Chapter 4

That there is no other form of motion opposed as contrary to the circular may be proved in various ways. In the first place, there is an obvious tendency to oppose the straight line to the circular. For concave and convex are a not only regarded as opposed to one another, but they are also coupled together and treated as a unity¹ in opposition² to the straight. And so, if there is a contrary to circular motion, motion in a straight line must be recognized as having the best claim to that name. But the two forms of rectilinear motion are opposed to one another by reason of their places; for up and down is a difference and a contrary opposition in place. Secondly³, it may be thought that the same reasoning which holds good of the rectilinear path applies also the circular, movement from A to B being opposed as contrary to movement from B to A. But what is meant is still rectilinear motion. For that is limited to a single path, while the circular paths which pass through the same two points are infinite in number. Even if we are confined to the single semicircle and the opposition is between movement from C to D and from D to C along that semicircle, the case is no better. For the motion is the same as that along the diameter, since we invariably regard the distance between two points as the length of the straight line which joins them. It is no more satisfactory to construct a circle and treat motion ‘along one semicircle as contrary to motion along the other. For example, taking a complete circle, motion from E to F on the semicircle G may be opposed to motion from F to E on the semicircle H. But even supposing these are contraries, it in no way follows that the reverse motions on the complete circumference⁴ contraries. Nor again can motion along the circle from A to B be regarded as the contrary of motion from A to C: for the motion goes from the same point towards the same point, and contrary motion was distinguished⁵ as motion from a contrary to its contrary. And even if the motion round a circle is the contrary of the reverse motion, one of the two would be ineffective: for both move to the same point, because that which moves in a circle, at whatever point it begins, must necessarily pass through all the contrary places alike. (By contrarieties of place I mean up and down, back and front, and right and left; and the contrary oppositions⁶ of movements are determined⁷ by those of places.) One of the motions, then, would be ineffective, for if the two motions were of equal strength, there would be no movement either way, and if one of the two were preponderant, the other would be inoperative. So that if both bodies were there, one of them, inasmuch as it would not be moving with its own movement, would be useless, in the sense in which a shoe is useless when it is not worn. But God and nature create nothing that has not its use.

1 unity   

n.团结，联合，统一；和睦，协调

参考例句：

• When we speak of unity,we do not mean unprincipled peace.所谓团结，并非一团和气。
• We must strengthen our unity in the face of powerful enemies.大敌当前，我们必须加强团结。

2 opposition   

n.反对，敌对

参考例句：

• The party leader is facing opposition in his own backyard.该党领袖在自己的党內遇到了反对。
• The police tried to break down the prisoner's opposition.警察设法制住了那个囚犯的反抗。

3 secondly   

adv.第二，其次

参考例句：

• Secondly,use your own head and present your point of view.第二，动脑筋提出自己的见解。
• Secondly it is necessary to define the applied load.其次，需要确定所作用的载荷。

4 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。

5 distinguished   

adj.卓越的，杰出的，著名的

参考例句：

• Elephants are distinguished from other animals by their long noses.大象以其长长的鼻子显示出与其他动物的不同。
• A banquet was given in honor of the distinguished guests.宴会是为了向贵宾们致敬而举行的。

6 oppositions   

（强烈的）反对( opposition的名词复数 )； 反对党； （事业、竞赛、游戏等的）对手； 对比

参考例句：

• That's fine because all perihelic oppositions of Mars are spectacular. 但它和最近的几次区别不大，因为火星所有的近日对冲都很壮观。
• He tried his best to bear down all of his oppositions. 他尽全力击败一切反对意见。

7 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。