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Zhoubi Suanjing
《周髀算经》
The oldest mathematical classic in China, Zhou,bi Suanjing or The Arith-metical Classic of the Gnomon and the Circular Paths of Heaven,is an astronomy text as well.It is thought to have been compiled sometime between 500 BC and 200 AD.During the Tang Dynasty, the book was listed as the first of all the texts included in the Ten, Mathematical Classics.It contains some important mathe-matical sections and measures the positions of the heavenly bodies.How a gno-mon might be used is described in a conversation between Duke of Zhou and his as astrologer Shang Gao in the text:
《周髀算经》是中国历史上最早的一部数学典籍，也是一部天文学著作。成书时间大约在公元前5世纪与公元2世纪之间，唐代被收入《算经十书》，并被列为《十经》的第一部。该书包括许多重要的数学内容，还对天体方位作了测定。例如书中周公与商高的一段对话描述了如何用日圭标竿进行测量：
Duke of Zhou: How great is the art of numbers? Tell me something about the application of the gnomon.
周公日：“大哉言数！请问用矩之道？”
Shang Gao: Level up one leg of the gnomon and use the other leg as a plumb line. When the gnomon is turned up, it can measure height; when it is turned o-ver, it can measure depth and when it lies horizontally it can measure distance.Revolve the gnomon about its vertex and it can draw a circle; combine two gno-mons and they form a square.
商高日：“平矩以正绳，偃矩以望高，覆矩以测深，卧矩以知远，环矩以为圆，合矩以为方。”
Zhoubi Suanjin,g is a collection of 246 problems encountered during the conver-sations between the Duke of Zhou and Shang Gao. Each question has stated their numerical answer and corresponding arithmetic algorithm. The author of the Zhou-bi Suanjing writes that Emperor Yu quells floods, deepens rivers and streams, sur-veys high places and low places by using the Gougu rule. And this book contains one of the first recorded proofs of the Gougu rule, or the Pythagorean Theorem in the world.
《周髀算经》中周公与商高之间的对话涉及246个问题，每个问题都以相应数学算法得到解决。其中谈到了勾股定理（亦称毕达哥拉斯定理）及其在测量上的应用，记载了大禹如何运用勾股定理治理水灾、加深河床、测量高低。这是世界上关于勾股定理最早的文字记录之一。
The text of the Zhoubi Suanjin,g also explains that the reason that mathematics can be applied to so many different cases i-s as a result of the way that mathemati-cal reasoning allows one to pass from particular to general situations. This realiza-tion of the abstract nature of mathematics is important.
《周髀算经》还解释了数学在各方面广泛应用的一个原因，即数学推理使人们能够从个别推及普遍，这是对抽象的数学性质的一个重要认识。
Zhoubi Suanjin,g contains calculations of the movement of the sun through the year as well as observations of the moon and the stars, particularly the pole star.
此外，《周髀算经》还计算了太阳在一年内的运动，并对月亮和星星，尤其是北极星作了观察。
