Aristotle · a new plain-English translation from the original language
1| So if we posit what is possible, it will be true to say now that this thing is last year and, generally, in the time that is past. And considering the matter physically too, not just in general terms, it is impossible either for what is everlasting to have perished at an earlier time, or for what did not exist at an earlier time to be everlasting later. For all perishable and generated things are alterable, and things that exist by nature are altered by their contraries and by the things out of which they are constituted, and by these same things they perish. Book Two.
2| 1 That the whole heaven, then, neither has come to be nor admits of perishing, as some say it does, but is one and everlasting, having neither beginning nor end of its whole duration, but having and containing infinite time within itself — this may be taken as established both from what has been said and from the opinion of those who speak otherwise and generate it. For if it is possible for it to be as we say, while it is not possible for it to have come to be in the way those others describe, this fact too would carry great weight toward conviction about its immortality and everlastingness. It is therefore well to persuade oneself of the truth of the ancient accounts, and above all those handed down by our own forebears, that there is something immortal and divine among things that have motion — motion of such a kind that there is no limit to it, but rather it is the limit of the others. For the limit belongs to things that contain, and this circular motion, being complete, contains the incomplete motions and those that have a limit and a stopping-point, itself having neither beginning nor end but being unceasing through infinite time, while of the other motions it is in some cases the cause of their beginning, in others the recipient of their stopping.
3| The ancients assigned the heaven and the region above to the gods, on the ground that it alone is immortal; and our present account bears witness that it is imperishable and ungenerated, and further that it is unaffected by any of the troubles that beset mortal things, and beyond this, free from toil, because it needs no forced compulsion to hold it back and prevent it from being carried in some other direction natural to it. For anything of that sort is toilsome, the more so the more everlasting it is, and has no share in the best condition. This is why we should not suppose the matter to stand as in the myth of the ancients, who say that it needs some Atlas for its preservation; for those who put together that account seem to have held the same supposition as later thinkers, since they too, treating all the bodies above as having weight and being earthy, propounded for it, in mythical form, an animate compelling force. Nor, again, should we suppose that because of its whirling motion it attains a speed greater than its own proper downward tendency, and is thereby preserved for so long a time, as Empedocles says. Nor, again, is it reasonable that it is held everlasting by a soul compelling it to remain so; for it is not possible for such a life of the soul to be free of pain and blessed. For the motion must, if it is compelled — given that the first body is naturally disposed to move otherwise and something else moves it continually — be laborious and stripped of all intelligent ease, seeing that it does not even have, as the soul of mortal animals has, the rest that comes about for the body in sleep, but must instead hold to some portion like that of Ixion, everlasting and unwearied.
4| If, then, as we have said, it is possible for the first motion to be as described, not only is it more fitting to hold this view about its everlastingness, but it is also only in this way that we could declare our account to be in agreement with the divination concerning the god. But let this much be enough for the present on such arguments. 2 Since there are some who say that the heaven has a right and a left, as the so-called Pythagoreans do (for the doctrine belongs to them), we must consider whether the matter stands as they say, or rather otherwise, if indeed these principles must be attached to the body of the universe at all. For in the first place, straight off, if the right and the left belong to it, we must suppose that principles still prior to these belong to it as well. Now this has been determined in the works on the motions of animals, since it is a matter proper to their nature; for it is plainly apparent in animals that some have all such parts — I mean, for example, right and left — while others have only some of them, and plants have only up and down. And if we must attach any such thing to the heaven as well, then, as we have said, it is reasonable that the first of these, as it belongs to animals, should belong to it too; for there are three pairs, each of which is a kind of principle. I mean the three: up and down, front and back, and right and left.
5| It's reasonable that all these dimensions belong to perfect bodies. Now up is the starting point of length, right is the starting point of breadth, and front is the starting point of depth. Again, there is another way of taking them, in terms of motions: I call these starting points the points from which motions first begin in things that have them. Growth proceeds from above, locomotion from the right, and perception from the front — for I call "front" the direction the senses face. This is why we should not look for up and down, right and left, front and back in every body, but only in those that have a starting point of motion within themselves by being ensouled. For among soulless things we see none in which there is a source of motion. Some do not move at all, while others move but not in the same way from every part — fire, for instance, moves only upward, and earth only toward the center. But in these cases we speak of 284a up and down and right and left by referring them back to ourselves: either in accordance with our own right, as diviners do, or by analogy with our own, as with the parts of a statue, or the opposite of our position — calling right what corresponds to our left, and left what corresponds to our right, and back what corresponds to our front — since in the things themselves we see no difference at all.
6| For if the thing is turned around, we call the opposite sides right and left, up and down, front and back. This is why one might be surprised at the Pythagoreans for naming only these two starting points, right and left, while leaving out the other four, which are no less authoritative. For up and down, and front and back, differ in all animals no less than right and left do. Some pairs differ only in power, others also in shape; and up and down belong alike to all ensouled things, both animals and plants, whereas right and left do not belong to plants. Further, just as length is prior to breadth, so, if up is the starting point of length and right the starting point of breadth, and the starting point of what is prior is itself prior, up would be prior to right in order of coming-to-be — since "prior" is said in many ways. Beyond this: if up is that from which motion begins, right is that from which motion begins, and forward is that toward which motion goes, then in this respect too up would have a certain power of a starting point over the other kinds.
7| It is fair to criticize them, then, both for leaving out the more authoritative starting points, and because they supposed these two applied alike to everything. As for us, since it has been established earlier that these powers belong to things that have a starting point of motion, and the heaven is ensouled and has a starting point of motion, it is clear that it has up and down and right and left. For we need not be puzzled, on the ground that the shape of the whole is spherical, how it can have a right and a left when all its parts are alike and are moving for all time; rather we should think of it as we would if someone, in a case where right differs from left even in shape, then wrapped it in a sphere: it will still have the power differing, though it will not appear to, because of the sameness of the shape. The same holds for the starting point of its motion: even if it never began, it must nonetheless have a starting point from which it would have begun, had it begun moving — and even if it should come to rest, it would move again from there. By its length I mean the distance measured along the poles, and of the poles I call one up and the other down; for it is only with respect to these that we see a difference between the hemispheres, since the poles do not move.
8| At the same time we are also accustomed to calling the sides of the universe not up and down but the region along the poles, taking this to be its length; for the sideways direction is what runs alongside up and down. Of the poles, the one that appears above us is the lower part, and the one invisible to us is the upper. For we call "right" of each thing the point from which the starting point of locomotion is; and of the heaven, the starting point of its revolution is the point from which the risings of the stars occur, so that this would be its right, and the point of the settings would be its left. If, then, it begins from the right and revolves toward the right, the up must be the invisible pole; for if the visible pole were up, the motion would be toward the left, which we do not say. It is clear, then, that the invisible pole is the up. And those who live there are in the upper hemisphere and toward the right, while we are in the lower and toward the left — the opposite of what the Pythagoreans say; for they make us the upper ones, in the right-hand part, and put the people there below, in the left-hand part.
9| But the opposite is the case. Yet with respect to the second revolution — that of the planets, for instance — we are among the upper and right-hand parts, and they are among the lower and left-hand ones; for in these the starting point of the motion is reversed, because their movements are opposite, so that it turns out that we are near the starting point and they near the end. Let this much, then, be said about the parts determined by dimension and by position.
10| 3 Since circular motion is not the contrary of circular motion, we must consider why there are several circular movements, even though we are attempting to carry out this inquiry from far off — not so much far off in place, but far more in that we grasp very few of the things that hold true of them. Nevertheless, let us speak. The cause concerning them must be grasped from the following starting point. Each thing whose function it is exists for the sake of that function. And the activity of god is immortality — that is, everlasting life. So the divine must have everlasting motion. Since the heaven is of this kind (for it is a divine body of a sort), it has for this reason the circularly-moving body, which by nature always moves in a circle. Why, then, is not the whole body of the heaven of this kind? Because it is necessary that something of the body carried in a circle remain — namely, what is at the center — and none of this can remain, either as a whole or in its center-part. For its motion in accordance with nature would have been toward the center; but by nature it moves in a circle — for otherwise the motion would not be everlasting, since nothing contrary to nature is everlasting. What is contrary to nature is later than what is in accordance with nature, and what is contrary to nature is a kind of departure, in the process of coming-to-be, from what is in accordance with nature.
11| There must, then, be earth; for this is what is at rest at the center. Let this be assumed for now, and it will be demonstrated later. But if there is earth, there must also be fire; for if one of a pair of contraries exists by nature, the other must also exist by nature, provided it truly is a contrary, and there must be some nature belonging to it — for the matter of contraries is the same. And affirmation is prior to privation (I mean, for example, hot is prior to cold), and rest and heaviness are spoken of as the privation of lightness and motion. But further, if fire and earth exist, the bodies between them must also exist; for each of the elements has a contrariety to each of the others. Let this too be assumed for now, and an attempt will be made to demonstrate it later. Given these things, it is clear that coming-to-be must occur, since none of these can be everlasting; for they are acted on and act upon one another as contraries, and are destructive of one another. Further, it is not reasonable that something movable should be everlasting if the motion that belongs to it by nature cannot be everlasting; and the motion of these bodies is toward one of these places. That coming-to-be must occur is clear, then, from this. And if there is coming-to-be, there must also be another circular motion, either one or several.
12| For according to the arrangement of the whole, the elements of bodies must stand toward one another in the same way. This too will be discussed more clearly in what follows; but for now this much is clear: the reason there are several bodies moving in a circle is that there must be coming-to-be — and there must be, if indeed there is fire; and fire requires the other elements too, if indeed earth exists; and earth requires that something always remain at rest, if indeed something is always in motion.
13| 4 The heaven must have a spherical shape; for this is the shape most proper to its substance, and first by nature. Let us first speak generally about shapes, asking which is first, both among plane figures and among solids. Now every plane figure is either rectilinear or curvilinear. The rectilinear is bounded by more than one line, while the curvilinear is bounded by one. Since in each kind the one is by nature prior to the many, and the simple prior to the composite, the circle would be first among plane figures. Further, if the complete is that outside of which nothing further of it can be taken, as was defined earlier, and if addition is always possible to a straight line but never to that of a circle, it is clear that the line enclosing the circle would be complete; so that if the complete is prior to the incomplete, then for this reason too the circle would be prior among figures. In the same way the sphere is prior among solids; for it alone is enclosed by a single surface, while rectilinear solids are enclosed by several; for as the circle stands among plane figures, so the sphere stands among solids. Further, those who divide bodies into planes and generate them out of planes appear to bear witness to this;
14| for alone among solids they do not divide the sphere, on the ground that it has no more than one surface; for division into planes is not carried out in the way that one cutting the whole into parts would divide it, but rather as into things different in kind. That the sphere, then, is first among solid figures is clear. And it is also most reasonable, on the view of those who assign an order according to number, that the circle corresponds to the one and the triangle to the dyad, since its angles are together equal to two right angles; but if the one were assigned to the triangle, the circle would no longer be a figure at all. And since the first figure belongs to the first body, and the first body is that in the outermost revolution, the body carried with the circular motion would be spherical. And so too would the body continuous with it; for what is continuous with the spherical is spherical. Likewise too the bodies toward the middle of these; for what is enclosed by, and touches, the spherical must be wholly spherical; and the bodies below the sphere of the planets touch the sphere above them. So the whole would be spherical; for all the parts touch and are continuous with the spheres.
15| Further, since it appears, and is assumed, that the whole revolves in a circle, and it has been demonstrated that outside the outermost revolution there is neither void nor place, it is necessary for this reason too that it be spherical. For if it were rectilinear, it would follow that there is place, and body, and void outside it; for a rectilinear figure turning in a circle will never occupy the same region, but where a body was before, there it will not be now, and where it now is not, it will be again, because of the shifting of its angles. Likewise too if it should be some other shape not having equal lines from the middle, such as lens-shaped or egg-shaped; for in all these cases it will follow that there is place and void outside its motion, because the whole does not occupy the same region. Further, if the measure of motions is the revolution of the heaven, because it alone is continuous, uniform, and eternal, and in each kind the measure is the least, and the least motion is the swiftest, it is clear that the motion of the heaven would be the swiftest of all motions. But indeed, of lines running from the same point to the same point, the line of a circle is the least;
16| and motion along the least line is the swiftest; so that if the heaven moves in a circle and moves most swiftly, it must be spherical. One might also derive this conviction from the bodies situated around the middle. For if water lies around the earth, air around the water, fire around the air, and the upper bodies stand in the same relation (they are not continuous with these, but they do touch them), and the surface of water is spherical, and what is continuous with the spherical, or lies around the spherical, must itself be of the same shape, then through this too it would be clear that the heaven is spherical. But that the surface of water is indeed of this kind is clear once one takes as a starting-point that water is naturally disposed always to flow together into the more hollow place; and the more hollow is that which is nearer the center. Let AB and AC, then, be drawn from the center, and let BC be joined. The line drawn to the base, namely AD, is then less than the lines from the center; the place is therefore more hollow. So the water will flow around, until it is made equal.
17| And AE is equal to the lines from the center. So the water must lie at the same distance as the lines from the center; for then it will be at rest. And the line touching the points equidistant from the center is circular; the surface of the water, then, namely BEC, is spherical. That the universe, then, is spherical is clear from these considerations, and that it is turned with such precision that nothing made by hand comes close to it, nor anything else that appears before our eyes among the things around us. For of the things from which its composition is made, nothing is so capable of receiving uniformity and precision as the nature of the encompassing body; for it is clear that the outer bodies stand in an analogous relation, as water does to earth, and likewise the elements that are ever more distant.
18| 5 Since it is possible to move on the circle in two ways — for example from A, one motion toward B and the other toward C — it has already been said that these are not contrary motions. But if nothing that happens as chance would have it, nor from spontaneity, can occur among eternal things, and the heaven is eternal, and so is its circular motion, for what reason does it move in the one direction rather than the other? For this too must either be a principle, or have a principle of its own. Now perhaps to attempt to declare something about a few matters, and about all matters, and to pass over nothing, might seem to be a mark either of great simple-mindedness or of great eagerness. Still, it is not right to censure everyone alike; rather one must see what the reason is for speaking, and further how one stands with respect to conviction — whether in a merely human way or with more fortitude. When, then, one arrives at 288a the more exact necessities, one ought to be grateful to those who discover them; but for now what appears reasonable must be stated. For if nature always does the best of what is possible, and just as, among motions on a straight line, the motion toward the upper place is more honorable (for the upper place is more divine than the lower), in the same way too motion forward is more honorable than motion backward — and this does hold, if indeed right and left also hold, as was said before (and the difficulty just mentioned bears witness that it does hold), namely that there is a before and an after; for this cause resolves the difficulty. For if it holds in the way that is best among what is possible, this would be the cause of what has just been said as well; for it is best to move with a motion that is simple and unceasing, and to move it toward the more honorable direction.
19| 6 About its motion, that it is uniform and not non-uniform, would be the next thing to go through after what has been said. I mean this about the first heaven and about the first motion; for in the bodies below, several motions have already combined into one. For if it moves non-uniformly, clearly there will be intensification and a culmination and a slackening of the motion; for every non-uniform motion has both a slackening and an intensification and a culmination. And the culmination is either the point from which it is carried, or the point to which, or the midpoint — as, presumably, for things moving in accordance with nature it is the point to which they are carried, for things moving contrary to nature it is the point from which, and for things thrown it is the midpoint. But of circular motion there is neither a "from which" nor a "to which" nor a midpoint; for it has neither starting point nor limit nor midpoint at all, since it is eternal in time and, in respect of length, closed up and unbroken. So that if there is no culmination of its motion, there could not be non-uniformity either; for non-uniformity comes about through slackening and intensification. Further, since everything that is moved is moved by something, the non-uniformity of the motion must come about either through the mover, or through the thing moved, or through both.
20| For either the mover does not move with the same power, or the thing moved is altered and does not remain the same, or both change — in any of these cases nothing prevents the thing moved from moving non-uniformly. But none of these can occur in the case of the heaven. For it has been shown that the thing moved is primary and simple and ungenerated and indestructible and altogether unchangeable, and it is far more reasonable that the mover should be of this kind too; for what is primary is what moves what is primary, what is simple moves what is simple, and what is indestructible and ungenerated moves what is indestructible and ungenerated. Since, then, the thing moved, being a body, does not change, neither would the mover change, being bodiless. So that the motion too cannot be non-uniform. And indeed, if it does become non-uniform, either it changes as a whole — becoming at one time faster and again at another slower — or its parts do. Now that the parts are not non-uniform is clear.
21| For otherwise there would already have arisen, in infinite time, a separation among the stars, one moving faster and another slower. But nothing appears to be otherwise with respect to their distances. But indeed neither is it possible for the whole to change; for the slackening of each thing comes about through incapacity, and incapacity is contrary to nature; for indeed the incapacities found in animals are all contrary to nature — for example old age and wasting. For presumably the whole constitution of animals is composed of things that differ in their proper places; for none of the parts has its own place. If, then, in the case of the primary things there is nothing contrary to nature (for they are simple and unmixed and in their own proper place, and nothing is contrary to them), then there could be no incapacity either, so that there would be neither slackening nor intensification; for if there is intensification, there is also slackening. Further, it is also unreasonable that the mover should be incapable for infinite time, and again capable for another infinite time; for nothing appears to be contrary to nature for infinite time (and incapacity is contrary to nature), nor for a time equal to the time it is contrary to nature and in accordance with nature, nor is it possible in any other way for it to be both capable and incapable. And it is necessary, if the motion slackens, that it slacken for infinite time.
22| But indeed it is not possible either for it to intensify forever or, again, to slacken forever; for then the motion would be infinite and indeterminate, and we say every motion is from something to something and determinate. Further, if one should take there to be some minimum time in which it is not possible for the heaven to be moved in less — just as it is not possible to walk or to play the cithara in any time whatever, but for each action there is a determinate minimum time such that it cannot be gone below, so too it is not possible for the heaven to be moved in any time whatever — if this is true, then there could not always be an intensification of the motion, and if not intensification, then not slackening either; for both go together, and likewise either one, since it intensifies by the same speed or a greater one, and for infinite time. It remains, then, to say that the faster and the slower alternate in the motion; but this is utterly unreasonable and like a fabrication. Further, it is also more reasonable that in these matters nothing should escape notice; for things set beside one another are more easily perceived. That there is, then, only one heaven, and that it is ungenerated and eternal, and further that it moves uniformly, let this much be said by us.
23| 7 About the so-called stars it would be next to speak — of what they are composed, and in what shapes, and what their motions are. It is most reasonable, and follows on what has been said, that we should hold each of the stars to be made of that body in which it happens to have its motion, since we said there is something whose nature it is to move in a circle. For just as those who say the stars are fiery say this because they hold the upper body to be fire — thinking it reasonable that each thing should be composed of the things among which it is — so too do we say. The heat and light from them arise because the air is rubbed off by their motion. For motion has by nature the power to kindle even wood and stones and iron; more reasonable, then, is it to kindle what is nearer to fire, and nearer is air — as also in the case of missiles carried in flight; for these very things are kindled to such a degree that leaden bullets melt, and since they themselves are kindled, the air around them must undergo this same thing. Now these are heated up because they are carried through air, which becomes fire through the blow of the motion; but each of the bodies above is carried in its sphere, so that they themselves are not kindled, but since the air lies beneath the sphere of the circularly-moving body, that air must be heated when the sphere is carried around, and most of all in that region in which the sun happens to be set. This is why, as the sun draws near and rises and is above us, the heat comes to be. That they are, then, neither fiery nor carried in fire — let this be said by us about them.
24| 8 Since both the stars and the whole heaven appear to shift their place, it must be that the change comes about either with both at rest, or with both in motion, or with the one at rest and the other in motion. Now for both to be at rest is impossible, at least with the earth at rest; for the appearances would not come about. Let it be assumed that the earth is at rest. It remains, then, either that both are moved, or that the one is moved and the other at rest. If, then, both are to be moved, it is unreasonable that the speeds of the stars and of the circles should be the same; for each star would then be equal in speed to the circle in which it is carried. For they appear, together with the circles, to be re-established again in the same place. It follows, then, that the star has traversed the circle and the circle has been carried through its own motion, having traversed its own circumference, at the same time. But it is not reasonable that the speeds of the stars should stand in the same ratio as the sizes of the circles. For that the circles should have their speeds proportionate to their sizes is nothing strange but even necessary, but that this should hold of each of the stars in them is in no way reasonable; for whether it is of necessity that what moves on the larger circle should be faster, clearly, even if the stars were transposed into one another's circles, one would be faster and the other slower —
25| On this view they would not have a motion of their own, but would be carried along by the circles. But even if this happened by chance, it is not reasonable that in every case alike the circle should be larger and the motion of the star in it faster; for that one or two should be so is nothing strange, but that all should be alike so looks like a fabrication. At the same time, what happens by chance does not occur in the things of nature, nor does what belongs everywhere and to all things come about by chance. But again, on the other hand, if the circles remain still and the stars themselves move, this too will be equally unreasonable; for it will follow that the outer ones move faster, and that the speeds correspond to the sizes of the circles. Since, then, it is not reasonable either that both should move, or that the star alone should move, it remains that the circles move and the stars are at rest and are carried along bound fast to the circles; for only in this way does nothing unreasonable follow. For that the speed should be greater for the larger circle is reasonable when they are bound about the same center (for just as in other cases the larger body is carried faster in its own proper motion, so too in the case of things moving in circles;
26| for the segment cut off by the lines from the center is greater for the larger circle, so that reasonably the larger circle will be carried round in the same time), and it also follows from this — and from the fact that the whole has been shown to be continuous — that the heaven does not tear apart. Further, since the stars are spherical, as others say and as we too may say in agreement, at least they generate their light out of that body, and there are two motions belonging to a sphere in its own right, rolling and spinning: if, then, the stars were moved through themselves, they would move with one or the other of these; but plainly they move with neither. For if they were spinning, they would remain in the same place and would not change their position, and this is both what appears and what everyone says. Further, it is reasonable that all should move with the same motion, but of the stars only the sun seems to do this, in its rising — or rather even this is not due to the sun itself but to the distance of our sight; for sight, stretched out over a long distance, wavers because of its weakness. This is perhaps also the cause of the fixed stars appearing to twinkle, while the planets do not twinkle; for the planets are near, so that our sight, being still strong, reaches them;
27| but toward the fixed stars it wavers because of the distance, being stretched out too far. And the trembling of our sight makes it seem that the star itself is moving; for it makes no difference whether it is the sight that moves or the thing seen. But that the stars do not roll either is plain; for what rolls must turn over, but the so-called face of the moon is always visible. So since, if they moved through themselves, it would be reasonable for them to move with their proper motions, and they plainly do not move with these, it is clear that they would not move through themselves. Besides this, it would be unreasonable for nature to have given them no organ for motion; for nature does nothing at random, and it is not likely that she took thought for animals but overlooked things so honorable — rather she seems, as if on purpose, to have removed everything by which they might have been able to advance on their own, and to have set them as far as possible from those things that have organs for motion. This is why it would reasonably seem that both the whole heaven is spherical and each of the stars is too. For with a view to motion in the same place, the sphere is the most serviceable of the shapes (for in this way it would move most quickly and would most hold to the same place), while for forward motion it is the most useless;
28| for it is least like the things that move themselves forward; for it has nothing detached from it and nothing projecting, as the rectilinear shape does, but is furthest removed in its shape from bodies capable of forward progress. Since, then, the heaven must move with the motion in the same place, while the other stars must not advance through themselves, it would reasonably follow that each is spherical; for in this way each would best do the one thing — move — or the other — remain still. 9 It is clear from these considerations that the claim that a harmony arises from the things carried around, on the ground that the sounds they produce are consonant, though stated cleverly and with unusual ingenuity by those who have said it, is nevertheless not the truth of the matter. For some think it necessary that bodies of such size, moving as they do, should produce a sound, since even bodies among us do so, though they have neither equal bulk nor are carried with such speed; and given the sun and moon, and further given so great a number and size of stars moving with such speed, it is impossible, they think, that a motion of this kind should not produce a sound whose magnitude is inconceivable. Assuming this, and that the speeds, from the distances, have the ratios of the musical concords, they say that the sound given off by the stars as they move in a circle is harmonious. But since it seems unreasonable that we should not hear this sound along with the rest, they say the cause of this is that the sound is present in things from the moment they come to be, so that it is not distinguishable against the silence that would contrast with it; for the recognition of sound and silence comes from setting them against each other, so that just as it seems to make no difference to smiths, through habituation, the same thing happens with human beings. Now these things, as has been said before, are stated elegantly and in a musical spirit, but it is impossible that the matter should be so.
29| For it is not only absurd that we hear nothing — which is the point they try to resolve by their explanation — but also that the bodies here should undergo no effect at all apart from perception. For sounds that exceed a certain measure wear away the very mass of even lifeless bodies — for instance, the sound of thunder splits stones and the hardest of bodies. But given that so many bodies are moving, and that the sound travels in proportion to the size of what moves, it would be necessary that a many-times-greater magnitude should reach us here, and that the force of its violence should be inconceivable. But reasonably we neither hear it, nor do the bodies here appear to undergo any violent effect, because there is in fact no sound. And at the same time the cause of this is clear, and it is also a piece of testimony for the truth of the account we have given; for the very difficulty that led the Pythagoreans to say that a concord arises from the things carried around is itself evidence for us. For whatever moves by itself produces sound and impact; but whatever is bound up or inheres within a moving thing, as the parts do in a ship, cannot produce sound, nor again can the ship itself, if it is being carried along on a river. And yet by the same reasoning one might say it is absurd that the mast and the stern of so great a ship do not produce a loud sound, if they are not themselves separately moving, or again that the ship itself does not, when it is moving.
30| But what moves within something not itself moving produces sound; whereas what is continuous with a moving thing, and does not strike against it, cannot produce sound. So here one must say that if the bodies in question were being carried either through a plenum of air poured through the whole, or through fire, as everyone says, they would necessarily produce a sound of surpassing magnitude, and if this happened, it would reach us here and would wear things away. Since, then, this plainly does not happen, none of them is carried with a motion that is either animate or forced — as if nature had foreseen what was going to happen, and had arranged that, if the motion did not occur in this way, none of the things around this region here would remain in the same condition. That the stars, then, are spherical, and that they do not move through themselves, has been stated.
31| 10 As for their order — the way in which each is placed, some being prior and others posterior, and how they stand to one another in their distances — let this be studied from the works on astronomy; for it is stated there sufficiently. It turns out that the motions of each correspond in ratio to their distances, in that some are faster and some slower; for since it is laid down that the outermost revolution of the heaven is simple and fastest, while the revolutions of the others are slower and more numerous (for each moves in the direction opposite to the heaven, along its own circle), it is reasonable, then, that the one nearest to the simple and first revolution should traverse its own circle in the longest time, and the one farthest away in the least, while among the rest, the nearer one always takes longer, and the farther one less. For the nearest is most mastered by it, and the farthest is least of all mastered, because of its distance; and the ones in between correspond, in due proportion, to their distance, as the mathematicians also show.
32| 11 One might most reasonably suppose that the shape of each of the stars is spherical. For since it has been shown that they are not by nature capable of moving of themselves, and nature does nothing without reason or in vain, it is clear that she has given to these motionless bodies the shape that is least capable of motion. And the sphere is least capable of motion, because it has no organ for motion. So it is clear that their bulk would be spherical. Further, all the stars are alike and of one kind; and the moon is shown, through what concerns sight, to be spherical — for otherwise, as it waxes and wanes, it would not for the most part appear crescent-shaped or gibbous, and only once exactly halved. And again this is shown through astronomical observations, since otherwise the eclipses of the sun would not be crescent-shaped. So if one of them is of this shape, it is clear that the rest would also be spherical.
33| 12 There are two puzzles, about which anyone might reasonably be puzzled, and we must try to state what seems to be the case, holding that eagerness deserves respect rather than boldness, if someone, through thirst for philosophy, is content even with small means of understanding concerning matters about which we have the greatest difficulties. Among the many puzzles of this kind, one of the most remarkable is not least this: for what cause is it not always the case that the bodies farther removed from the first motion move with more motions, but rather the bodies in between move with the most? For it would seem reasonable that, since the first body moves with a single motion, the body nearest to it should move with the fewest motions, say two, and the next with three, or some other such order. But in fact the opposite happens: the sun and moon move with fewer motions than some of the wandering stars, and yet these are farther from the middle and nearer to the first body than the sun and moon are. This has become clear about some of them even to sight: we have seen the moon, when it was halved, pass beneath the star of Ares, and be hidden as it entered the moon's dark part, and emerge again at its bright and shining part. And the Egyptians and Babylonians, who have observed for very many years from ancient times, say the same about the other stars as well, and from them we have many confirmations concerning each of the stars — so one might rightly raise this puzzle too, and also for what cause it is that in the first motion there is such a multitude of stars that the whole array seems innumerable, while of the others each one stands apart by itself, and two or more are never seen bound together in the same motion.
34| Concerning these matters, it is well to inquire and to seek fuller understanding, even though we have scanty resources for it and are at so great a distance from the events themselves; nevertheless, when one views things from such a standpoint, the puzzle now raised would seem in no way unreasonable. But we think about the stars only as bodies, as units having an order but wholly soulless; whereas we ought to suppose that they share in action and in life — for then nothing about what happens will seem unreasonable. For it seems that, for what is in the best condition, well-being belongs without action; for what is nearest to it, through little action and a single one; for things farther off, through more actions — just as with a body: one man is in good condition without even exercising, another after a little walking, another needs running and wrestling and the dust of the wrestling-ground besides, while yet another, however much he labors, could still not attain this good, but only some other good. Now succeeding is difficult either in doing many things or in doing them often — for instance, to throw the Coan cast ten thousand times with astragals is impossible, but one or two is easier. And again, when this must be done for the sake of that, and that for the sake of something else, and this again for yet another thing, it is easy to succeed in one or two steps, but the more steps there are, the harder it becomes.
35| For this reason we must suppose that the action of the stars is also of the same kind as that of animals and plants. For here too the actions of man are the most numerous — since he is able to attain many good things, so that he does many things, and for the sake of other things besides; whereas for what is in the best condition no action at all is needed, since it is itself that for the sake of which, and action always involves two terms, whenever there is both that for the sake of which and that which is for its sake. The actions of the other animals are fewer, and those of plants are perhaps small in number and one only; for either there is some one thing a plant might attain, as with man, or even its many actions are all a road toward the best. So one thing both has and shares in the best; another arrives near it through few steps, another through many; and another does not even attempt it, but is content to come near the last stage — as, for example, if health is the end: one thing is always healthy, another becomes so by reducing, another by running and reducing, another by doing something else for the sake of running, so that its motions are more numerous; while another is unable to arrive at health at all, but only at running, or only at reducing.
36| and one or the other of these is the end for them. For it is best of all for everyone to attain that very end; but failing that, it is always better the nearer one is to the best. And for this reason the earth does not move at all, while the things near it have few motions — for they do not arrive at the furthest stage, but only so far as they can attain a share of the most divine principle. But the first heaven attains its end at once, through a single motion. And the things between the first and the outermost do arrive at their end, but arrive through more motions. Now as to the puzzle, why under the first motion, being single, a great multitude of stars is arranged together, while each of the others has taken its own motions separately, one might first reasonably suppose this to hold for one reason: we must recognize that there is a great superiority of the life and the principle of the first motion over the others, and this would come about reasonably as follows. The first motion, being one, moves many of the divine bodies, while the many motions each move only one; for any single one of the wandering stars is carried through several motions. Nature equalizes things in this way, then, and produces a certain order, assigning many bodies to the one motion, and many motions to the one body;
37| and further, the other motions have one body each for this reason: the spheres before the last — the one carrying a single star — move many bodies; for the last sphere is carried bound within many spheres, and each sphere happens to be some body. The work of that last sphere would therefore be a shared one — for each sphere has its own proper motion by nature, and this last motion is, as it were, added on to them, and the power of every finite body has a finite object. We have now spoken about the stars that move with the circular motion — what sort of things they are as to substance and as to shape, and about their motion and their order.
38| 13 It remains to speak about the earth — where it happens to be situated, and whether it belongs among the things at rest or among the things in motion, and about its shape. Now concerning its position, not everyone holds the same opinion; but while most people, who say that the whole heaven is finite, say that the earth lies at the middle, those in Italy called the Pythagoreans say the opposite. For they say that fire is at the middle, and that the earth, being one of the stars, produces night and day by being carried in a circle about the middle. And further they construct another earth opposite to this one, which they call by the name counter-earth — not seeking their accounts and causes with a view to the observed facts, but rather dragging the observed facts toward certain accounts and opinions of their own, and trying to fit them together. But many others too would agree that one ought not to assign the middle region to the earth, gathering their conviction not from the observed facts but rather from theoretical accounts. For they think that the most honorable place befits the most honorable thing, and that fire is more honorable than earth, and that the limit is more honorable than the things between, while the extreme and the middle are limits;
39| So reasoning from these considerations, they do not think the earth lies at the center of the sphere, but rather fire. Further, the Pythagoreans hold this also because they think the most authoritative part of the whole ought especially to be guarded, and the center is such a thing. What occupies this place they call the "guard-post of Zeus" — the fire — just as "the middle" is spoken of without qualification, and the middle of the magnitude is also the middle of the thing and of its nature. Yet just as in animals the middle of the animal and the middle of the body are not the same, so one should suppose it is rather that way concerning the whole heaven too. For this reason, then, there is no need for them to be troubled about the universe, nor to introduce a guard over that middle; for in the one case the middle is a starting point and something honorable, but the middle of place seems to be more like an end than a starting point. For the middle is what is bounded, and the boundary is what bounds; and what surrounds and bounds is more honorable than what is bounded, since the one is matter, the other the substance of the composition. Concerning the place of the earth, then, some hold this opinion, and likewise concerning its being at rest and in motion.
40| For not all suppose it in the same way; rather, those who say it does not even lie at the center hold that it moves in a circle about the middle — and not only it, but also the counter-earth, as we said before. Some think that several such bodies may move about the middle, invisible to us because the earth blocks the view. This is also why they say the eclipses of the moon are more frequent than those of the sun: each of the moving bodies blocks it in turn, not the earth alone. For since the earth is not at the center, but a whole hemisphere's distance from it, they think nothing prevents the appearances turning out the same for us though we do not dwell at the center, just as would be the case even if the earth were not at the middle; for even as things are, our being a half-diameter's distance away produces no noticeable effect. Others say that the earth, though it does lie at the center, spins and moves about the axis stretched through the whole, as is written in the Timaeus. Similarly there is dispute about its shape too: some think it is spherical, others that it is flat and drum-shaped in form. As evidence they offer the fact that the sun, setting and rising, appears to make its disappearance behind the earth along a straight line rather than a curved one — as it would have to, they say, if the earth were spherical, the cut-off edge becoming curved; they fail to reckon in the distance of the sun from the earth and the great size of the earth's circumference, relative to us —
41| given which, in circles that appear small, a straight line appears from far off. So because of this appearance there is no reason for them to disbelieve that the mass of the earth is spherical in shape. But they add further, and say that because of its being at rest it is necessary that it have this shape. And indeed the accounts given about its motion and its rest happen to be many. Now it is necessary for everyone to run into this puzzle; for it may perhaps belong to a less troubled mind not to wonder how it is that a small part of earth, if raised up and released, moves and is unwilling to remain still, and the more of it there is the faster it moves, yet if someone were to raise up the whole earth and release it, it would not move at all — while as things are, so great a weight remains at rest. But further, if one were to remove the earth from beneath one of its moving parts before it fell, that part will be carried downward, nothing offering resistance. So it is reasonable that puzzling over this became a subject of philosophical inquiry for everyone; but one might be surprised that the solutions given about it do not seem more absurd than the puzzle itself. For some, because of these difficulties, say that the region below the earth is infinite, saying that it is rooted to infinity, as Xenophanes of Colophon did, so that they would not have the trouble of seeking the cause;
42| for which reason Empedocles also rebuked them, saying: "if indeed the depths of the earth are boundless and the ether abundant, as has been poured out vainly from the tongues of many mouths that have seen but little of the whole." Others say it rests upon water. For this is the oldest account we have received, which they say Thales of Miletus stated — that it remains because it is able to float, like a log or something else of that kind (for none of these is naturally suited to remain upon air, but upon water) — as though the same account did not hold concerning the earth as concerning the water that supports the earth; for water too is not naturally suited to remain aloft, but rests upon something. Further, just as air is lighter than water, and water than earth, how then do they suppose that the lighter thing lies beneath what is by nature heavier? Further, if the whole is naturally suited to remain upon water, clearly so is each of its parts; but as things are this evidently does not happen — rather, any given part is carried down to the depths, and the larger part faster. But they seem to inquire only up to a certain point, and not as far as the puzzle can be pushed. For it is customary with all of us not to direct our inquiry toward the matter itself but toward the person who says the opposite;
43| for indeed each person inquires within himself only up to the point where he himself no longer has anything to say against himself. Hence the one who is going to inquire well must be skilled at raising objections through the objections proper to the kind in question, and this comes from having surveyed all the differentiae. Anaximenes and Anaxagoras and Democritus say that its flatness is the cause of its remaining still. For it does not cut the air beneath it but covers it like a lid, which is what bodies having flatness evidently do; for such bodies are hard to move even against winds, because of the resistance they offer. They say the earth does this same thing to the air lying beneath it by its flatness; and the air, not having sufficient room to shift away all at once, remains still underneath, like the water in water-clocks. That the air, when cut off and kept in place, can bear a great weight, they offer many proofs. Now first, if the shape of the earth were not flat, it would not on this account remain at rest. And yet, on the grounds of what they themselves say, it is not flatness that is the cause of its remaining still, but rather size. For it is because of the narrowness of the space that the air, having no passage out, remains still on account of its quantity —
44| and it is great in quantity because it is shut in by so great a magnitude of earth. So this will hold true even if the earth is spherical, provided it is of such a size; for it will remain still according to their own account. In general, as against those who speak this way about motion, the dispute is not about parts but about some whole and total thing. For from the start one must determine whether there is some motion belonging to bodies by nature, or none belongs to them, and whether it does not belong by nature but does belong by force. Since we have already determined earlier, as far as our present capacity allowed, concerning these matters, we must proceed on the assumption that they hold. For if none of their motion is by nature, neither will it be forced; but if it is neither by nature nor by force, nothing at all will be moved; for that this is a necessary consequence has been determined earlier, and in addition to this, that it is not even possible for it to be at rest — for just as motion belongs either by force or by nature, so too does rest. But surely if there is some motion in accordance with nature, the violent motion of translation would not be the only kind, nor would rest be only violent; so that if the earth now remains at rest by force, it also came together at the middle by being carried there through the vortex.
45| Everyone gives this cause, drawing it from what happens in liquids and in the air: in these, the larger and heavier things always move toward the center of the vortex. This is why all those who generate the heavens say that the earth came together at the center; but as to why it stays there, they seek the cause, and some say it is because of its breadth and size, while others, like Empedocles, say that the revolution of the heavens, running around in a circle and moving faster, prevents the motion of the earth—just as the water in a ladle: for this too, when the ladle is carried around in a circle, often ends up beneath the bronze, yet does not move downward though it is by nature disposed to move downward, for the same reason. And yet, if neither the vortex nor the breadth were preventing it, but the air had withdrawn from under it, where would it be carried? Toward the center it moves by force, and it stays there by force; but according to nature there must be some motion belonging to it. Is this motion, then, upward or downward, or where is it? For there must be some motion; and if it is no more downward than upward, while the air above does not prevent the upward motion, then neither would the air beneath the earth prevent the downward motion; for the same things must be causes of the same things.
46| Further, one might say this against Empedocles too: when the elements stood apart under the rule of Strife, what was the cause of the earth's staying still? For surely he will not claim the vortex as the cause then as well. And it is also absurd not to notice that, while earlier the parts of the earth were carried toward the center on account of the vortex's whirling, now, for what cause do all things that have weight move toward it? For the vortex certainly does not come near us. Further, for what cause does fire move upward? Certainly not because of the vortex. But if fire is by nature disposed to move somewhere, clearly the same must be thought true of earth. Moreover, heavy and light are not in fact determined by the vortex; rather, of things already heavy and light beforehand, some go to the center and others rise to the surface on account of the motion. So there was heavy and light even before the vortex came to be—and by what were these determined, and how and where were they by nature disposed to move? For if the universe is infinite, it is impossible for there to be an up or a down, and yet heavy and light are determined by these.
47| Most people, then, spend their time on these causes. But there are some who say the earth stays still because of similarity, as Anaximander among the ancients did: for what is situated at the center and stands in a similar relation to the extremes has no more reason to move up than down or sideways; and it is impossible for it to move in opposite directions at once; so it necessarily stays still. This is stated cleverly, but it is not true. For according to this argument, everything whatsoever that is placed at the center must stay still, so that fire too would come to rest there—but what has been said is not peculiar to earth. Moreover it is not even necessary. For the earth is observed not only to stay at the center, but also to move toward the center. For wherever any part of it moves, the whole must move there too; and where it moves by nature, there it also stays by nature. It is not, then, because it stands in a similar relation to the extremes: for that is common to everything, whereas moving toward the center is peculiar to earth. And it is also absurd
48| to ask why the earth stays at the center, but not to ask why fire stays at the extreme. For if that place too is by nature the extreme's place for fire, clearly there must likewise be some place that belongs by nature to earth; but if it is not by nature this place, but rather it stays there through the necessity of similarity—as in the argument about the hair that, though pulled strongly, is pulled equally in every direction and so will not snap, and about the man who, starving and dying of thirst, is equally and at an equal distance from food and drink on every side (for he too must remain still)—then they need to inquire, on the same grounds, into the staying-put of fire at the extremes. And it is also strange to inquire into staying-still but not to inquire into their motion—for what cause the one moves upward and the other toward the center, when nothing hinders it. But in fact what is said is not even true. It is true only accidentally: that everything for which it is no more fitting to move this way than that way must stay at the center. But by this very argument it will not stay still but will move—not, however, as a whole, but scattered apart.
49| For the same argument will fit the case of fire as well: for it too, once placed there, must stay still in the same way as the earth, since it will stand in a similar relation to any of the extreme points whatsoever. But nevertheless it will move away from the center, just as it is in fact observed to move, if nothing hinders it, toward the extreme—except not as a whole toward one point (for that is the only thing that follows of necessity from the argument about similarity), but rather each proportional part toward the corresponding proportional part of the extreme—I mean, for example, a quarter part toward a quarter part of what surrounds it; for no body is a mere point. And just as a thing might come together, being compressed, from a large space into a smaller place, so too it might, becoming rarer, spread from a smaller space into a larger one; so that even earth might, on the same principle of similarity, be moved away from the center in this manner, unless this place belonged to earth by nature. As for the views held about its shape, about its place and staying still and motion, this is roughly the sum of them.
50| 14 Let us now say first whether it has motion or stays still. For as we said, some make it one of the stars, while others, positing it at the center, say it spins and moves about the middle pole. That this is impossible is clear if one takes as a starting point that, whether it is carried while outside the center or at the center, it must be moved by force with this motion; for this motion does not belong to the earth itself—otherwise each of its parts would have this same motion; but as it is, all parts move in a straight line toward the center. So this motion cannot be eternal, since it is forced and contrary to nature; but the order of the universe is eternal. Further, all things that move with the circular motion are observed to lag behind and to be moved with more than one motion, apart from the first sphere; so that the earth too, whether it moves about the center or lies at the center, must be moved with two motions. But if this were so, there would have to occur shiftings and turnings of the fixed stars. Yet this is not observed to happen; rather, the same stars always rise and set at the same points of the earth.
51| Further, the natural motion of the parts of the earth, and of the whole of it, is toward the center of the universe; this is in fact why it happens to lie now at the center. One might raise a difficulty: since the center of the earth and the center of the universe are the same, toward which of the two do heavy things and the parts of the earth move by nature—is it toward the center because it is the center of the universe, or because it is the center of the earth? It must be toward that of the universe; for light things too, and fire, moving in the opposite direction from heavy things, move toward the extreme of the place that surrounds the center. And it has come about that the center of the earth and of the universe are the same; for a thing does move toward the center of the earth too, but only accidentally, in that the earth has its center within the center of the universe. That it moves toward the center of the earth is shown by the fact that the heavy things that move toward it do not move parallel to each other
52| ...is not carried but toward similar angles, so that it is carried toward one thing, the center — and this is true of earth as well. It is clear, then, that the earth must be at the center and motionless, both for the reasons already stated, and because bodies with weight that are forcibly thrown upward travel back down along a straight line to the same place, even if the force that throws them out is unlimited. That the earth, then, neither moves nor lies outside the center is clear from these considerations; and beyond this the cause of its remaining at rest is plain from what has been said. For if it is by nature such as to be carried from every direction toward the center, as it evidently is, and fire, conversely, from the center toward the extremity, then it is impossible for any part of the earth to be carried away from the center except by force. For there is one motion, and a simple one, for what is one and simple, and not opposite motions; but motion away from the center is the opposite of motion toward the center. If, then, it is impossible for any part of the earth to be carried away from the center, it is clear that it is still more impossible for the whole earth to be; for where a part is naturally disposed to be carried, there too the whole is naturally disposed to be. So that, since it is impossible for it to be moved except by a superior force, it must be necessary for the earth to remain at the center.
53| What the mathematicians say about astronomy bears witness to these points as well; for the appearances that occur as the figures by which the order of the stars is determined change are consistent with the earth's lying at the center. Concerning its place, then, and its remaining at rest and its motion, and how these stand, let this much be said about it. It must necessarily have a spherical shape; for each of its parts has weight until it reaches the center, and the smaller part, being pushed by the larger, cannot heave up in waves, but is rather compressed further and each part yields to the other, until it comes to be at the center. One must understand what is being said as one would understand a coming-to-be occurring in the manner some of the natural philosophers describe. Except that they attribute the downward motion to force; it is better to state the truth, and to say that this happens because whatever has weight is naturally disposed to be carried toward the center. When the mixture, then, existed potentially, the elements being separated out were carried alike from every direction toward the center. Whether, then, the parts, being divided off equally from the extremities, were drawn together toward the center, or whether they stood in some other relation, the result will be the same. That, then, when things are carried alike from every direction, from the extremities, toward one center, the resulting mass must become uniform in every direction, is clear;
54| for when an equal amount is added on every side, the extremity must be equally distant from the center in every direction — and this shape is that of a sphere. Nor will it make any difference to the argument even if its parts did not run together toward the center alike from every side. For the greater part must always push forward the lesser part that lies before it toward the center, since both have their tendency there, and the heavier part, in pushing forward, does so as far as this point, pushing the lesser weight along with it. And whatever difficulty one might raise here has the same solution as these points give. For if, the earth being at the center and spherical, a many-times-greater weight should come to be added to one hemisphere, then the center of the whole and the center proper to the earth will no longer be the same; so that either the earth will not remain at the center, or, if it does remain, it will be at rest even though it does not have the center it is naturally disposed to move toward, as it does now. 297b This, then, is the difficulty; and it is not hard to see the answer if we press the point a little further and distinguish how we hold that any magnitude whatever, having weight, is carried toward the center. For it is clear that its extremity is carried not merely until it touches the center, but the greater part must prevail until it too takes the center as its own center; for up to that point it retains its tendency.
55| It makes no difference, then, whether one states this about a clod of earth or about any chance part, or about the whole earth; for what happens has been stated not on account of smallness or greatness, but holds for anything whatsoever that has a tendency toward the center. So that whether the whole was carried from somewhere, or a part was, it must be carried until it reaches this point, until it takes the center equally from every direction, the smaller portions being made to conform to the larger ones by the forward pressure of their tendency, and this makes no difference. So then, if it came to be, it must have come to be in this manner, so that it is clear that its coming to be was spherical; and if it is ungenerated and always remains, it must be in the same condition it would have been in had it come to be at the first, on this account. On this reasoning, then, its shape must necessarily be spherical, and also because all heavy things are carried toward similar angles, and not alongside one another; and this is characteristic of what is by nature spherical. Either, then, it is spherical, or at least it is spherical by nature. And one must call each thing to be of the character that it wishes by nature to be and that belongs to it, and not what it is by force and contrary to nature. Further, this is shown also through what appears to perception; for otherwise the eclipses of the moon would not have such shapes at their cutoff edges;
56| for as it is, in its monthly configurations it takes on divisions of every kind (for it becomes straight-edged and convex on both sides and concave), but during eclipses it always has a convex line marking it off, so that, since it is eclipsed on account of the earth's screening it, the circumference of the earth, being spherical, would be the cause of this shape. Further, through the appearance presented by the stars, it is clear not only that the earth is round, but also that it is not great in size; for when we shift our position only a little toward the south or the north, the horizon circle becomes noticeably different, so that the stars overhead undergo a great change, and the same stars are not seen as we move toward the north and toward the south. For some stars are seen in Egypt and around Cyprus, but are not seen in the regions toward the north, and stars that are always visible in the regions toward the north set in those southern places. So that it is clear from these facts not only that the shape of the earth is round, but also that it is a sphere not great in size; for otherwise such a small shift in position would not so quickly make the difference apparent. This is why those who suppose that the region around the Pillars of Heracles is joined to the region around India, and that in this way the sea is one, should not be thought to be supposing something too incredible;