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 (??????? ??????), 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 (???e?a? ??p??). 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 (?p? ????? ??a??a???s??): 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 is subjected to a fate like Ixion’s — ceaseless and unyielding revolution. Now our reasonings, if admissible, respecting the First or Circular Motion (p??t?? f????) 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 (t? a?te?? t? pe?? t?? ?e??). 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 ???a? can properly be ascribed to the body of the Universe; for, if these can be ascribed, much more may the other ???a? prior to them be ascribed to it. Of ???a? ????se?? (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 ???a? or d?ast?se?? 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 (? ?at? t?? a?s??s??), or the line in which sensible impressions are propagated (?f’ ? a?s??se??). Up is the source from whence motion originates (t? ??e? ? ????s?? — s. 6); Right, the point from which the direction of the motion starts; Forward, the point towards which it goes (t? ?f’ ?). 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 ???? ????se??, 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 (??????). 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 (?p? t? d???a pe??f??eta?), 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 (p??? t??? de?????); 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 (t?? de?t??a? pe??f????) 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 (p?????e?) — 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).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 (?at? ????e?a? ??t????? ??t??), 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 (?p? t? t???te???, s. 2).

CH. 6. — I have now to show that this motion of the First Heaven is uniform and not irregular (?a??? ?a? ??? ???a???): I speak only of the First Heaven and 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 (???) thereof. Now the maximum of motion must take place either at the terminus ad quem, as in things moved according to nature; or at the terminus a quo, as in things moved contrary to nature; or during the interval between, as in things thrown (?? t??? ??pt???????). But in circular motion, there is neither terminus a quo, nor terminus ad 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 (t? ??e? s??????? ?a? ???ast??). 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 (t? ??? p??t?? t?? p??t?? ????t????); 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 (f???), 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 (e? ??? ?p?tas??, ?a? ??es??, 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: ?pe???? ??? ?? e?? ?a? ????st?? ? ????s??. ?pasa? d? fae? ?? t???? e?? t? e??a?, ?a? ???s???? — 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 (t?? ?a??????? ?st???). 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 takes place; 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 (?a? ta?t? ???sta, ? ? ????? tet????e? ??dede????).

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 (e??st?e?a). 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 (e?te ?p? ta?t??t?? s???pese?) 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).

So much for the hypothesis, that both stars and circles are in motion. Let us now assume that one is at rest, and the other in motion; and first, let the circles be at rest, and the stars in motion. This again will lead to absurdities; for we shall still be unable to explain how it happens that the outermost stars are moved most quickly, and that their velocities are proportioned to the magnitudes of the circles.

Since then we cannot assume either that both are moved, or that the star alone is moved, we must adopt the third supposition, that the circles are moved, and that the stars, being themselves at rest, are fastened in the circles and carried round along with them. This is the only hypothesis which entails no unreasonable consequences. For it is reasonable that, of circles fastened round the same centre, the greater velocity should belong to the greatest. For, as in all the varieties of body the heavier fragment is carried with greater velocity than the lighter in its appropriate motion, so it happens with the encyclical body. When two straight lines are drawn from the centre, the segment of the greater circle intercepted between them will be greater than the segment of the smaller; and it is consistent with reason that the greater circle should be carried round in equal time. This is one reason why the Kosmos is not split into separate parts; another reason is, because the universe has been shown to be continuous (s. 4, 5).

Now we all agree that the stars are of spherical figure: and spherical bodies have two motions of their own — rolling and rotatory (????s?? ?a? d???s??). If they were moved of themselves, they would be moved in one or other of these two ways; but we see that they are so in neither. They do not rotate; for, if they did, they would remain always in the same place, which contradicts universal observation and belief. Besides, it is reasonable to suppose that all the stars move in the same manner, but the Sun is the only one that is seen so to move, when he rises or sets; and he too, not by any movement of his own, but through the distance of our vision, which when stretched to a great distance, rotates from weakness (s. 6). This is perhaps the reason why the stars fastened (in the outer sphere) twinkle, while the planets do not twinkle; for the planets are near to us, so that our vision reaches them while yet strong; whereas in regard to the unmoved stars it is made to quiver in consequence of the great distance from being stretched out too far, and its quivering causes the appearance of motion in the star. For there is no difference between moving the vision and moving the object seen (????? ??? d?af??e? ???e?? t?? ???? ? t? ???e??? — s. 6).

Again, neither do the stars roll nor revolve forward. For that which rolls forward must necessarily turn round; but the same side of the moon — what is called the face of the moon — is always clearly visible to us (s. 7).

Since it is reasonable to believe, therefore, that, if the stars were moved in themselves, they would be moved in their own special variety of motion (i.e., rolling or rotatory), and since it has been shown that they are not moved in either of these two ways, we see plainly that they cannot be moved in themselves (but are carried round in the revolution of the AplanÊs).

Besides, if they were moved in themselves, it is unreasonable that Nature should have assigned to them no organ suitable for motion, since Nature does nothing by haphazard; and that she should have been considerate in providing for animals, while she overlooked objects so honourable as the stars. The truth rather is, that she has withheld from them, as it were by express purpose, all aids, through which it was possible for them to advance forward in themselves, and has placed them at the greatest possible distance from objects furnished with organs for motion (s. 8).

Hence it would seem to be the reasonable doctrine — That the entire Heaven is spherical, and that each of the stars (fastened in it) is also spherical. For the sphere is the most convenient of all figures for motion in the same place, so that the Heaven being spherical would be moved most rapidly and would best maintain its own place. But for forward motion the sphere is of all figures the most inconvenient; for it least resembles self-moving bodies; it has no outlying appendage or projecting end, as rectilinear figures have, and stands farthest removed from the figures of marching bodies.

Since therefore it is the function of (de?) the Heaven to be moved by a motion in the same place (???e?s?a? t?? ?? a?t? ????s??), and that of the stars not to make any advance by themselves (t? ???a d’ ?st?a ? p?????a? d?’ a?t??), it is with good reason that both of them are spherical. For thus will the Heaven best be moved, and the stars will best be at rest.

CH. 9. — From what I have said, it is plain that those who affirm that the revolving celestial bodies emit in their revolutions sounds harmonious to each other, speak cleverly and ingeniously, but not consistently with the truth. There must necessarily be sound (they say) from the revolution of such vast bodies. Since bodies near to us make sound in motion, the sun, moon, and stars, being so much larger and moving with so much greater velocity, must make an immense sound; and, since their distances and velocities are assumed to be in harmonic proportion, the sounds emitted in their revolution must also be in harmony. To the question put to them — Why do we not hear this immense sound? they reply, that we have been hearing it constantly from the moment of our birth; that we have no experience of an opposite state, or state of silence, with which to contrast it, and that sound and silence are discriminated only by relation to each other (?ste ? d??d???? e??a? p??? t?? ??a?t?a? s????· p??? ?????a ??? f???? ?a? s???? e??a? t?? d?????s??); that men thus cease to be affected by it, just as blacksmiths from constant habit cease to be affected by the noise of their own work (s. 1).

The reasoning of these philosophers (the Pythagoreans), as I have just said, is graceful and poetical, yet nevertheless inadmissible. For they ought to explain, upon their hypothesis, not merely why we hear nothing, but why we experience no uncomfortable impressions apart from hearing. For prodigious sounds pierce through and destroy the continuity even of inanimate bodies; thus thunder splits up stones and other bodies of the greatest strength. The impression produced here by the sound of the celestial bodies must be violent beyond all endurance. But there is good reason why we neither hear nor suffer any thing from them; viz., that they make no sound. The cause thereof is one which attests the truth of my doctrine laid down above — That the stars are not moved of themselves, but carried round by and in the circle to which they are fastened. Bodies thus carried round, make no sound or shock: it is only bodies carried round of themselves that make sound and shock. Bodies which are fastened in, or form parts of, a revolving body, cannot possibly sound, any more than the parts of a ship moving, nor indeed could the whole ship sound, if carried along in a running river. Yet the Pythagoreans might urge just the same reasons to prove that bodies so large as the mast, the stern, and the entire ship, could not be moved without noise. Whatever is carried round, indeed, in a medium not itself carried round, really makes sound; but it cannot do so, if the medium itself be carried round continuously. We must therefore in this case maintain that, if the vast bodies of the stars were carried round in a medium either of air or of fire (whose motion is rectilinear), as all men say that they are, they must necessarily make a prodigious sound, which would reach here to us and would wear us out (d?a??a?e??). Since nothing of this nature occurs, we may be sure that the stars are not carried round in a current of their own, either animated or violent. It is as if Nature had foreseen the consequence, that, unless the celestial motions were carried on in the manner in which they are carried on, nothing of what now takes place near us (t?? pe?? t?? de??? t?p??), could have been as it is now. I have thus shown that the stars are spherical, and that they are not moved by a motion of their own (ss. 2-5).

CH. 10. — Respecting the arrangement of the stars — how each of them is placed, some anterior others posterior, and what are their distances from each other — the books on astronomy must be consulted and will explain. It consists with the principles there laid down, that the motions of the stars (planets) should be proportional to their distances, some quicker, others slower. For, since the farthest circle of the Heaven has a revolution both simple and of extreme velocity, while the revolutions of the other stars (planets) are many in number and slower, each of them being carried round in its own circle in the direction contrary to that of the first or farthest circle of the Heaven, the reasonable consequence is, that that planet which is nearest to the first and simple revolving circle takes the longest time to complete its own (counter-revolving) circle, while that which is most distant from the same circle takes the shortest time, and the remaining planets take more or less time in proportion as they are nearer or farther. For the planet nearest to the first revolving circle has its own counterrevolution most completely conquered or overpowered thereby; the planet farthest from the same, has its own counterrevolution least conquered thereby; and the intermediate planets more or less in inverse proportion to their distances from the same, as mathematicians demonstrate.

CH. 11. — We may most reasonably assume the figure of the stars to be spherical. For, since we have shown that it is not their nature to have any motion of their own, and since Nature does nothing either irrational or in vain, it is plain that she has assigned to the immovables that figure which is least fit for motion; which figure is the sphere, as having no organ for motion. Besides, what is true of one is true of all (?t? d’ ????? ?? ?pa?ta ?a? ??): now the Moon may be shown to be spherical, first, by the visible manifestations which she affords in her waxings and wanings, next, from astronomical observations of the eclipses of the Sun. Since therefore one among the stars is shown to be spherical, we may presume that the rest will be so likewise.

CH. 12. — I proceed to two other difficulties, which are well calculated to perplex every one. We must try to state what looks most like truth, considering such forwardness not to be of the nature of audacity, but rather to deserve respect, when any one, stimulated by the thirst for philosophy, contents himself with small helps and faint approximations to truth, having to deal with the gravest difficulties.

1. Why is it, that the circles farthest from the outermost circle (or AplanÊs) are not always moved by a greater number of motions than those nearer to it? Why are some of the intermediate circles (neither farthest nor nearest) moved by a greater number of motions than any of the others? For it would seem reasonable, when the First Body is moved by one single rotatory current, that the one nearest to it should be moved by two, the next nearest by three, and so on in regular sequence to those which are more distant. But we find that the reverse occurs in fact: Sun and Moon have fewer movements than some of the planets, which are nevertheless farther from the centre, and nearer to the First Body. In regard to some of the planets, we know this by visual evidence; for we have seen the Moon when at half-moon passing under Mars, who was occulted by the dark part of her body, and emerged on the bright side of it. The like is attested respecting the other planets, by the Egyptians and Babylonians, the most ancient of all observers.

2. Why is it, that in the First Revolution (in the revolution of the First Heaven or First Body) there is included so vast a multitude of stars as to seem innumerable; while in each of the others there is one alone and apart, never two or more fastened in the same current?

Here are two grave difficulties, which it is well to investigate and try to understand, though our means of information are very scanty, and though we stand at so great a distance from the facts. Still, as far as we can make out from such data, these difficulties would not seem to involve any philosophical impossibility or incongruity. Now we are in the habit of considering these celestial bodies as bodies only; and as monads which have indeed regular arrangement, but are totally destitute of soul or vital principle. (When Aristotle here says we, he must mean the philosophers whose point of view he is discussing: for the general public certainly did not regard the Sun, Moon, and stars as ????a p?pa?, but, on the contrary, considered this as blameable heresy, and looked upon them as Gods.) We ought, however, to conceive them as partaking of life and action (de? d’ ?? ete???t?? ?p??a??e?? p???e?? ?a? ????); and in this point of view the actual state of the case will appear nowise unreasonable (s. 2). For we should naturally expect that to that which is in the best possible condition, such well-being will belong without any agency at all; to that which is next best, through agency single and slight; to such as are farther removed in excellence of condition, through action more multiplied and diversified. Just so in regard to the human body: the best constituted body maintains its good condition without any training at all; there are others which will do the same at the cost of nothing more than a little walking; there are inferior bodies which require, for the same result, wrestling, running, and other motions; while there are even others which cannot by any amount of labour attain a good condition, but are obliged to be satisfied with something short of it (s. 3). Moreover it is difficult to succeed in many things, or to succeed often: you may throw one or two sixes with the dice, but you cannot throw ten thousand; and, farther, when the conditions of the problem become complicated — when one thing is to be done for the sake of another, that other for a third result, and that third for a fourth, &c. — success, which may be tolerably easy when the steps are only few, the more they are multiplied, becomes harder and harder.

Hence we must consider the agency of the stars as analogous to that of plants and animals. For here the agency of man is most multifarious, since he is capable of attaining many varieties of good, and accordingly busies himself about many things and about one thing for the sake of others. The agency of other animals on the other hand is more restricted; that of plants yet more so, being of slight force and only of one special character (s. 4). But that which exists in the best possible condition stands in no need of acting or agency; for it already possesses that for the sake of which action is undertaken. Now action always includes two elements — that for the sake of which and what is for the sake thereof — the end and the means: there is either some one end, which the agent may attain, as in the case of man; or there are many different matters all of which may be used as means towards the best possible condition. Thus one agent possesses and partakes of the best possible condition; another comes near to it with little trouble; a third, with much trouble; a fourth does not even aspire to the end, but is competent only to arrive near to the last of the means. For example, let health be the end: one man is always in health; a second becomes so, by being starved down; a third by that, combined with running exercise; a fourth is obliged to take some additional exercise, in order to qualify himself for running, so that his motions are multiplied; a fifth is incapable of arriving at health, but arrives only at the running and the being thinned down, one of which in this case serves as end. For it would be best for all, if they could attain the supreme end — health; but, if that be impossible, then the next best thing is to get as near to the best as possible (ss. 5-7).

For this reason the Earth is not moved at all, and the matters near the Earth are moved with few motions; since they do not arrive at the extreme best, but only as near as their ability permits to obtain or hit the supremely divine principle; while the First Heaven, on the contrary, obtains or hits it at once, through one single motion; and the bodies intermediate between the First Heaven and those which are last (or nearest to the Earth), obtain it or arrive at it also, but only through a greater number of motions.

There is the other difficulty also to be considered — that vast multitude of stars are put all together in the one single First Current or Revolution, but each of the other stars (planets) has its own motions singly and apart. The principal reason of this we may fairly suppose to be that it follows as a natural consequence from the vast superiority of the first, in each variety of life and in each beginning, over all posterior to the first. Here the First Current or Revolution, being one and by itself, moves many of the divine bodies, while the others (secondary or countercurrents), numerous as they are, move each only one; for each one of these wandering bodies or planets is carried by many different currents. Thus Nature establishes equalization and a sort of symmetry, by assigning, in the one case, many bodies to one current, and in the other, many currents to one body (ss. 8-10). Beside this principal reason, there is also another. The other currents have each one body only, because motion is given to many bodies by all of them prior to the last which bears the one star. For the last sphere is carried round fastened into many spheres, and each sphere is a body (ss. 11, 12. I do not clearly understand the lines that follow:— ??e???? ?? ??? ?????? e?? t? ?????· a?t? ?? ??? ???st? ? ?d??? f?se? f???· a?t? d? ???? p??s?e?ta?. pa?t?? d? pepe?as???? s?at?? p??? pepe?as???? ? d??a?? ?st??.).1

1 [See Prantl’s note on this difficult passage in his German translation of the De Coelo, p. 309 (Leipzig, 1857).]