by Aristotle
If the earth was generated, then, it must have been formed in this way, and so [15] clearly its generation was spherical; and if it is ungenerated and has remained so always, its character must be that which the initial generation, if it had occurred, would have given it. But the spherical shape, necessitated by this argument, follows also from the fact that the motions of heavy bodies always make equal angles, and are not parallel. This would be the natural form of movement towards what is [20] naturally spherical. Either then the earth is spherical or it is at least naturally spherical. And it is right to call anything that which nature intends it to be, and which belongs to it, rather than that which it is by constraint and contrary to nature. The evidence of the senses further corroborates this. How else would eclipses of the moon show segments shaped as we see them? As it is, the shapes which the moon [25] itself each month shows are of every kind—straight, gibbous, and concave—but in eclipses the outline is always curved; and, since it is the interposition of the earth that makes the eclipse, the form of this line will be caused by the form of the earth’s surface, which is therefore spherical. Again, our observations of the stars make it [30] evident, not only that the earth is circular, but also that it is a circle of no great size. For quite a small change of position on our part to south or north causes a manifest alteration of the horizon. There is much change, I mean, in the stars which are overhead, and the stars seen are different, as one moves northward or southward. [298a1] Indeed there are some stars seen in Egypt and in the neighbourhood of Cyprus which are not seen in the northerly regions; and stars, which in the north are never beyond the range of observation, in those regions rise and set. All of which goes to [5] show not only that the earth is circular in shape, but also that it is a sphere of no great size; for otherwise the effect of so slight a change of place would not be so quickly apparent. Hence one should not be too sure of the incredibility of the view of those who conceive that there is continuity between the parts about the pillars of Hercules and the parts about India, and that in this way the ocean is one. As further [10] evidence in favour of this they quote the case of elephants, a species occurring in each of these extreme regions, suggesting that the common characteristic of these extremes is explained by their continuity. Also, those mathematicians who try to [15] calculate the size of the earth’s circumference arrive at the figure 400,000 stades.15 This indicates not only that the earth’s mass is spherical in shape, but also that as compared with the stars it is not of great size. [20]
BOOK III
1 · We have already discussed the first heaven and its parts, the moving stars within it, the matter of which these are composed and their nature, and we have also [25] shown that they are ungenerated and indestructible. Now things that we call natural are either substances or functions and attributes of substances. As substances I class the simple bodies—fire, earth, and the other terms of the series—and all things composed of them; for example, the heaven as a whole and its [30] parts, animals, again, and plants and their parts. By attributes and functions I mean the movements of these and of all other things in which they have power in themselves to cause movement, and also their alterations and reciprocal transformations. It is obvious, then, that the greater part of the inquiry into nature concerns [298b1] bodies; for a natural substance is either a body or a thing which cannot come into existence without body and magnitude. This appears plainly from an analysis of the [5] character of natural things, and equally from specialized studies. Since, then, we have spoken of the primary element, of its nature, and of its freedom from destruction and generation, it remains to speak of the other two. In speaking of them we shall be obliged also to inquire into generation and destruction. For if there [10] is generation anywhere, it must be in these elements and things composed of them.
This is indeed the first question we have to ask: is generation a fact or not? Earlier speculation was at variance both with itself and with the views here put forward as to the true answer to this question. Some removed generation and [15] destruction from the world altogether. Nothing that is, they said, is generated or destroyed, and our conviction to the contrary is an illusion. So maintained the school of Melissus and Parmenides. But however excellent their theories may otherwise be, anyhow they cannot be held to speak as students of nature. There may be things not subject to generation or any kind of movement, but if so they belong to [20] another and a higher inquiry than the study of nature. They, however, had no idea of any form of being other than the substance of things perceived; and when they saw, what no one previously had seen, that there could be no knowledge or wisdom without some such unchanging entities, they naturally transferred what was true of them to things perceived. Others, perhaps intentionally, maintain precisely the [25] contrary opinion to this. It had been asserted that everything in the world was subject to generation and nothing was ungenerated, but that after being generated some things remained indestructible while the rest were again destroyed. This had been asserted in the first instance by Hesiod and his followers, but afterwards outside his circle by the earliest natural philosophers. But what these thinkers [30] maintained was that all else is being generated and is flowing, nothing having any stability, except one single thing which persists as the basis of all these transformations. So we may interpret the statements of Heraclitus of Ephesus and many others. And some subject all bodies whatever to generation, by means of the [299a1] composition and separation of planes.
Discussion of the other views may be postponed. But this last theory which composes every body of planes is, as is seen at a glance, in many respects in plain [5] contradiction with mathematics. It is, however, wrong to remove the foundations of a science unless you can replace them with others more convincing. And, secondly, the same theory which composes solids of planes clearly composes planes of lines and lines of points, so that a part of a line need not be a line. This matter has been [10] already considered in our discussion of movement, where we have shown that an indivisible length is impossible.16 But with respect to natural bodies there are impossibilities involved in the view which asserts indivisible lines, which we may briefly consider at this point. For the impossible consequences which result from this view in the mathematical sphere will reproduce themselves when it is applied to [15] physical bodies, but there will be difficulties in physics which are not present in mathematics; for mathematics deals with an abstract and physics with a more concrete object. There are many attributes necessarily present in physical bodies which are necessarily absent from indivisibles. There can be nothing divisible in an indivisible thing, but the attributes of bodies are all divisible in one of two ways. [20] They are divisible into kinds, as colour is divided into white and black, and they are divisible per accidens when that which has them is divisible. In this latter sense attributes which are simple are all divisible. Attributes of this kind will serve, therefore, to illustrate the impossibility of the view. It is impossible, if two parts of a [25] thing have no weight, that the two together should have weight. But either all perceptible bodies or some, such as earth and water, have weight, as these thinkers would themselves admit. Now if the point has no weight, clearly the lines have not either, and, if they have not, neither have the planes. Therefore no body has weight. It is, further, manifest that the point cannot have weight. For while a heavy thing [30] may always be heavier than something and a light thing lighter than something, a thing which is heavier or lighter than something need not be itself heavy or light, [299b1] just as a large thing is larger, but what is larger is not always large. A thing which, judged absolutely, is small may none the less be larger than other things. Whatever, then, is heavy and also heavier than something else, must be greater in [5] weight. A heavy thing therefore is always divisible. But it is agreed that a point is indivisible. Again, suppose that what is heavy is a dense body, and what is light rare. Dense differs from rare in containing more matter in the same bulk. A point, then, if it may be heavy or light, may be dense or rare. But the dense is div
isible while a [10] point is indivisible. And if what is heavy must be either hard or soft, an impossible consequence is easy to draw. For a thing is soft if its surface can be pressed in, hard if it cannot; and if it can be pressed in it is divisible.
Moreover, no weight can consist of parts not possessing weight. For how, [15] except by the merest fiction, can they specify the number and character of the parts which will produce weight? And, further, if it is weight by which one weight is greater than another, then every indivisible part possesses weight. For suppose that a body of four points possesses weight. A body composed of more than four points will be superior in weight to it, a thing which has weight. But what makes something [20] heavier than a heavy thing must be heavy, just as what makes something whiter than a white thing must be white. Here the difference which makes the superior weight heavier is the single point which remains when the common number, four, is subtracted. A single point, therefore, has weight.
Further, to assume that the planes can only be put in linear contact would be ridiculous. For just as there are two ways of putting lines together, namely, end to [25] end and side by side, so there must be two ways of putting planes together. Lines can be put together so that contact is linear by laying one along the other, though not by putting them end to end. But if in putting the planes together, superficial contact is also allowed there will be bodies which are not any element nor composed of [30] elements, viz. bodies put together from planes put together in this way. Again, if it is the number of planes in a body that makes one heavier than another, as the Timaeus17 explains, clearly the line and the point will have weight. For the cases [300a1] are, as we said before, analogous. But if the reason of differences of weight is not this, but rather the heaviness of earth and the lightness of fire, then some of the [5] planes will be light and others heavy (which involves a similar distinction in the lines and the points); the earth-plane, I mean, will be heavier than the fire-plane. In general, the result is either that there is no magnitude at all, or that all magnitude could be done away with. For a point is to a line as a line is to a plane and as a plane [10] is to a body. Now the various forms in passing into one another will each be resolved into its ultimate constituents. It might happen therefore that nothing existed except points, and that there was no body at all. A further consideration is that if time is similarly constituted, there would be, or might be, a time at which it was done away with. For the indivisible now is like a point in a line. The same consequences follow [15] from composing the heaven of numbers, as some of the Pythagoreans do who make all nature out of numbers. For natural bodies are manifestly endowed with weight and lightness, but an assemblage of units can neither be composed to form a body nor possess weight.
[20] 2 · The necessity that each of the simple bodies should have a natural movement may be shown as follows. They manifestly move, and if they have no proper movement they must move by constraint; and the constrained is the same as the unnatural. Now an unnatural movement presupposes a natural movement [25] which it contravenes, and which, however many the unnatural movements, is always one. For naturally a thing moves in one way, while its unnatural movements are manifold. The same may be shown from the fact of rest. Rest, also, must either be constrained or natural, constrained in a place to which movement was constrained, natural in a place to which movement was natural. Now manifestly [30] there is a body which is at rest at the centre. If then this rest is natural to it, clearly motion to this place is natural to it. If, on the other hand, its rest is constrained, what is hindering its motion? Something, perhaps, which is at rest; but if so, we shall simply repeat the same argument; and either we shall come to an ultimate [300b1] something to which rest where it is is natural, or we shall have an infinite process, which is impossible. The hindrance to its movement, then, we will suppose, is a moving thing—as Empedocles says that it is the vortex which keeps the earth still—: but in that case where would it have moved to? It could not move infinitely; [5] for to traverse an infinite is impossible, and impossibilities do not happen. So the moving thing must stop somewhere, and there rest not by constraint but naturally. But a natural rest proves a natural movement to the place of rest.
Hence Leucippus and Democritus, who say that the primary bodies are in [10] perpetual movement in the void or infinite, may be asked to explain the manner of their motion and the kind of movement which is natural to them. For if the various elements are constrained by one another to move as they do, each must still have a natural movement which the constrained contravenes, and the prime mover must [15] cause motion not by constraint but naturally. If there is no ultimate natural cause of movement and each preceding term in the series is always moved by constraint, we shall have an infinite process. The same difficulty is involved even if it is supposed, as we read in the Timaeus,18 that before the world was made the elements moved without order. Their movement must have been due either to constraint or to their nature. And if their movement was natural, careful consideration shows that there [20] was already a world. For the prime mover must cause motion in virtue of its own natural movement, and the other bodies, moving without constraint, as they came to rest in their proper places, would fall into the order in which they now stand, the heavy bodies moving towards the centre and the light bodies away from it. But that is the order of their distribution in our world. There is a further question, too, which [25] might be asked. Is it not possible that bodies in unordered movement should combine in some cases into combinations like those of which bodies of nature’s composing are composed, such, I mean, as bones and flesh? This is what Empedocles asserts to have occurred under Love. ‘Many a head’, he says ‘came to [30] birth without a neck’.19
The answer to the view that there are infinite bodies moving in an infinite is that, if the cause of movement is single, they must move with a single motion, and therefore not without order; and if, on the other hand, the causes are of infinite [307a1] variety, their motions too must be infinitely varied. For a finite number of causes would produce a kind of order, since absence of order is not proved by diversity of direction in motions: indeed, in the world we know, not all bodies, but only bodies of the same kind, have a common goal of movement. Again, disorderly movement means in reality unnatural movement, since the order proper to perceptible things is [5] their nature. And there is also absurdity and impossibility in the notion that the disorderly movement is infinitely continued. For the nature of things is the nature which most of them possess for most of the time. Thus their view brings them into the contrary position that disorder is natural, and order or system unnatural. But no [10] natural fact can originate in chance. This is a point which Anaxagoras seems to have thoroughly grasped; for he starts his cosmogony from unmoved things. The others, it is true, make things collect together somehow before they try to produce motion and separation. But it is unreasonable to start generation from an original state in which bodies are separated and in movement. Hence Empedocles begins [15] after the process ruled by Love; for he could not have constructed the heaven by building it up out of bodies in separation, making them to combine by the power of Love, since our world has its constituent elements in separation, and therefore presupposes a previous state of unity and combination.
These arguments make it plain that every body has its natural movement, [20] which is not constrained or contrary to its nature. We go on to show that there are certain bodies whose impetus must be that of weight and lightness. Of necessity, we assert, they must move, and a moved thing which has no natural impetus cannot move either towards or away from the centre. Suppose a body A without weight, [25] and a body B endowed with weight. Suppose the weightless body to move the distance CD, while B in the same time moves the distance CE, which will be greater since the heavy thing must move further. Let the heavy body then be divided in the [30] proportion CE:CD (for there is no reason why a part of B should not stand in this relation to the whole). Now if the whole moves the whole distance CE, the part must in the same time move the
distance CD. A weightless body, therefore, and one which has weight will move the same distance, which is impossible. And the same [301b1] argument would fit the case of lightness. Again, a body which is in motion but has neither weight nor lightness, must be moved by constraint, and must continue its constrained movement infinitely. For there will be a force which moves it, and the [5] smaller and lighter a body is the further will a given force move it. Now let A, the weightless body, be moved the distance CE, and B, which has weight, be moved in the same time the distance CD. Dividing the heavy body in the proportion CE:CD, [10] we subtract from the heavy body a part which will in the same time move the distance CE, since the whole moved CD; for the relative speeds of the two bodies will be in inverse ratio to their respective sizes. Thus the weightless body will move the same distance as the heavy in the same time. But this is impossible. Hence, since [15] the motion of the weightless body will cover a greater distance than any that is suggested, it will continue infinitely.