FOR THE HUMAN MIND the absolute continuity of motion is inconceivable. The laws of motion of any kind only become comprehensible to man when he examines units of this motion, arbitrarily selected. But at the same time it is from this arbitrary division of continuous motion into discontinuous units that a great number of human errors proceeds.

We all know the so-called sophism¹ of the ancients, proving that Achilles would never overtake the tortoise, though Achilles walked ten times as fast as the tortoise. As soon as Achilles passes over the space separating him from the tortoise, the tortoise advances one-tenth of that space: Achilles passes over that tenth, but the tortoise has advanced a hundredth, and so on to infinity². This problem seemed to the ancients insoluble. The irrationality³ of the conclusion (that Achilles will never overtake the tortoise) arises from the arbitrary assumption of disconnected units of motion, when the motion both of Achilles and the tortoise was continuous.

By taking smaller and smaller units of motion we merely approach the solution of the problem, but we never attain⁴ it. It is only by assuming an infinitely⁵ small magnitude, and a progression rising from it up to a tenth, and taking the sum of that geometrical progression, that we can arrive at the solution of the problem. A new branch of mathematics, dealing⁶ with infinitely small quantities, gives now in other more complex problems of dynamics⁷ solutions of problems that seemed insoluble.

This new branch of mathematics, unknown to the ancients, by assuming infinitely small quantities, that is, such as secure the chief condition of motion (absolute continuity), corrects the inevitable⁸ error which the human intellect cannot but make, when it considers disconnected units of motion instead of continuous motion.

In the

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1 sophism
n.诡辩
参考例句：
Have done with your foolish sophism.结束你那愚蠢的诡辩。 I wasn't taken in by his sophism.我没有被他的诡辩骗倒。

2 infinity
n.无限，无穷，大量
参考例句：
It is impossible to count up to infinity.不可能数到无穷大。 Theoretically,a line can extend into infinity.从理论上来说直线可以无限地延伸。

3 irrationality
n. 不合理，无理性
参考例句：
Such stoppages as are observed in practice are thus attributed to mistakes or even irrationality. 在实际情况中看到的这些停工，要归因于失误或甚至是非理性的东西。 For all its harshness and irrationality, it is the only world we've got. 尽管它严酷而又不合理，它终究是我们具有的唯一的世界。

4 attain
vt.达到，获得，完成
参考例句：
I used the scientific method to attain this end. 我用科学的方法来达到这一目的。 His painstaking to attain his goal in life is praiseworthy. 他为实现人生目标所下的苦功是值得称赞的。

5 infinitely
adv.无限地，无穷地
参考例句：
There is an infinitely bright future ahead of us.我们有无限光明的前途。 The universe is infinitely large.宇宙是无限大的。

6 dealing
n.经商方法，待人态度
参考例句：
This store has an excellent reputation for fair dealing.该商店因买卖公道而享有极高的声誉。 His fair dealing earned our confidence.他的诚实的行为获得我们的信任。

7 dynamics
n.力学，动力学，动力，原动力；动态
参考例句：
In order to succeed,you must master complicated knowledge of dynamics.要取得胜利，你必须掌握很复杂的动力学知识。 Dynamics is a discipline that cannot be mastered without extensive practice.动力学是一门不做大量习题就不能掌握的学科。

8 inevitable
adj.不可避免的，必然发生的
参考例句：
Mary was wearing her inevitable large hat.玛丽戴着她总是戴的那顶大帽子。 The defeat had inevitable consequences for British policy.战败对英国政策不可避免地产生了影响。

9 investigation
n.调查，调查研究
参考例句：
In an investigation,a new fact became known, which told against him.在调查中新发现了一件对他不利的事实。 He drew the conclusion by building on his own investigation.他根据自己的调查研究作出结论。

10 precisely
adv.恰好，正好，精确地，细致地
参考例句：
It's precisely that sort of slick sales-talk that I mistrust.我不相信的正是那种油腔滑调的推销宣传。 The man adjusted very precisely.那个人调得很准。

11 proceeding
n.行动，进行，(pl.)会议录，学报
参考例句：
This train is now proceeding from Paris to London.这次列车从巴黎开往伦敦。 The work is proceeding briskly.工作很有生气地进展着。

12 calculus
n.微积分；结石
参考例句：
This is a problem where calculus won't help at all.对于这一题，微积分一点也用不上。 After studying differential calculus you will be able to solve these mathematical problems.学了微积分之后，你们就能够解这些数学题了。

13 habitual
adj.习惯性的；通常的，惯常的
参考例句：
He is a habitual criminal.他是一个惯犯。 They are habitual visitors to our house.他们是我家的常客。

14 plunder
vt.劫掠财物，掠夺；n.劫掠物，赃物；劫掠
参考例句：
The thieves hid their plunder in the cave.贼把赃物藏在山洞里。 Trade should not serve as a means of economic plunder.贸易不应当成为经济掠夺的手段。

15 slaughter
n.屠杀，屠宰；vt.屠杀，宰杀
参考例句：
I couldn't stand to watch them slaughter the cattle.我不忍看他们宰牛。 Wholesale slaughter was carried out in the name of progress.大规模的屠杀在维护进步的名义下进行。

16 inquiry
n.打听，询问，调查，查问
参考例句：
Many parents have been pressing for an inquiry into the problem.许多家长迫切要求调查这个问题。 The field of inquiry has narrowed down to five persons.调查的范围已经缩小到只剩5个人了。

17 detailed
adj.详细的，详尽的，极注意细节的，完全的
参考例句：
He had made a detailed study of the terrain.他对地形作了缜密的研究。 A detailed list of our publications is available on request.我们的出版物有一份详细的目录备索。

18 favourably
adv. 善意地，赞成地 =favorably
参考例句：
The play has been favourably commented by the audience. 本剧得到了观众的好评。 The open approach contrasts favourably with the exclusivity of some universities. 这种开放式的方法与一些大学的封闭排外形成了有利的对比。

19 warfare
n.战争(状态)；斗争；冲突
参考例句：
He addressed the audience on the subject of atomic warfare.他向听众演讲有关原子战争的问题。 Their struggle consists mainly in peasant guerrilla warfare.他们的斗争主要是农民游击战。

20 vibration
n.颤动，振动；摆动
参考例句：
There is so much vibration on a ship that one cannot write.船上的震动大得使人无法书写。 The vibration of the window woke me up.窗子的震动把我惊醒了。

21 devoted
adj.忠诚的，忠实的，热心的，献身于...的
参考例句：
He devoted his life to the educational cause of the motherland.他为祖国的教育事业贡献了一生。 We devoted a lengthy and full discussion to this topic.我们对这个题目进行了长时间的充分讨论。