Chapter 14

Let us first decide the question whether the earth moves or is at rest. For, as we said, there are some who make it one of the stars, and others who, setting it at the centre, suppose it to be ‘rolled’ and in motion about the pole as axis¹. That both views are untenable will be clear if we take as our starting-point the fact that the earth’s motion, whether the earth be at the centre or away from it, must needs be a constrained² motion. It cannot be the movement of the earth itself. If it were, any portion of it would have this movement; but in fact every part moves in a straight line to the centre. Being, then, constrained and unnatural³, the movement could not be eternal. But the order of the universe is eternal. Again, everything that moves with the circular movement, except the first sphere, is observed to be passed, and to move with more than one motion. The earth, then, also, whether it move about the centre or as stationary⁴ at it, must necessarily move with two motions. But if this were so, there would have to be passings and turnings of the fixed⁵ stars. Yet no such thing is observed. The same stars always rise and set in the same parts of the earth.

Further, the natural movement of the earth, part and whole alike, is the centre of the whole-whence the fact that it is now actually situated⁶ at the centre-but it might be questioned since both centres are the same, which centre it is that portions of earth and other heavy things move to. Is this their goal because it is the centre of the earth or because it is the centre of the whole? The goal, surely, must be the centre of the whole. For fire and other light things move to the extremity⁷ of the area which contains the centre. It happens, however, that the centre of the earth and of the whole is the same. Thus they do move to the centre of the earth, but accidentally, in virtue⁸ of the fact that the earth’s centre lies at the centre of the whole. That the centre of the earth is the goal of their movement is indicated by the fact that heavy bodies moving towards the earth do not parallel but so as to make equal angles, and thus to a single centre, that of the earth. It is clear, then, that the earth must be at the centre and immovable, not only for the reasons already given, but also because heavy bodies forcibly thrown quite straight upward return to the point from which they started, even if they are thrown to an infinite distance. From these considerations then it is clear that the earth does not move and does not lie elsewhere than at the centre.

From what we have said the explanation of the earth’s immobility is also apparent. If it is the nature of earth, as observation shows, to move from any point to the centre, as of fire contrariwise to move from the centre to the extremity, it is impossible that any portion of earth should move away from the centre except by constraint⁹. For a single thing has a single movement, and a simple thing a simple: contrary movements cannot belong to the same thing, and movement away from the centre is the contrary of movement to it. If then no portion of earth can move away from the centre, obviously still less can the earth as a whole so move. For it is the nature of the whole to move to the point to which the part naturally moves. Since, then, it would require a force greater than itself to move it, it must needs stay at the centre. This view is further supported by the contributions of mathematicians¹⁰ to astronomy, since the observations made as the shapes change by which the order of the stars is determined¹¹, are fully¹² accounted for on the hypothesis that the earth lies at the centre. Of the position of the earth and of the manner of its rest or movement, our discussion may here end.

Its shape must necessarily be spherical¹³. For every portion of earth has weight until it reaches the centre, and the jostling of parts greater and smaller would bring about not a waved surface, but rather compression and convergence of part and part until the centre is reached. The process should be conceived by supposing the earth to come into being in the way that some of the natural philosophers describe. Only they attribute the downward movement to constraint, and it is better to keep to the truth and say that the reason of this motion is that a thing which possesses weight is naturally endowed with a centripetal¹⁴ movement. When the mixture, then, was merely potential, the things that were separated off moved similarly from every side towards the centre. Whether the parts which came together at the centre were distributed at the extremities¹⁵ evenly, or in some other way, makes no difference. If, on the one hand, there were a similar movement from each quarter of the extremity to the single centre, it is obvious that the resulting mass would be similar on every side. For if an equal amount is added on every side the extremity of the mass will be everywhere equidistant from its centre, i.e. the figure will be spherical. But neither will it in any way affect the argument if there is not a similar accession of concurrent¹⁶ fragments from every side. For the greater quantity, finding a lesser¹⁷ in front of it, must necessarily drive it on, both having an impulse whose goal is the centre, and the greater weight driving the lesser forward till this goal is reached. In this we have also the solution of a possible difficulty. The earth, it might be argued, is at the centre and spherical in shape: if, then, a weight many times that of the earth were added to one hemisphere, the centre of the earth and of the whole will no longer be coincident. So that either the earth will not stay still at the centre, or if it does, it will be at rest without having its centre at the place to which it is still its nature to move. Such is the difficulty. A short consideration will give us an easy answer, if we first give precision to our postulate¹⁸ that any body endowed with weight, of whatever size, moves towards the centre. Clearly it will not stop when its edge touches the centre. The greater quantity must prevail until the body’s centre occupies the centre. For that is the goal of its impulse. Now it makes no 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, necessitated¹⁹ 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 corroborates²⁰ 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 alteration²¹ of the horizon. There is much change, I mean, in the stars which are overhead, and the stars seen are different, as one moves northward²² 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 circumference²³ 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.

1 axis   

n.轴，轴线，中心线；坐标轴，基准线

参考例句：

• The earth's axis is the line between the North and South Poles.地轴是南北极之间的线。
• The axis of a circle is its diameter.圆的轴线是其直径。

2 constrained   

adj.束缚的,节制的

参考例句：

• The evidence was so compelling that he felt constrained to accept it. 证据是那样的令人折服，他觉得不得不接受。
• I feel constrained to write and ask for your forgiveness. 我不得不写信请你原谅。

3 unnatural   

adj.不自然的；反常的

参考例句：

• Did her behaviour seem unnatural in any way?她有任何反常表现吗？
• She has an unnatural smile on her face.她脸上挂着做作的微笑。

4 stationary   

adj.固定的，静止不动的

参考例句：

• A stationary object is easy to be aimed at.一个静止不动的物体是容易瞄准的。
• Wait until the bus is stationary before you get off.你要等公共汽车停稳了再下车。

5 fixed   

adj.固定的，不变的，准备好的；(计算机)固定的

参考例句：

• Have you two fixed on a date for the wedding yet?你们俩选定婚期了吗？
• Once the aim is fixed,we should not change it arbitrarily.目标一旦确定，我们就不应该随意改变。

6 situated   

adj.坐落在...的，处于某种境地的

参考例句：

• The village is situated at the margin of a forest.村子位于森林的边缘。
• She is awkwardly situated.她的处境困难。

7 extremity   

n.末端，尽头；尽力；终极；极度

参考例句：

• I hope you will help them in their extremity.我希望你能帮助在穷途末路的他们。
• What shall we do in this extremity?在这种极其困难的情况下我们该怎么办呢？

8 virtue   

n.德行，美德；贞操；优点；功效，效力

参考例句：

• He was considered to be a paragon of virtue.他被认为是品德尽善尽美的典范。
• You need to decorate your mind with virtue.你应该用德行美化心灵。

9 constraint   

n.(on)约束，限制；限制(或约束)性的事物

参考例句：

• The boy felt constraint in her presence.那男孩在她面前感到局促不安。
• The lack of capital is major constraint on activities in the informal sector.资本短缺也是影响非正规部门生产经营的一个重要制约因素。

10 mathematicians   

数学家( mathematician的名词复数 )

参考例句：

• Do you suppose our mathematicians are unequal to that? 你以为我们的数学家做不到这一点吗？ 来自英汉文学
• Mathematicians can solve problems with two variables. 数学家们可以用两个变数来解决问题。 来自哲学部分

11 determined   

adj.坚定的；有决心的

参考例句：

• I have determined on going to Tibet after graduation.我已决定毕业后去西藏。
• He determined to view the rooms behind the office.他决定查看一下办公室后面的房间。

12 fully   

adv.完全地，全部地，彻底地；充分地

参考例句：

• The doctor asked me to breathe in,then to breathe out fully.医生让我先吸气，然后全部呼出。
• They soon became fully integrated into the local community.他们很快就完全融入了当地人的圈子。

13 spherical   

adj.球形的；球面的

参考例句：

• The Earth is a nearly spherical planet.地球是一个近似球体的行星。
• Many engineers shy away from spherical projection methods.许多工程师对球面投影法有畏难情绪。

14 centripetal   

adj.向心的

参考例句：

• After some treatment of centripetal force,he deduces Kepler's third law.在向心力的一些论述之后，他推出了开普勒的第三定律。
• It is called the centripetal acceleration.这叫做向心加速度。

15 extremities   

n.端点( extremity的名词复数 )；尽头；手和足；极窘迫的境地

参考例句：

• She was most noticeable, I thought, in respect of her extremities. 我觉得她那副穷极可怜的样子实在太惹人注目。 来自辞典例句
• Winters may be quite cool at the northwestern extremities. 西北边区的冬天也可能会相当凉。 来自辞典例句

16 concurrent   

adj.同时发生的，一致的

参考例句：

• You can't attend two concurrent events!你不能同时参加两项活动！
• The twins had concurrent birthday. 双胞胎生日在同一天。

17 lesser   

adj.次要的，较小的；adv.较小地，较少地

参考例句：

• Kept some of the lesser players out.不让那些次要的球员参加联赛。
• She has also been affected,but to a lesser degree.她也受到波及，但程度较轻。

18 postulate   

n.假定，基本条件；vt.要求，假定

参考例句：

• Let's postulate that she is a cook.我们假定她是一位厨师。
• Freud postulated that we all have a death instinct as well as a life instinct.弗洛伊德曾假定我们所有人都有生存本能和死亡本能。

19 necessitated   

使…成为必要，需要( necessitate的过去式和过去分词 )

参考例句：

• Recent financial scandals have necessitated changes in parliamentary procedures. 最近的金融丑闻使得议会程序必须改革。
• No man is necessitated to do wrong. 没有人是被迫去作错事的。

20 corroborates   

v.证实，支持（某种说法、信仰、理论等）( corroborate的第三人称单数 )

参考例句：

• This article narrates a innovated dynamic penetration test method that mainly corroborates soil bearing capacity. 探讨了一种改进的动力触探方法，主要用于确定土的承载力。 来自互联网
• David, soon to be king of Israel, had an experience that corroborates this idea. 大卫即将成为以色列的国王之际，曾有过一次这样的经历。 来自互联网

21 alteration   

n.变更，改变；蚀变

参考例句：

• The shirt needs alteration.这件衬衣需要改一改。
• He easily perceived there was an alteration in my countenance.他立刻看出我的脸色和往常有些不同。

22 northward   

adv.向北；n.北方的地区

参考例句：

• He pointed his boat northward.他将船驶向北方。
• I would have a chance to head northward quickly.我就很快有机会去北方了。

23 circumference   

n.圆周，周长，圆周线

参考例句：

• It's a mile round the circumference of the field.运动场周长一英里。
• The diameter and the circumference of a circle correlate.圆的直径与圆周有相互关系。