1. 解析几何的产生并不是偶然的。在笛卡尔写《几何学》以前，就有许多学者研究过用两条相交直线作为一种坐标系；也有人在研究天文、地理的时候，提出了一点位置可由两个“坐标”（经度和纬度）来确定。这些都对解析几何的创建产生了很大的影响。

1. The emergence of analytical geometry was not accidental. Before Descartes wrote "Geometry," many scholars had already studied using two intersecting lines as a coordinate system; some also proposed that a point's position could be determined by two "coordinates" (longitude and latitude) when studying astronomy and geography. All these had a significant impact on the creation of analytical geometry.

2. 1806年，公爵在抵抗拿破仑统帅的法军时不幸阵亡，这给高斯以沉重打击。他悲痛欲绝，长时间对法国人有一种深深的敌意。大公的去世给高斯带来了经济上的拮据，德国处于法军奴役下的不幸，以及第一个妻子的逝世，这一切使得高斯有些心灰意冷，但他是位刚强的汉子，从不向他人透露自己的窘况，也不让朋友安慰自己的不幸。人们只是在19世纪整理他的未公布于众的数学手稿时才得知他那时的心态。在一篇讨论椭圆函数的手搞中，突然插入了一段细微的铅笔字："对我来说，死去也比这样的生活更好受些。"

2. In 1806, the Duke, while resisting the French army led by Napoleon, unfortunately met his demise, which dealt Gauss a heavy blow. He was overwhelmed with grief and harbored a deep resentment towards the French for a long time. The death of the Duke brought financial hardship to Gauss, the misfortune of Germany under the yoke of the French army, and the passing of his first wife, all of which left Gauss somewhat despondent. However, he was a strong man who never revealed his difficulties to others and never allowed friends to comfort him in his misfortune. People only learned about his state of mind when they整理ed his unpublished mathematical manuscripts in the 19th century. In one of his drafts discussing elliptic functions, there was a sudden insertion of a faint pencil note: "For me, death would be more bearable than such a life."

3. 章54篇，翻译《死魂灵》第二部残稿三章并作附记两则，复信270多封，并给不少青

3. Chapter 54, translated three chapters of the unfinished manuscript of the second part of "The Dead Souls" and wrote two annotations, replied to more than 270 letters, and helped many young people.

4. 莱布尼兹在阿尔特道夫大学获得博士学位后便投身外交界。在出访巴黎时，莱布尼兹深受帕斯卡事迹的鼓舞，决心钻研高等数学，并研究了笛卡儿、费尔马、帕斯卡等人的著作。他的兴趣已明显地朝向了数学和自然科学，开始了对无穷小算法的研究，独立地创立了微积分的基本概念与算法，和牛顿并蒂双辉共同奠定了微积分学。1700年被选为巴黎科学院院士，促成建立了柏林科学院并任首任院长。

4. After obtaining his doctorate from the University of Alt돈, Leibniz threw himself into the diplomatic world. During his visit to Paris, Leibniz was greatly inspired by Pascal's achievements and decided to delve into higher mathematics, studying the works of Descartes, Fermat, Pascal, and others. His interests had clearly shifted towards mathematics and natural sciences, beginning his research on infinitesimal algorithms. He independently established the basic concepts and algorithms of calculus, and, together with Newton, laid the foundation for the discipline of calculus. In 1700, he was elected to the Académie des Sciences in Paris, which contributed to the establishment of the Berlin Academy of Sciences and served as its first president.

5. 高斯的研究领域，遍及纯粹数学和应用数学的各个领域，并且开辟了许多新的数学领域，从最抽象的代数数论到内蕴几何学，都留下了他的足迹。从研究风格、方法乃至所取得的具体成就方面，他都是18—19世纪之交的中坚人物。如果我们把18世纪的数学家想象为一系列的高山峻岭，那么最后一个令人肃然起敬的巅峰就是高斯；如果把19世纪的数学家想象为一条条江河，那么其源头就是高斯。

5. Gauss's research areas covered all fields of pure mathematics and applied mathematics, and he opened up many new areas of mathematics, leaving his mark from the most abstract algebraic number theory to intrinsic geometry. From his research style, methods, to his specific achievements, he was a key figure at the turn of the 18th to the 19th century. If we imagine 18th-century mathematicians as a series of towering mountains, then the last majestic peak is Gauss; if we envision 19th-century mathematicians as a series of rivers, then Gauss is the source.

6. 的时间，鲁迅一直住在上海虹口公园附近，从他的住地到公园只有几分钟的路程，却

6. During this period, Lu Xun has been living near Hongkou Park in Shanghai. The distance from his residence to the park is only a few minutes' walk, yet

7. 在全世界广为流传的一则故事说，高斯10岁时算出布特纳给学生们出的将1到100的所有整数加起来的算术题，布特纳刚叙述完题目，高斯就算出了正确答案。不过，这很可能是一个不真实的传说。据对高斯素有研究的著名数学史家E·T·贝尔（ETBell）考证，布特纳当时给孩子们出的是一道更难的加法题：81297+81495+81693+…+100899。

7. A widely circulated story across the world tells that when Gauss was 10 years old, he solved the arithmetic problem given by Butner, which was to add up all the integers from 1 to 100. As soon as Butner finished explaining the problem, Gauss calculated the correct answer. However, this is likely an unfounded legend. According to the research of E.T. Bell, a renowned historian of mathematics who specialized in Gauss, Butner actually gave the children a more difficult addition problem at that time: 81297 + 81495 + 81693 + … + 100899.

8. 有一句格言说：“只因准备不足，导致失败。”这句话可以写在无数可怜失败者的墓志铭上。有些人虽然肯努力、肯牺牲，但由于在知识和经验上准备不足，做事大费周折，始终达不到目的、实现不了成功的梦想。

8. There is a proverb that says, "Failure is due to insufficient preparation." This sentence could be inscribed on the gravestones of countless可怜 failures. Some people may be willing to work hard and make sacrifices, but due to insufficient preparation in terms of knowledge and experience, they face great difficulties in their endeavors, and they can never achieve their goals or realize their dreams of success.

9. 总的来说，解析几何运用坐标法可以解决两类基本问题：一类是满足给定条件点的轨迹，通过坐标系建立它的方程；另一类是通过方程的讨论，研究方程所表示的曲线性质。

9. In general, analytical geometry, using the coordinate method, can solve two basic types of problems: one is the trajectory of points that satisfy given conditions, establishing its equation through the coordinate system; the other is studying the properties of the curve represented by the equation through discussions of the equation.

10. 、我国国画大师齐白石，坚持每日作画，除身体不适外，从不间断。85岁那

10. China's renowned master of traditional Chinese painting, Qi Baishi, was committed to painting every day, never taking a break except when he was physically unwell. At the age of 85, he still...

11. 莱布尼兹出生于德国东部莱比锡的一个书香之家，广泛接触古希腊罗马文化，阅读了许多著名学者的著作，由此而获得了坚实的文化功底和明确的学术目标。15岁时，他进了莱比锡大学学习法律，还广泛阅读了培根、开普勒、伽利略、等人的著作，并对他们的著述进行深入的思考和评价。在听了教授讲授欧几里德的《几何原本》的课程后，莱布尼兹对数学产生了浓厚的兴趣。17岁时他在耶拿大学学习了短时期的数学，并获得了哲学硕士学位。

11. Leibniz was born into a scholarly family in Leipzig, eastern Germany, and had extensive exposure to ancient Greek and Roman culture, reading the works of many famous scholars, which gave him a solid cultural foundation and a clear academic goal. At the age of 15, he enrolled at the University of Leipzig to study law and extensively read the works of Bacon, Kepler, Galileo, and others, deeply thinking and evaluating their writings. After listening to a professor's lecture on Euclid's "Elements," Leibniz developed a strong interest in mathematics. At the age of 17, he studied mathematics for a short period at the University of Jena and obtained a Master's degree in philosophy.

12. 为了不使德国失去最伟大的天才，德国著名学者洪堡（BAVon Humboldt）联合其他学者和政界人物，为高斯争取到了享有特权的哥丁根大学数学和天文学教授，以及哥丁根天文台台长的职位。1807年，高斯赴哥丁根就职，全家迁居于此。从这时起，除了一次到柏林去参加科学会议以外，他一直住在哥丁根。洪堡等人的努力，不仅使得高斯一家人有了舒适的生活环境，高斯本人可以充分发挥其天才，而且为哥丁根数学学派的创立、德国成为世界科学中心和数学中心创造了条件。同时，这也标志着科学研究社会化的一个良好开端。

12. In order to prevent Germany from losing its greatest genius, the famous German scholar, Baron von Humboldt, joined forces with other scholars and political figures to secure for Gauss the position of a privileged professor of mathematics and astronomy at the University of Göttingen, as well as the post of director of the Göttingen Observatory. In 1807, Gauss moved to Göttingen to take up his post, and the whole family settled there. From this time on, except for one trip to Berlin to attend a scientific conference, he lived in Göttingen. The efforts of Humboldt and others not only provided Gauss and his family with a comfortable living environment but also allowed Gauss to fully utilize his genius. Moreover, these efforts created conditions for the establishment of the Göttingen School of Mathematics and for Germany to become a world center of science and mathematics. At the same time, this also marked a good beginning for the socialization of scientific research.

13. 、鲁迅以“时间就是生命”的格言律己，从事无产阶级文艺事业30年，视时间

己如生命，鲁迅以“时间就是生命”的格言律己，从事无产阶级文艺事业30年，视时间如生命。 Translation: 13. Lu Xun, governed by the maxim "Time is life," dedicated himself to the cause of proletarian literature and art for 30 years, treating time as if it were his life. Lu Xun adhered to the maxim "Time is life" to discipline himself, and for 30 years, he engaged in the cause of proletarian literature and art, valuing time as his life.

14. 莱布尼兹是17、18世纪之交德国最重要的数学家、物理学家和哲学家，一个举世罕见的科学天才。他博览群书，涉猎百科，对丰富人类的科学知识宝库做出了不可磨灭的贡献。

14. Leibniz was the most important mathematician, physicist, and philosopher in Germany at the turn of the 17th and 18th centuries, a world-renowned scientific genius. He had read extensively, delved into encyclopedias, and made an indelible contribution to the treasure trove of human scientific knowledge.

15. 然而关于微积分创立的优先权，数学上曾掀起了一场激烈的争论。实际上，牛顿在微积分方面的研究虽早于莱布尼兹，但莱布尼兹成果的发表则早于牛顿。莱布尼兹在1684年10月发表的《教师学报》上的论文，"一种求极大极小的奇妙类型的计算"，在数学史上被认为是最早发表的微积分文献。牛顿在1687年出版的《自然哲学的数学原理》的第一版和第二版也写道："十年前在我和最杰出的几何学家G

15. However, there has been a fierce debate in mathematics regarding the priority of the creation of calculus. In fact, although Newton's research in calculus was earlier than Leibniz's, the publication of Leibniz's work was earlier than Newton's. Leibniz's paper, "A wonderful type of calculation for finding maxima and minima," published in the "Journal of the Teacher" in October 1684, is considered the earliest published document on calculus in the history of mathematics. Newton also wrote in the first and second editions of his book "Principia Mathematica Philosophiae Naturalis" published in 1687: "Ten years ago, in collaboration with the most outstanding geometers G..."

16. 在平面解析几何中，除了研究直线的有关直线的性质外，主要是研究圆锥曲线（圆、椭圆、抛物线、双曲线）的有关性质。

16. In analytical geometry in the plane, besides studying the properties of lines, the main focus is on the properties of conic sections (circles, ellipses, parabolas, hyperbolas).

17. 这是一个著名的悖论，称为“罗素悖论”。这是由英国哲学家罗素提出来的，他把关于集合论的一个著名悖论用故事通俗地表述出来。

17. This is a famous paradox known as the "Russell's Paradox." It was proposed by the British philosopher Russell, who expressed a well-known paradox in set theory in a popular story form.

18. △法国科学幻想小说家儒勒·凡尔纳，为了写作《月球探险记》，就认真阅读了500多种图书资料。他一生之中共创作了104部科幻小说。读书笔记达二万五千本。

18. △The French science fiction writer Jules Verne, in order to write "The Journey to the Moon," carefully read over 500 types of books and materials. Throughout his life, he wrote a total of 104 science fiction novels. His reading notes reached 25,000 in number.

19. 所有成功的背后，都是苦苦堆积的坚持；所有人前的风光，都是背后傻傻的不放弃。只要你愿意，并为之坚持，总有一天，你会活成自己喜欢的模样！

19. Behind all success is the relentless accumulation of perseverance; all the glitz and glamour in front of others is the foolish determination behind the scenes. As long as you are willing and persevere, one day, you will live out the image of yourself that you like!

20. 即使在商业领域也如此。那些学识渊博、经验丰富的人，比那些庸庸碌碌、不学无术的人，成功的机会更大。

20. This is also true in the commercial field. People with extensive knowledge and rich experience have a greater chance of success than those who are mundane and lack scholarly skills.

21. 没有比脚更长的路，没有比人更高的山，没有做不到的事，只有想不到的人。阻挡你前进的不是高山大海，而往往是自己鞋底一粒小小的沙粒！

21. There is no path longer than a person's feet, no mountain higher than a person, no task that cannot be accomplished, and only people who cannot think of it. What hinders your progress is often not the great mountains and seas, but rather a tiny grain of sand on the bottom of your shoes!

22. 为了实现上述的设想，笛卡尔茨从天文和地理的经纬制度出发，指出平面上的点和实数对(x,y)的对应关系。x,y的不同数值可以确定平面上许多不同的点，这样就可以用代数的方法研究曲线的性质。这就是解析几何的基本思想。

22. To realize the above vision, Descartes started from the astronomic and geographic systems of latitude and longitude, pointing out the correspondence between points on a plane and real number pairs (x, y). Different values of x and y can determine many different points on the plane, which allows the study of the properties of curves using algebraic methods. This is the fundamental idea of analytical geometry.

23. 椭圆、双曲线、抛物线的有些性质，在生产或生活中被广泛应用。比如**放映机的聚光灯泡的反射面是椭圆面，灯丝在一个焦点上，影片门在另一个焦点上；探照灯、聚光灯、太阳灶、雷达天线、卫星的天线、射电望远镜等都是利用抛物线的原理制成的。

23. Some properties of ellipses, hyperbolas, and parabolas are widely applied in production or daily life. For example, the reflector of a projector's spotlight is an elliptical surface, with the filament at one focus and the film gate at the other; searchlights, spotlights, solar cookers, radar antennas, satellite antennas, radio telescopes, and so on are all made using the principle of parabolas.

24. 年作者看稿，病中坚持写日记。病逝前三天，还给一翻译小说写序言。在逝世前六年

24. The author reviewed the manuscript while sick and persevered in writing a diary. Three days before his death, he even wrote a preface for a translated novel. In the six years before his death,

25. 高 斯

25. Gauss

26. 到报道的日子，林肯来到报道处考试，当他来到报道处时，发现监场的人是他曾经得罪过的人，他带着沉重的考完。当他问起那件得罪过他的事时，那个人说：“有吗？我不记得了。”

26. By the time of the report, Lincoln came to the reporting place for the exam. When he arrived at the reporting place, he found that the proctor was someone he had once offended. He finished the exam with a heavy heart. When he inquired about the incident that had offended him, the person said, "Is there such a thing? I don't remember."

27. 了吃饭、睡觉、活动，几乎没有闲过。每天延长工作时间就等于延长了生命。因此，

27. I have hardly had any leisure time for eating, sleeping, and activities. Extending work hours every day is like extending life. Therefore,

28. 比如这种人：在商店里工作多年，只会按顾客的要求拿东西，对商业一窍不通。他只是在挣钱糊口，不思考，不关心商品的特点和顾客的需求，如果他不被淘汰的话，只能当一辈子售货员。那些精明强干、善于思考的年轻人，却能在短时间内发现一个行业的秘密，时机一旦成熟，就能独当一面。

28. For instance, such people: they have worked in stores for many years, only knowing how to fetch items according to customers' requests, with no knowledge of business. They are just earning a living, without thinking or caring about the characteristics of products and customers' needs. If they are not eliminated, they can only be sales clerks for a lifetime. On the other hand, those clever and capable young people can discover the secrets of an industry in a short time. Once the right moment comes, they can stand on their own two feet.

29. 一天晚上，携爱妃举办烛光晚会，大宴群臣。酒至半酣，忽然一阵大风把蜡烛吹灭。一名武将欲乘黑调戏爱妃，被爱妃一把扯下盔上红缨，爱妃建议楚王即刻点灯，看看哪个家伙盔上红缨已失，严加惩办。朋友妻不可欺呀，何况是领导之妻呢？岂料庄王大度能容，下令众将全都摘去盔上红缨，然后方可点灯。不久，楚王御驾亲征与敌国开战，被困重围，手下兵将四散奔逃，楚王命悬一发，忽然窜出一将拼死力战，保楚王杀出重围，捡回一条性命。楚王激动地说：“别人都自逃性命，唯有爱卿肯舍命救驾，你叫什么？是哪个单位的？”该将答曰：“俺就是那日烛光晚会上调戏您媳妇的人啊！”

29. One evening, accompanied by his beloved concubine, he held a candlelit party and grandly entertained his ministers. As the wine was flowing, a sudden strong wind blew out the candles. A warrior wanted to take advantage of the darkness to flirt with the concubine, but she swiftly pulled off his helmet's red plume. The concubine suggested that the King of Chu immediately light the candles and see which scoundrel had lost his helmet's red plume, and severely punish him. "A friend's wife cannot be deceived, let alone the leader's wife?" she said. Unexpectedly, King Zhuang, with a magnanimous heart, ordered all the warriors to remove the red plumes from their helmets before lighting the candles. Soon, King of Chu led a personal expedition against the enemy and was besieged. His soldiers scattered and ran away, and King of Chu's life was hanging by a thread. Suddenly, a general emerged and fought fiercely to save King of Chu and break through the encirclement, saving his life. Overwhelmed with emotion, King of Chu said, "While everyone else was saving their own lives, only you were willing to sacrifice yours to save me. What is your name, and which unit are you from?" The general replied, "I am the one who flirted with your wife at the candlelit party that day!"

30. 从一个年轻人怎样利用零碎时间就可以预见他的前途。自强不息、随时求进步的精神，是一个人卓越超群的标志，更是一个人成功的征兆。

30. From how a young person utilizes spare time, one can foresee his future prospects. The spirit of self-improvement and constant pursuit of progress is a sign of a person's excellence and superiority, and it is also a harbinger of success.

31. 刘徽的一生是为数学刻苦探求的一生．他虽然地位低下，但人格高尚．他不是沽名钓誉的庸人，而是学而不厌的伟人，他给我们中华民族留下了宝贵的财富．

31. Liu Hui's life was a life of diligent pursuit of mathematics. Despite his lowly status, he possessed a noble character. He was not a commoner seeking fame and fortune, but a great person who never tired of learning. He has left behind a valuable heritage for our Chinese nation.

32. 解析几何的创立，引入了一系列新的数学概念，特别是将变量引入数学，使数学进入了一个新的发展时期，这就是变量数学的时期。解析几何在数学发展中起了推动作用。恩格斯对此曾经作过评价“数学中的转折点是笛卡尔的变数，有了变书，运动进入了数学；有了变数，辩证法进入了数学；有了变数，微分和积分也就立刻成为必要的了，……”

32. The establishment of analytical geometry introduced a series of new mathematical concepts, particularly the introduction of variables into mathematics, which led mathematics into a new period of development, known as the era of variable mathematics. Analytical geometry played a driving role in the development of mathematics. Engels once made an evaluation: "The turning point in mathematics is Descartes' variable; with the variable, motion entered mathematics; with the variable, dialectics entered mathematics; with the variable, differential and integral calculus also immediately became necessary,..."

33. 7岁那年，高斯第一次上学了。头两年没有什么特殊的事情。1787年高斯10岁，他进入了学习数学的班次，这是一个首次创办的班，孩子们在这之前都没有听说过算术这么一门课程。数学教师是布特纳（Buttner），他对高斯的成长也起了一定作用。

33. In his seventh year, Gauss began his first year of school. Nothing special happened in the first two years. In 1787, when Gauss was 10 years old, he entered a class for studying mathematics, which was a newly established class, and the children had never heard of a subject called arithmetic before. The mathematics teacher was Buttner, who also played a certain role in Gauss's growth.

34. 我还有不少在律师事务所的朋友，按从业时间来说，他们的资格够老的了，但他们仍然担任着平庸的职务，赚着低微的薪金。

34. I still have many friends at law firms, and by the length of their practice, they are quite experienced. However, they still hold mundane positions and earn modest salaries.

35. 运用坐标法解决问题的步骤是：首先在平面上建立坐标系，把已知点的轨迹的几何条件“翻译”成代数方程；然后运用代数工具对方程进行研究；最后把代数方程的性质用几何语言叙述，从而得到原先几何问题的答案。

35. The steps to solve problems using the coordinate method are as follows: First, establish a coordinate system on the plane and "translate" the geometric conditions of the trajectory of the known points into algebraic equations; then use algebraic tools to study the equations; finally, describe the properties of the algebraic equations in geometric language, thereby obtaining the answer to the original geometric problem.

36. 高斯的计算能力，更主要地是高斯独到的数学方法、非同一般的创造力，使布特纳对他刮目相看。他特意从汉堡买了最好的算术书送给高斯，说："你已经超过了我，我没有什么东西可以教你了。"接着，高斯与布特纳的助手巴特尔斯(JMBartels)建立了真诚的友谊，直到巴特尔斯逝世。他们一起学习，互相帮助，高斯由此开始了真正的数学研究。

36. Gauss's computational ability, but more importantly, his unique mathematical methods and extraordinary creativity, impressed Böttner greatly. He特意 purchased the best arithmetic books from Hamburg to gift to Gauss, saying, "You have surpassed me, and there is nothing I can teach you." Subsequently, Gauss and Böttner's assistant, Bartels (J.M. Bartels), formed a sincere friendship that lasted until Bartels' death. They studied together, helped each other, and it was through this that Gauss began his true mathematical research.

37. 我的一个朋友在一个律师事务所任职三年，尽管没有获得晋升，但他在这三年中，把律师事物所的门道都摸清了，还拿到了一个业余法律进修学院的毕业证书。一切都是为了开办他自己的律师事务所。

37. A friend of mine worked at a law firm for three years, although he did not receive a promotion, he got to know all the ins and outs of the law firm during these three years and also obtained a graduation certificate from an amateur law advanced study college. Everything was for the purpose of opening his own law firm.

38. 具体地说，平面解析几何的基本思想有两个要点：第一，在平面建立坐标系，一点的坐标与一组有序的实数对相对应；第二，在平面上建立了坐标系后，平面上的一条曲线就可由带两个变数的一个代数方程来表示了。从这里可以看到，运用坐标法不仅可以把几何问题通过代数的方法解决，而且还把变量、函数以及数和形等重要概念密切联系了起来。

38. Specifically, the basic ideas of plane analytical geometry consist of two main points: first, a coordinate system is established in the plane, where the coordinates of a point correspond to a set of ordered real number pairs; second, after establishing a coordinate system on the plane, a curve on the plane can be represented by an algebraic equation with two variables. From this, it can be seen that the use of the coordinate method not only solves geometric problems through algebraic methods but also closely connects important concepts such as variables, functions, numbers, and shapes.

39. 刘徽思想敏捷，方法灵活，既提倡推理又主张直观．他是我国最早明确主张用逻辑推理的方式来论证数学命题的人．

39. Liu Hui was quick-witted and flexible in his methods, advocating both reasoning and intuition. He was one of the earliest individuals in our country to explicitly advocate for using logical reasoning to prove mathematical propositions.

40. 笛卡尔的《几何学》，作为一本解析几何的书来看，是不完整的，但重要的是引入了新的思想，为开辟数学新园地做出了贡献。

40. Descartes' "Geometry" is incomplete when viewed as a book on analytical geometry, but what is important is that it introduced new ideas and contributed to the opening of a new garden in mathematics.

41. 年，一天他一连作画四幅后，又特为昨天补画一幅，并题字道：“昨日大风雨，心绪

41. One year, after he had painted four pictures in a row, he specially painted one more for yesterday and inscribed it: "Yesterday, there was a big storm and heavy rain, my mood..."

42. 有位商界的杰出人物这样说：“我的所有职员都从最基层做起。俗话说：‘对工作有利的，就是对自己有利的。’任何人在开始工作时如果能记住这句话，前途一定不可限量。”

42. An outstanding figure in the business world said this: "All of my staff start from the very bottom. As the saying goes, 'What is beneficial for the work is also beneficial for oneself.' If anyone can remember this phrase when they start working, their prospects are boundless."

43. 人能力有大小，水平有高低，但在心灵的质地上，人无贵贱之分，关键是要活出自己的本色。

43. People vary in abilities and levels, but in terms of the essence of the mind, there is no distinction between the noble and the humble. The key is to live out one's true character.

44. （生于公元250年左右），是中国数学史上一个非常伟大的数学家，在世界数学史上，也占有杰出的地位．他的杰作《九章算术注》和《海岛算经》，是我国最宝贵的数学遗产．

44. (Born around 250 AD), he was a very great mathematician in the history of Chinese mathematics and also occupied an outstanding position in the history of world mathematics. His masterpieces, "Commentaries on the Nine Chapters on the Mathematical Art" and "Mathematical Treatise on the Sea Island", are among our most precious mathematical heritage.

45. 1792年，高斯进入布伦兹维克的卡罗琳学院继续学习。1795年，公爵又为他支付各种费用，送他入德国著名的哥丁根大家，这样就使得高斯得以按照自己的理想，勤奋地学习和开始进行创造性的研究。1799年，高斯完成了博士论文，回到家乡布伦兹维克，正当他为自己的前途、生计担忧而病倒时—虽然他的博士论文顺利通过了，已被授予博士学位，同时获得了讲师职位，但他没有能成功地吸引学生，因此只能回老家-又是公爵伸手救援他。公爵为高斯付诸了长篇博士论文的印刷费用，送给他一幢公寓，又为他印刷了《算术研究》，使该书得以在1801年问世；还负担了高斯的所有生活费用。所有这一切，令高斯十分感动。他在博士论文和《算术研究》中，写下了情真意切的献词："献给大公"，"你的仁慈，将我从所有烦恼中解放出来，使我能从事这种独特的研究"。

45. In 1792, Gauss entered the Caroline College in Braunschweig to continue his studies. In 1795, the Duke again paid for various expenses and sent him to the famous University of Göttingen in Germany, thus allowing Gauss to study diligently and begin creative research according to his own ideals. In 1799, Gauss completed his doctoral dissertation and returned to his hometown of Braunschweig. Just as he was sick due to worry about his future and livelihood — although his doctoral dissertation was successfully passed, he was awarded the doctoral degree and also obtained a position as a lecturer, but he was unable to successfully attract students, so he had to return to his hometown — once again, the Duke came to his rescue. The Duke paid for the printing costs of Gauss's lengthy doctoral dissertation, gave him an apartment, and had his "Arithmetic Research" printed, making it possible for the book to be published in 1801; he also bore all of Gauss's living expenses. All of this deeply moved Gauss. In his doctoral dissertation and "Arithmetic Research," he wrote heartfelt dedications: "To the Duke," "Your kindness has freed me from all troubles, allowing me to engage in this unique research."

46. 友情是两心相交，友情是不求回报，友情是没有烦恼，友情是温暖拥抱，友情是相伴到老。友情是你我快乐的微笑！

46. Friendship is the meeting of two hearts, friendship is without expectation of return, friendship is free from worries, friendship is a warm embrace, friendship is a companionship till old age. Friendship is the joyful smile between you and me!

47. 有志始知蓬莱近，无为总觉咫尺远。

47. It is only when one has ambition that they realize how close Penglai is; without it, they always feel it is far away.

48. 一天，萨维尔村理发师挂出一块招牌：“村里所有不自己理发的男人都由我给他们理发，我也只给这些人理发。”于是有人问他：“您的头发由谁理呢”理发师顿时哑口无言。

48. One day, the barber in Saville village hung up a sign that read: "I will give haircuts to all the men in the village who do not cut their own hair, and I will only cut hair for these people." Upon this, someone asked him, "Who cuts your hair?" The barber was left speechless.

49. 只有一条路不能选择，那就是放弃的路；只有一条路不能拒绝，那就是成长的路。你要的比别人多，就必须付出得比别人多。?>

49. There is only one path that cannot be chosen, and that is the path of giving up; there is only one path that cannot be refused, and that is the path of growth. If you want more than others, you must also pay more than others.

50. 两相比较，前者立志坚定、注意观察、勤于思考、善于学习，并能利用业余时间深造，他将获得成功；后者恰恰相反，不管他们是否满足于现状，他们这样庸庸碌碌地混日子，永无出头之日。

50. When compared, the former is resolute in his ambition, observant, diligent in thought, and skilled in learning, and he can further his studies during his leisure time; he will achieve success. The latter, on the other hand, is exactly the opposite. Whether or not they are satisfied with the current situation, they lead a mundane and lazy life, and there will be no day of breakthrough for them.

51. 许多天赋很高的人，终生处在平庸的职位上，导致这一现状的原因是不思进取。而不思进取的突出表现是不读书、不学习。宁可把业余时间消磨在娱乐场所或闲聊中，也不愿意看书。也许，他们对目前所掌握的职业技能感到满意了，意识不到新知识对自身发展的价值；也许，他们下班后很疲倦，没有毅力进行艰苦的自我培训。

51. Many highly talented individuals spend their entire lives in平庸 positions, and the main reason for this situation is a lack of ambition. The most prominent manifestation of this is not reading or learning. They would rather spend their leisure time at entertainment venues or engaging in idle chatter than read books. Perhaps, they are satisfied with the current professional skills they possess and are unaware of the value of new knowledge for their own development; perhaps, they are too exhausted after work to have the perseverance for arduous self-training.

52. 一个人只有把自己的事业和祖国的事业联系起来才能有所进步，才能有所作为。―― 马蒂

52. One can only make progress and achieve something by linking one's career with the cause of one's country. -- Martí

53. 想像力比知识更重要，因为知识是有限的，而想像力概括着世界的一切，推动着进步，并且是知识进化的源泉。严格地说，想像力是科学研究中的实在因素。―― 爱因斯坦

53. Imagination is more important than knowledge, for knowledge is limited, whereas imagination embraces the entire world, stimulating progress, and is the source of knowledge evolution. In a strict sense, imagination is a real factor in scientific research. -- Einstein

54. 坚持把简单的事情做好，就是不简单！坚持把平凡的事情做好，就是不平凡！所谓成功，就是简单事情坚持做，重复做，用心做，在平凡中做出不平凡的坚持！

54. It's not simple to consistently do simple things well! It's not ordinary to consistently do ordinary things well! What we call success is to persistently do simple things, to repeat them, to do them with care, and to make extraordinary persistence in the ordinary!

55. 坐标法的思想促使人们运用各种代数的方法解决几何问题。先前被看作几何学中的难题，一旦运用代数方法后就变得平淡无奇了。坐标法对近代数学的机械化证明也提供了有力的工具。

55. The concept of the coordinate method has prompted people to apply various algebraic methods to solve geometric problems. Once the algebraic method is applied, what were previously considered difficult problems in geometry become rather ordinary. The coordinate method also provides a powerful tool for the mechanized proof in modern mathematics.

56. 1637年，法国的哲学家和数学家笛卡尔发表了他的著作《方法论》，这本书的后面有三篇附录，一篇叫《折光学》，一篇叫《流星学》，一篇叫《几何学》。当时的这个“几何学”实际上指的是数学，就像我国古代“算术”和“数学”是一个意思一样。

56. In 1637, the French philosopher and mathematician Descartes published his work "The Method," which included three appendices at the end. One of the appendices was titled "Optics," another was titled "Meteorology," and the third was titled "Geometry." At that time, this "Geometry" actually referred to mathematics, just as the ancient "arithmetics" and "mathematics" in our country meant the same thing.

57. 一个人失败的原因，在于本身性格的缺点，与环境无关。

57. The reason for a person's failure lies in their own character flaws, not related to the environment.

58. 一个前途光明的年轻人随时随地都注意磨练自己的工作能力，任何事情都想比别人做得更好。对于一切接触到的事物，他都细心地观察、研究，对重要的东西务必弄得一清二楚。他也随时随地把握机会来学习，珍惜与自己前途有关的一切学习机会，对他来说，积累知识比积累金钱更要紧。他随时随地注意学习做事的方法和为人处世的技巧，有些极小的事情，也认为有学好的必要，对于任何做事的方法都仔细揣摩、探求其中的诀窍。如果他把所有的事情都学会了，他所获得的内在财富要比有限的薪水高出无数倍。

58. A promising young person is always alert to refine his work abilities at any time and in any place, always striving to do anything better than others. He carefully observes and studies everything he comes across, making sure he understands the important things thoroughly. He also takes every opportunity to learn, valuing any learning opportunity related to his future prospects. To him, accumulating knowledge is more important than accumulating money. He is always attentive to learning the methods of doing things and the skills of social interaction. He even considers it necessary to excel in the tiniest matters, carefully pondering and seeking the secrets in any method of doing things. If he masters all the skills, the inner wealth he acquires will be countless times greater than the limited salary.

59. 高斯的学术地位，历来为人们推崇得很高。他有"数学王子"、"数学家之王"的美称、被认为是人类有史以来"最伟大的三位（或四位）数学家之一"（阿基米德、牛顿、高斯或加上欧拉）。人们还称赞高斯是"人类的骄傲"。天才、早熟、高产、创造力不衰、……，人类智力领域的几乎所有褒奖之词，对于高斯都不过份。

59. Gauss's academic status has always been highly revered by people. He is known as the "Prince of Mathematics" and the "King of Mathematicians," and is considered one of the "three (or four) greatest mathematicians in human history" (Archimedes, Newton, Gauss, or including Euler). People also praise Gauss as "the pride of humanity." Genius, precocity, productivity, enduring creativity,... almost all encomiums in the realm of human intelligence are not excessive for Gauss.

60. 一个人的梦想也许不值钱，但一个人的努力很值钱。

60. A person's dreams may not be valuable, but their efforts are very valuable.

61. 永不放弃是你梦想实现的唯一秘诀。

61. Never give up is the only secret to the realization of your dreams.

62. 慷慨、仁慈的资助人去世了，因此高斯必须找一份合适的工作，以维持一家人的生计。由于高斯在天文学、数学方面的杰出工作，他的名声从1802年起就已开始传遍欧洲。彼得堡科学院不断暗示他，自从1783年欧拉去世后，欧拉在彼得堡科学院的位置一直在等待着象高斯这样的天才。公爵在世时坚决劝阻高斯去俄国，他甚至愿意给高斯增加薪金，为他建立天文台。现在，高斯又在他的生活中面临着新的选择。

62. The generous and benevolent patron has passed away, therefore Gauss must find a suitable job to maintain the livelihood of his family. Due to Gauss's outstanding work in astronomy and mathematics, his reputation had begun to spread throughout Europe as early as 1802. The Academy of Sciences in St. Petersburg continually hinted to him that since Euler's death in 1783, the position of Euler at the Academy of Sciences in St. Petersburg had been waiting for a genius like Gauss. The Duke had strongly dissuaded Gauss from going to Russia while he was alive, even offering to increase Gauss's salary and establish an observatory for him. Now, Gauss is facing a new choice in his life once again.

63. 只有莱布尼兹和牛顿将积分和微分真正沟通起来，明确地找到了两者内在的直接联系：微分和积分是互逆的两种运算。而这是微积分建立的关键所在。只有确立了这一基本关系，才能在此基础上构建系统的微积分学。并从对各种函数的微分和求积公式中，总结出共同的算法程序，使微积分方法普遍化，发展成用符号表示的微积分运算法则。

63. Only Leibniz and Newton truly communicated the relationship between integration and differentiation, clearly identifying the intrinsic direct connection between the two: differentiation and integration are inverse operations. This is the key to the establishment of calculus. Only by establishing this fundamental relationship can a systematic calculus be built upon it. And from the differential and integral formulas of various functions, a common algorithmic procedure can be summarized, making the calculus method generalized, and developing into symbolic calculus operational rules.

64. 《海岛算经》一书中， 刘徽精心选编了九个测量问题，这些题目的创造性、复杂性和富有代表性，都在当时为西方所瞩目．

64. In the book "Calculation Techniques in Island", Liu Hui carefully selected nine measurement problems. The creativity, complexity, and representativeness of these questions were all highly regarded by the Western world at that time.

65. 《九章算术》约成书于东汉之初，共有246个问题的解法．在许多方面：如解联立方程，分数四则运算，正负数运算，几何图形的体积面积计算等，都属于世界先进之列，但因解法比较原始，缺乏必要的证明，而刘徽则对此均作了补充证明．在这些证明中，显示了他在多方面的创造性的贡献．他是世界上最早提出十进小数概念的人，并用十进小数来表示无理数的立方根．在代数方面，他正确地提出了正负数的概念及其加减运算的法则；改进了线性方程组的解法．在几何方面，提出了"割圆术"，即将圆周用内接或外切正多边形穷竭的一种求圆面积和圆周长的方法．他利用割圆术科学地求出了圆周率π=314的结果．刘徽在割圆术中提出的"割之弥细，所失弥少，割之又割以至于不可割，则与圆合体而无所失矣"，这可视为中国古代极限观念的佳作．

65. The "Nine Chapters on the Mathematical Art" was approximately compiled in the early Eastern Han Dynasty, containing solutions to 246 problems. In many aspects, such as solving simultaneous equations, performing arithmetic operations on fractions, calculating the operations on positive and negative numbers, and calculating the volume and area of geometric figures, it belongs to the forefront of the world. However, due to the relatively primitive solutions and the lack of necessary proofs, Liu Hui supplemented these proofs. Among these proofs, his creative contributions in various aspects were displayed. He was the first person in the world to propose the concept of decimal fractions and used decimal fractions to represent the cube root of irrational numbers. In algebra, he correctly proposed the concept of positive and negative numbers and their rules for addition and subtraction; he improved the solution method for linear equation systems. In geometry, he proposed the "sectional circle method," which is a method to calculate the area and circumference of a circle by exhausting it with an inscribed or circumscribed regular polygon. He used the sectional circle method to scientifically obtain the result that the circumference of a circle π = 314. Liu Hui's proposal in the sectional circle method, "The more you cut, the less you lose; when you can't cut anymore, it fits the circle and nothing is lost," can be regarded as a fine work of the ancient Chinese concept of limits.

66. 因为，如果他给自己理发，那么他就属于自己给自己理发的那类人。但是，招牌上说明他不给这类人理发，因此他不能自己理。如果由另外一个人给他理发，他就是不给自己理发的人，而招牌上明明说他要给所有不自己理发的男人理发，因此，他应该自己理。由此可见，不管怎样的推论，理发师所说的话总是自相矛盾的。

66. Because, if he gives himself a haircut, then he belongs to the category of people who give themselves a haircut. However, the sign states that he does not cut hair for people in this category, so he cannot cut his own hair. If another person cuts his hair, then he is someone who does not give himself a haircut, and the sign clearly states that he is to cut hair for all men who do not give themselves a haircut, therefore, he should cut his own hair. Thus, whatever the reasoning, the barber's words are always self-contradictory.

67. 解析几何又分作平面解析几何和空间解析几何。

67. Analytic geometry is further divided into plane analytic geometry and spatial analytic geometry.

68. 高斯的一生，是典型的学者的一生。他始终保持着农家的俭朴，使人难以想象他是一位大教授，世界上最伟大的数学家。他先后结过两次婚，几个孩子曾使他颇为恼火。不过，这些对他的科学创造影响不太大。在获得崇高声誉、德国数学开始主宰世界之时，一代天骄走完了生命旅程。

68. Gauss's life was a typical scholar's life. He always maintained the simplicity of a farmer, making it hard to imagine that he was a distinguished professor, the greatest mathematician in the world. He was married twice and several children once caused him considerable frustration. However, these had little impact on his scientific creation. When he achieved great fame and German mathematics began to dominate the world, a generation of brilliance concluded its journey through life.

69. 1874年，德国数学家康托尔创立了集合论，很快渗透到大部分数学分支，成为它们的基础。到19世纪末，全部数学几乎都建立在 集合论的基础之上了。就在这时，集合论中接连出现了一些自相矛盾的结果，特别是1902年罗素提出的理发师故事反映的悖论，它极 为简单、明确、通俗。于是，数学的基础被动摇了，这就是所谓的第三次“数学危机”。

69. In 1874, the German mathematician Cantor founded set theory, which quickly permeated most branches of mathematics and became their foundation. By the end of the 19th century, almost all of mathematics was built on the foundation of set theory. It was at this time that some paradoxical results emerged one after another in set theory, especially the paradox reflected by the barber story proposed by Russell in 1902, which was extremely simple, clear, and popular. As a result, the foundation of mathematics was shaken, which is known as the third "mathematical crisis."

70. 从没去公园玩过。这就是"把别人喝咖啡的功夫都用在工作上"的鲁迅。

70. I have never played in the park. That's the Lu Xun who "spent the time others would have been drinking coffee working."