destructible or Indestructible, are words used in many different senses, which must be discriminated (πολλαχῶς λεγόμενα). If a man uses these words in an affirmative proposition without such discrimination, his affirmation is indeterminate; you cannot tell in which of their many different senses he intends to affirm. Non-Generable means: (1) That which now is, having previously not been, even though without either generation or change, as, to touch or to be moved; for, according to some persons, touching or being moved are not cases of generation; you cannot become touching, or become moved; you are moved, or you are not moved; you touch, or you do not touch (οὐ γὰρ εἶναι γίνεσθαί φασιν ἁπτόμενον, οὐδὲ κινούμενον. He means, I presume, that to touch, and to be moved, are instantaneous acts, though how they can be said to occur ἄνευ μεταβολῆς, I do not see.). It means: (2) That which, though capable of coming to pass or of having come to pass (ἐνδεχόμενον γίνεσθαι ἢ γενέσθαι), nevertheless is not; for this too is non-generable, since it might have come to be. Again, it means: (3) That whichcannot by possibility sometimes exist, sometimes not exist. Impossible has two meanings: (1) That of which you cannot truly say that it might be generated (ὅτι γένοιτ’ ἄν); (2) That which cannot be generated easily, or quickly, or well (καλῶς). So also the Generable (τὸ γεννητόν) means: (1) That which, not existing previously, afterwards exists at one time and not at another, whether generated or not (he seems here to point to τὸ ἅπτεσθαι or τὸ κινεῖσθαι); (2) The possible, whether it be the strictly possible, or the easily possible; (3) That of which there is generation out of the nonexistent into existence, whether it now does actually exist, or may exist hereafter. The Destructible and Indestructible (φθαρτὸν καὶ ἄφθαρτον) have similar differences of meaning (ss. 1-6).
If we say that a man can raise a weight of 100 pounds, or march 100 stadia, we speak always with reference to a certain extreme, meaning to imply that he can also raise a weight of 50, 40, 30 pounds, and that he can also walk 50, 40, 30 stadia. If we say that he cannot raise a weight of 100 pounds, we mean to imply,Ã fortiori, that he cannot raise a weight of 110 pounds. In regard to sight and hearing, the case is opposite; he who can see a small object, can certainly see a large one; he who can hear a faint sound, can certainly hear a loud one. But he who can see a large object, is not necessarily able to see a small one; he who can hear a loud sound, is not necessarily able to hear a faint one. In sight and hearing, superior power is indicated by the less including the greater; in motion, by the greater including the less (ss. 7-8).
CH. 12. — If there are some things capable both of existence and of nonexistence, we must define on which falls the major portion of time; for, if we cannot in either case define the time, and can only say that it is greater than any assumed length of time and never less than any assumed length, — the same thing will be capable both of existence and of non-existence for an infinite time; which is an impossibility. We must take our departure from this principle: Impossibility is one thing, Falsehood another. Both the impossible and the false are, however, either conditional (as when it is said to be impossible that the triangle should have its three angles equal to two right angles, if such and such things are granted, and that the diameter should be commensurate with the periphery, if such and such positions were true), or absolute. But there are matters absolutely false, which are not absolutely impossible. When you are standing, I affirm that you are sitting: this is absolutely false, but not absolutely impossible. On the other hand, if I affirm that you are at the same time sitting and standing, or that the diameter is commensurable with the periphery, the proposition is not merely absolutely false, but absolutely impossible. An assumption simply false is not the same thing as an assumption absolutely impossible: from an impossible assumption there follow other impossibilities. The power of sitting or standing means that you can do either one at any given time — one at one time, the other at another; but not that you can do both at the same time. But, if any thing has throughout an infinite time the power of doing more things than one, it must have the power of doing more things than one at the same time; for this infinite time comprehends its whole existence. Accordingly, if any thing existing for an infinite time is nevertheless destructible, this means that it has the possibility not to exist. This being a possibility, let us imagine it realized: then the thing in question will both exist actually for an infinite time and yet not exist; which is a consequence not only false, but impossible, and thus proves the premiss assumed to be impossible (i.e., that a thing existing for an infinite time is nevertheless destructible). We thus see that what exists always is absolutely indestructible (ss. 1-3). It is also ungenerable; for, if generable, there will be a possibility that at some time or other it did not exist. That is generable, which may possibly have not existed at some anterior time, finite or infinite: so that, if τὸ ἀεὶ ὄν cannot possibly not exist, it cannot be generable. Now that which is always possible to exist, has, for its correlate negative (ἀπόφασις), that which is not always possible to exist; and that which is always possible not to exist, has, for its contrary, that which is not always possible not to exist. These two negatives must of necessity be true of the same subject: there must be something of which we may truly say — It has no possibility always to exist — It has no possibility always not to exist. This therefore is something intermediate between that which always exists, and that which always exists not, viz., That which may exist and may not exist (καὶ εἶναι μέσον τοῦ ἀεὶ ὄντος καὶ τοῦ ἀεὶ μὴ ὄντος, τὸ δυνάμενον εἶναι καὶ μὴ εἶναι); for both the negative predicates will find application, if it do not exist always. The possible to exist, and the possible not to exist, must therefore be the same thing — a mean between the two above-mentioned extremes (ss. 4, 5).
After a long metaphysical deduction, occupying from sections 6 to 17, Aristotle proceeds as follows.
We may also discern in the following manner that nothing which has been once generated, can continue indestructible; nothing which is ungenerable and which always existed heretofore, can ever be destroyed. For it is impossible that any thing which arises spontaneously (ἀπὸ τοῦ αὐτομάτου) can be either indestructible or ungenerable. The Spontaneous, and the Casual (τὸ ἀπὸ τῆς τύχης), are in antithesis to the always or the most frequently Ens or Fiens (παρὰ τὸ ἀεὶ καὶ τὸ ὡς ἐπὶ τὸ πολὺ ἢ ὂν ἢ γινόμενον — s. 18); but that which has existed for an infinite or a very long tine, must belong to this last category. Accordingly, such things must by nature sometimes exist, sometimes not exist. In them, both sides of the contradiction are alike true, owing to the matter of which they are composed: they exist, and they do not exist. But you cannot say with truth now that the thing exists last year; nor could you say last year that it exists now. Having once been non-existent, it cannot be eternal for future time; for it will still possess in future time the possibility of non-existence, yet not the power of non-existing at the moment when it does exist, nor with reference to last year and to past time; there being no power bearing upon past time, but only on present and future time. (Sections 21 and 22 are hardly intelligible to me.)
On physical grounds also it appears impossible that what is eternal in the past should be destroyed afterwards, or that what did not exist at some former time should afterwards be eternal. Those things which are destructible, are all of them generable and changeable (γεννητὰ καὶ ἀλλοιωτὰ πάντα). Those things which exist by nature, are changed by their opposites and by their component materials, and are destroyed by the same agencies (s. 23).
CH. 1. — The Heaven has not been generated nor can it be destroyed, as some (Plato) affirm: it is one and eternal, having neither beginning nor end of the whole Æon, holding and comprehending in itself infinite time. This we may believe not merely from the foregoing reasonings, but also from the opinion of opponents who suppose the Cosmos to be generated. For, since their opinion has been shown to be inadmissible, and our doctrine is at least admissible, even thus much will have great force to determine our faith in the immortality and eternity of the Heaven. Hence we shall do well to assist in persuading ourselves that the ancient doctrines, and especially those of our own country, are true — That there is among the substances endowed with motion one immortal and divine, whose motion is such that it has itself no limit but is rather itself the limit of all other motions, limit being the attribute of the circumscribing substance. The circular motion of the Heaven, being itself perfect, circumscribes and comprehends all the imperfect motions which are subject to limit and cessation. It has itself neither beginning nor end, but is unceasing throughout infinite time: in regard to other motions, it is the initiatory cause to some, while it is the recipient of the cessation of others (ss. 1, 2).
The ancients assigned Heaven to the Gods, as the only place which was immortal, and our reasonings show that it is not merely indestructible and ungenerable, but also unsusceptible of all mortal defect or discomfort. Moreover it feels no fatigue, because it is not constrained by any extraneous force to revolve contrary to its own nature: if it were so, that would be tiresome, and all the more since the motion is eternal; it would be inconsistent with any supremely good condition. The ancients therefore were mistaken in saying that the Heaven required to be supported by a person named Atlas: the authors of this fable proceeded upon the same supposition as recent philosophers; regarding the celestial body as heavy and earthy, they placed under it, in mythical guise, an animated necessity (ἀνάγκην ἔμψυχον), or constraint arising from vital force. But they are wrong; and so is Empedokles, when he says that the Heaven is kept permanently in its place by extreme velocity of rotation, which counteracts its natural inclination downwards (οἰκείας ῥοπῆς). Nor can we reasonably suppose that it is kept eternally in its place (i.e., contrary to its own nature) by the compulsion of a soul or vital force (ὑπὸ ψυχῆς ἀναγκαζούσης): it is impossible that the life of a soul thus acting can be painless or happy. The motion which it causes, being accompanied with violence and being also perpetual (as it is the nature of the First Body to cause motion continuously throughout the Kosmos), must be a tiresome duty, unrelieved by any reasonable relaxation; since this soul enjoys no repose, such as the letting down of the body during sleep affords to the soul of mortal animals, but issubjected to a fate like Ixion’s — ceaseless and unyielding revolution. Now our reasonings, if admissible, respecting the First or Circular Motion (πρώτης φορᾶς) afford not merely more harmonious conceptions respecting its eternity, but also the only way of speaking in language which will be allowed as consistent with the vague impressions respecting the Deity (τῇ μαντείᾳ τῇ περὶ τὸν θεόν). Enough, however, of this talk for the present (ss. 3-6).
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 differentrevolutions 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 generationmustcome 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).
Now, since the first figure belongs to the first body, which is that in the extreme or farthest circumference, this body which revolves constantly in a circle, will be spherical in figure. That which is continuous with it even to the centre, will also be spherical; and all the interior parts are in contact and continuity with it: the parts below the sphere of the planets touch the sphere above them. So that the whole revolving current, interior and exterior, will be spherical; for all things touch and are continuous with the spheres (s. 5).
There is another reason too why the universe is spherical in figure, since it has been shown to revolve in a circle. I have proved before that there exists nothing on the outside of the universe; neither place nor vacuum. If the figure of the Kosmos, revolving as it does in a circle, were any thing else but spherical — if it were either rectilinear or elliptical — it could not possibly cover exactly the same space during all its revolutions: there must therefore be place and vacuum without it; which has been shown to be impossible (s. 6).
Farthermore, the rotation of the Heaven is the measure of motions, because it is the only one continuous and uniform and eternal. Now in every department the measure is the least, and the least motion is the quickest; accordingly the rotation of the Heaven will be the quickest of all motions (s. 7). But among all curved lines from the same back to the same, the circumference of the circle is the shortest, and motion will be quickest over the shortest distance. Accordingly, since the Heaven revolves in a circle and with the quickest of all motions, its figure must be spherical (s. 8).
We may also draw the same conclusion from the bodies fixed in the central parts of the Kosmos. The Earth in the centre is surrounded by water; the water, by air; the air, by fire. The uppermost bodies surround the fire, following the like proportion or analogy; being not continuous therewith, but in contact therewith. Now the surface of water is spherical; and that which is either continuous with the spherical or surrounds the spherical, must itself be spherical also (s. 9). That the surface of the water is truly spherical, we may infer from the fact, that it is the nature of water always to flow together into the lowest cavities, that is, into the parts nearest to the centre (s. 10).
From all the foregoing reasonings, we see plainly that the Kosmos is spherical, and moreover turned with such a degree of exact sphericity (κατὰ ἀκρίβειαν ἔντορνος οὕτως), that no piece of human workmanship nor any thing ever seen by us on earth can be compared to it. For none of the component materials here on earth is so fit for receiving perfect level and accuracy as the nature of the First or Peripheral Body; it being clear that, in the same proportion as water is more exactly spherical, the elements surrounding the water become more and more spherical in proportion as they are more and more distant from the centre (s. 11).
CH. 5. — Circular revolution may take place in two directions; from the point A on one side towards B, or on the other side towards C. That these two are not contrary to each other, I have already shown. But, since in eternal substances nothing can possibly take place by chance or spontaneity, and since both the Heaven and its circular revolution are eternal, we may enquire what is the reason why this revolution takes place in one direction and not in the other. This circumstance either depends upon some first principle, or is itself a first principle (s. 1). Perhaps some may consider it a mark either of great silliness, or great presumption, to declare any positive opinion at all upon some matters, or upon all matters whatever, leaving out nothing. But we must not censure indiscriminately all who do this: we must consider what is the motive which prompts each person to declare himself, and with what amount of confidence he affirms, whether allowing for human fallibility or setting himself above it. Whenever a man can find out exact and necessary grounds for the conclusions which he propounds, we ought to be grateful to him: here we must deliver what appears to be the truth. Nature (we know) always does what is best among all the practicable courses. Now the upper place is more divine than the lower, and accordingly among rectilinear currents, that which is directed upwards is the more honourable. In the same manner, the current forwards is more honourable than backwards; and the current towards the right more honourable than that towards the left — as was before laid down. The problem above started indicates to us that there is here a real Prius and Posterius — a better and a worse; for, when we recognize this, the difficulty is solved. The solution is that this is the best practicable arrangement, viz., that the Kosmos is moved in a motion, simple, never-ending, and in the most honourable direction (ἐπὶ τὸ τιμιώτερον, s. 2).
CH. 6. — I have now to show that this motion of the First Heaven is uniform and not irregular (ὁμαλὴς καὶ οὐκ ἀνώμαλος): I speak only of the First Heavenand of the First Rotation; for in the substances lower than this many rotations or currents have coalesced into one. If the motion of the First Heaven be irregular, there will clearly be acceleration and remission of its motion, and an extreme point or maximum (ἀκμή) thereof. Now the maximum of motion must take place either at the terminusad quem, as in things moved according to nature; or at the terminusa quo, as in things moved contrary to nature; or during the interval between, as in things thrown (ἐν τοῖς ῥιπτουμένοις). But in circular motion, there is neither terminusa quo, nor terminusad quem, nor middle between the two — neither beginning, nor end, nor mean; for it is eternal in duration, compact as to length or space moved over, and unbroken (τῷ μήκει συνηγμένη καὶ ἄκλαστος). It thus cannot have any maximum or acceleration or remission; and of course, therefore, it cannot be irregular (s. 1).
Besides, since every thing that is moved is moved by some thing, the irregularity, if there be such, must arise either from the Movens, or the Motum, or both: the power of the Movens, or the quality of the Motum, or both, must undergo change. But nothing of the sort can happen with the Motum, being in this case the Heaven; for it has been shown to be a First, simple, ungenerable, indestructible, and in every way unchangeable. Much more then is it reasonable to believe that the Movens is such; for that which is qualified to move the First, must be itself a First (τὸ γὰρ πρῶτον τοῦ πρώτου κινητικόν); that which is qualified to move the simple, must be itself simple, &c. If then the Motum, which is a body, undergoes no change, neither will the Movens, being as it is incorporeal (s. 2). Accordingly the current, or motion (φορά), cannot possibly be irregular. For, if it comes to pass irregularly, its irregularity either pervades the whole, the velocity becoming alternately more or less, or certain parts only. But, in regard to the parts separately, there is certainly no irregularity: if there had been, the relative distances of the stars one from the other would have varied in the course of infinite time; now no such variation in their distances has ever been observed. Neither in regard to the whole is there any irregularity. For irregularity implies relaxation, and relaxation arises in every subject from impotence. Now impotence is contrary to nature: in animals, all impotences (such as old age or decay) are contrary to nature; for all animals, perhaps, are compounds put together out of elements each of which has a different place of its own and not one of which is in its own place. In the First Bodies, on the other hand, which are simple, unmixed, in their own places, and without any contrary, there can be no impotence, and therefore neither relaxation nor intensification, which always go together (εἰ γὰρ ἐπίτασις, καὶ ἄνεσις, s. 3). Besides, we cannot with any reason suppose that the Movens is impotent for an infinite time, and then again potent for an infinite time; nothing contrary to nature lasts for an infinite time, and impotence is contrary to nature; nor can it be for an equal time contrary to nature and agreeable to nature — impotent and potent. If the motion relaxes, it cannot go on relaxing for an infinite time, nor go on being intensified, nor the one and the other alternately. For in that case the motion would be infinite and indeterminate; which is impossible, since every motion must be from one term to another term and also determinate (s. 4: ἄπειρος γὰρ ἂν εἴη καὶ ἀόριστος ἡ κίνησις. ἅπασαν δέ φαμεν ἔκ τινος εἴς τι εἶναι, καὶ ὡρισμένην —i.e., all motion must be determined both in distance and direction).
Again, the supposition may be made that there is a minimum of time required for the revolution of the Heaven, in less than which the revolution could not be completed; just as there is a minimum of time indispensable for a man to walk or play the harp. Admitting this supposition, there cannot be perpetual increase in the intensity or velocity of the motion (the increase has an impassable limit), and therefore there cannot be perpetual relaxation; for both are on the same footing (s. 5).
It might be urged, indeed, that intensification and relaxation go on alternately; each proceeding to a certain length, and then giving place to the other. But this is altogether irrational — nothing better than a gratuitous fiction. Besides, if there were this alternation, we may reasonably assume that it could not remain concealed from us; for contrasting conditions coming in immediate sequence to each other are more easily discerned by sense. What has been said, then, is sufficient to prove — That the Heaven or Cosmos is one and only one; that it is ungenerable and eternal; that its motion is uniform (s. 6).
CH. 7. — Next in order, I have to speak of what are called the Stars (τῶν καλουμένων ἄστρων). Of what are they composed? What is their figure? What are their motions?
It is consistent with the foregoing reasonings, as well as in itself the most rational doctrine, to conceive each of the stars as composed of portions of that body in which its current of motion takesplace; that is, of that body, whose nature it is to move in a circle. For those who affirm the stars to be fire say this because they believe the upper body to be fire, assuming it as reasonable that each thing should be composed of the elements in which it is; and I assume the same also (s. 1). The heat and light of the stars arises from their friction with the air in their current of motion. If it is the nature of motion to inflame pieces of wood, and stones, and iron, it is still more reasonable that what is nearest to fire (that is, air) should be so inflamed. We see that darts projected are so inflamed, that their leaden appendages are melted; and, these being thus inflamed, the air around them must be modified in the same manner. Now objects like these darts are thus violently heated, because they are carried along in the medium of the air, which through the shock given by their motion becomes fire. But each of the upper bodies or stars is carried round (not in the air, but) in its appropriate sphere, so that they themselves are not inflamed; while the air which is under the sphere of the encyclical body becomes of necessity heated by the rotation of that sphere; and most of all at the point where the Sun has happened to be fastened in (καὶ ταύτῃ μάλιστα, ᾗ ὁ ἥλιος τετύχηκεν ἐνδεδεμένος).
Let it then be understood, that the stars are neither composed of fire, nor are they carried round in the medium of the fire (s. 2).
CH. 8. — It is seen as a fact, that both the stars, and the entire Heaven, change their place (μεθιστάμενα). Now, in this change, we must assume either that both continue at rest, or that both are in motion, or that one is at rest, and the other is in motion. Now it is impossible that both can be at rest, at least if we assume the earth to be at rest; for the facts which we see would not have taken place, upon that supposition (s. 1). Either therefore both are in motion, or one is in motion and the other at rest. Now, if both are in motion, it is against reason that the stars and the circles in which they are fastened should have equal velocities of motion. Each one of them must, be equal in velocity to the circle or sphere in which it is carried, since all come back round along with their circles to the same position; so that in one and the same time, the star has gone round its circle, and the circle has completed its revolution. It is not reasonable to suppose that the velocities of the stars and the magnitudes of the circles should be in the same proportion. Comparing one circle with another, indeed, it is not only not absurd, but even necessary, that the velocities should be in proportion to the magnitudes; but it is not reasonable that each of the stars in these circles should be of such velocity. For, if it be necessary that what is carried round in the larger circle should have the greater velocity, the consequence would be that, if the stars in one circle were transferred to another, their motions would become accelerated or retarded; which is equivalent to saying that they have no motion of their own at all, but are carried round by the revolution of the circles (s. 2). If, on the contrary, it be not necessary, but a spontaneous coincidence (εἴτε ἀπὸ ταὐτομάτου συνέπεσεν) that what is carried round in the greater circle has the greater velocity, neither upon this supposition is it reasonable that in all the circles without exception the circumference should be greater, and the motion of the star fastened in the greater circle quicker, in the same proportion. That this should happen with one or two of them, might be reasonably expected; but that it should happen with all alike, savours of fiction. Moreover chance has no place in matters according to nature; nor is that which occurs everywhere and belongs to all, ever the produce of chance (s. 3).