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difference whether we apply this to a clod or common fragment of earth or to the earth as a whole。 The fact indicated does not depend upon degrees of size but applies universally to everything that has the centripetal impulse。 Therefore earth in motion； whether in a mass or in fragments； necessarily continues to move until it occupies the centre equally every way； the less being forced to equalize itself by the greater owing to the forward drive of the impulse。 If the earth was generated； then； it must have been formed in this way； and so 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 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 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 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 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。 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 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 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 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 calculate the size of the earth's circumference arrive at the figure 400；000 stades。 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。
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 bodily constitution； and we have also 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 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 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 character of natural things； and equally from an inspection of the instances of inquiry into nature。 Since； then； we have spoken of the primary element； of its bodily constitution； 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 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 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 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 contrary opinion to this。 It has 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 maintained was that all else has been generated and； as they said； 'is flowing away； nothing having any solidity； 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 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 the most superficial observation shows； in many respects in plain 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 already considered in our discussion of movement； where we have shown that an indivisible length is impossible。 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 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 excluded by indivisibility； all attributes； in fact； which are divisible。 There can be nothing divisible in an indivisible thing； but the attributes of bodies are all divisible in one of two ways。 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 nevertheless divisible。 Attributes of this kind will serve； therefore； to illustrate the impossibility of the view。 It is impossible； if two parts of a 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 their point cannot have weight。 For while a heavy thing 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； just as a large thing is larger than others； 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 exceed this by something which is heavy。 A heavy thing therefore is always divisible。 But it is common ground that a point is indivisible。 Again； suppose that what is heavy or weight is a dense body； and what is light r