1. 数学是知识的工具，亦是其它知识工具的泉源。所有研究顺序和度量的科学均和数学有关。

1. Mathematics is a tool of knowledge and also the source of other tools of knowledge. All sciences that deal with order and measurement are related to mathematics.

2. 数学是人类知识活动留下来最具威力的知识工具，是一些现象的根源。数学是不变的，是客观存在的，上帝必以数学法则建造宇宙。

2. Mathematics is the most powerful knowledge tool left behind by human intellectual activities and is the source of some phenomena. Mathematics is immutable and objectively exists; God must have constructed the universe according to mathematical laws.

3. 越学习，越发现自己的无知。

3. The more one learns, the more one realizes the extent of one's ignorance.

4. 反对的意见在两方应对于我都有益，一方面是使我知道自我的错误，一方面是多数人看到的比一个人看到的更明白。

4. The opposing opinions are beneficial to me on both sides: one is that they make me aware of my own mistakes, and the other is that what a majority sees is clearer than what a single individual sees.

5. 要以探求真理为毕生的事业。

5. It is one's lifelong pursuit to seek the truth.

6. 笛卡尔名言名句,读一切好书，就是和许多高尚的人谈话：

6. A famous saying by Descartes: Reading all good books is like conversing with many noble individuals.

7. 野生的禽兽只有身体需要保护，就经常不断地从事寻求养身的食物；然而人的主要部分是心灵，就应该把主要精力放在寻求智慧上，智慧才是他真正的养料。

7. Wild animals only need to protect their bodies, so they constantly seek food for their health; however, the main part of humans is the soul, and thus their main energy should be focused on seeking wisdom, as wisdom is their true nourishment.

8. 意志、悟性、想像力以及感觉上的一切作用，全由思维而来。

8. All the functions of will, intellect, imagination, and the senses are derived from thought.

9. 意志悟性想象力以及感觉上的一切作用，全由思维而来。

9. Will, understanding, imagination, and all the functions of sensation are all derived from thought.

10. 读杰出的书籍，有如和过去最杰出的人物促膝交谈。

10. Reading outstanding books is like engaging in intimate conversations with the most distinguished figures of the past.

11. 仅仅是具备出色的智力是不够的，注要的问题是如何出色地使用它。

11. It is not enough to simply possess outstanding intelligence; the key issue is how to use it excellently.

12. 当感情只是劝咱们去做能够缓行的事的时候，应当克制自我不好立刻作出任何决定，用另一些思想使自我定务必神，直到时刻和休息使血液中的情绪完全安定下来。

12. When emotions merely urge us to do things that can be delayed, we should克制 ourselves from making any decisions immediately, and instead use other thoughts to steady ourselves, until time and rest allow the emotions in our blood to completely settle down.

13. 意志、悟性、想象力以及感觉上的一切作用，全由思维而来。

13. All the functions of will, intellect, imagination, and sensation are derived from thought.

14. 世界之大，而能获得最公平分配的是常识。

14. In the vastness of the world, common sense is the one that can achieve the fairest distribution.

15. 单靠加工别人的作品是很难做出十分完美的东西的。

15. It's difficult to create something perfectly exquisite solely by processing others' works.

16. 要想知道他们真正的看法，一定要看他们的实际行动，不能光听他们说的话。

16. To know their true opinions, one must observe their actual actions, not just listen to what they say.

17. 理智和良知是惟一使我们人之所以为人并与动物有区别的东西，我相信它是完整地存在于个人身上的。

17. Reason and conscience are the only things that distinguish us humans from animals, and I believe they exist fully within each individual.

18. 反对的意见在两方面对我有益，一方面是使我知道自己的错误，一方面是多数人看到的比一个人看到的更明白。

18. The opposing opinions were beneficial to me in two ways: one is that they made me aware of my own mistakes, and the other is that what the majority sees is clearer than what an individual sees.

19. 行动十分迁腐的人，只要始于循着正道前进，就能够比离开正道飞奔的人走在前面很多。

19. A person who acts very pedantically, as long as they start by going along the right path, can walk much ahead of those who rush off the path.

20. 怀疑中我常常处于迷失状态，幸亏思想最终让我发现“我是真实的”，我思故我在。

20. Often in doubt, I find myself lost, fortunate that my thoughts eventually led me to discover 'I am real', I think, therefore I am.

21. 一切的好书，读起来就像和过来世界上最出色的人们的说话。

21. All great books are like conversations with the most outstanding people in the world.

22. 在这个世界上，良知被分配得最为公平。

22. In this world, conscience is distributed the most fairly.

23. 怀疑是智慧的源头。

23. Doubt is the source of wisdom.

24. 关于经验，我还注意到了一件事，就是认识越进步越需要经验。

24. Regarding experience, I have also noticed one thing: the more advanced one's understanding becomes, the more experience is needed.

25. 读好书，有如探访著书的先贤，同他们促膝谈心，而且是一种精湛的交谈。

25. Reading good books is like visiting the sages who wrote them, engaging in close conversations with them, and it is a refined kind of dialogue.

26. 恐惧的主要原因是惊奇，摆脱它的最好办法是临事先思考，并使自己对所有不测事件（惊奇是由对它们的害怕引起的）有所准备。

26. The main cause of fear is surprise, and the best way to overcome it is to think about it beforehand and prepare yourself for all unforeseen events (which surprise is caused by fear of them).

27. 有了正确的判断，就可以有正确的行动，判断得尽可能正确，行动也就尽可能正确。

27. With correct judgment, there can be correct action; the more accurate the judgment, the more accurate the action.

28. 一个为情感所支配，行为便没有自主之权，而受命运的宰割。

28. Being dominated by emotions, one loses the autonomy of behavior and is at the mercy of fate.

29. 行动十分迁腐的人，只要始于循着正道前进，就可以比离开正道飞奔的人走在前面很多。

29. A person who is overly conservative in action, as long as they start by following the right path, can be much ahead of those who run away from the right path.

30. 我思，故我在。

30. I think, therefore I am.

31. 仅仅具备出色的智力是不够的，主要的问题是如何出色地使用它。

31. Merely having an outstanding intellect is not enough; the main issue is how to use it exceptionally well.

32. 越是希望好好利用今后的时间，就越应当精打细算，好好安排。

32. The more one hopes to make good use of the time ahead, the more careful one should be in budgeting and planning.

33. 当我怀疑一切事物的存在时，我却不用怀疑我本身的思想，正因此时我唯一能够确定的事就是我自我思想的存在。

33. When I doubt the existence of everything, I do not doubt the existence of my own thoughts; it is precisely because of this that the only thing I can be certain of at this moment is the existence of my own self-thought.

34. 我们的错误不能诿诸上帝。不过，上帝虽然没有给我们一个全知的理解，我们却万不能因此就说他是我们错误的造成者、因为被创造的智力其本性就是有限的，而有限的智力其本性就是不能把握一切事物的。

34. Our mistakes cannot be attributed to God. However, even though God has not given us a full understanding, we must never say that He is the cause of our errors, for the created intelligence has a finite nature, and the nature of finite intelligence is that it cannot grasp everything.

35. 意志悟性想像力以及感觉上的一切作用，全由思维而来。

35. Will, intellect, imagination, and all sensory functions are all derived from thought.

36. 实在说来，没有知识的人总爱议论别人的无知，知识丰富的人却时时发现自己的无知。

36. To be honest, those without knowledge are always fond of commenting on the ignorance of others, while those with abundant knowledge frequently discover their own ignorance.

37. 这三点对应着三种心理功能，外来的观念依赖于感觉；虚构的观念借助于想象；而天赋观念则出于纯粹理智。

37. These three points correspond to three psychological functions: external ideas depend on sensation; imaginative ideas rely on imagination; and innate ideas arise from pure reason.

38. 勒内笛卡儿简介

38. Introduction to René Descartes

39. 我决心放下那个仅仅是抽象的几何。这就是说，不再去研究那些仅仅是用来练思想的问题。我这样做，是为了研究另一种几何，即目的在于解释自然现象的几何。

39. I am resolved to put aside that geometry which is merely abstract. This means that I will no longer delve into those problems that are simply used to exercise the mind. I am doing this in order to study another type of geometry, which aims to explain natural phenomena.

40. 勒内·笛卡尔（又译作勒内·笛卡儿），生于法国安德尔-卢瓦尔省的图赖讷拉海，1650年2月11日逝世于瑞典斯德哥尔摩，是法国著名的哲学家、数学家、物理学家。他是西方近代资产阶级哲学奠基人之一。

40. René Descartes (also spelled René Descartes), born in Touraine-la-Rochette, Indre-et-Loire province of France, died on February 11, 1650 in Stockholm, Sweden. He was a renowned French philosopher, mathematician, and physicist. He is one of the founders of modern Western资产阶级 philosophy.

41. 无法做出决策的人，或欲望过大，或觉悟不足。

41. People who cannot make decisions are either too greedy or lack sufficient awareness.