Jiuzhang Suanshu
《九章算术》
The Jmzhang Suanshu ( Nine Chapters on the Mathematical Art ) is the longest suNiving and one of the most important in the ten ancient Chi-nese mathematical books. The book was finished in the early Eastern Han Dynasty(about lst century),indicating the formation of ancient Chinese mathematical sys-tem.It became the criterion of mathematical learning and research for mathemati-cians of later generations ever since then.
《九章算术》是中国古代数学专著，是“算经十书”中最重要的一种。《九章算术》大约于东汉初年（公元l世纪）成书，它的出现标志着中国古代数学体系的形成。后世的古代数学家，大都是从《九章算术》开始学习和研究数学的，许多人曾为它作过注释，其中最著名的有刘徽(263)、李淳风(656)等人。唐宋两代都由国家明令规定为教科书。1084年由当时的北宋朝廷进行刊刻，是世界上最早的印刷本数学书。《九章算术》在隋唐时期就已传入朝鲜、日本，现在它已被译成日、俄、德、英、法等多种文字。
Afterwards, the Jiuzhan,g Suanshu hcrve been annotated by many mathemati-aans, the most famous ones including Liu Hui (263) and Li Chunfeng (656). Dur-ing the Tang Dynasty and Song Dynasty, it was offcially declared to be the national mathematical textbook.The edition published by the Northem Song government in 1084 was the earliest mathematical book in the world.The book was introduced to Korea and Japan during the Sui and Tang dynasties.Now, il has been translated into several languages, including Japanese, Russian, German, English and French.The book is broken up into nine chapters containing 246 questions with their solutions and procedures.Here is a brief description of each chapter:
《九章算术》分为九章，收有246个数学问题及解法与步骤。各章主要内容分别是：第一章“方田”，研究田亩面积计算，用分数进行运算；第二章“粟米”，研究谷物粮食的按比例折换；第三章“衰分”，研究比例分配问题；第四章“少广”，已知面积、体积、求其一边长和径长；求数的平方根、立方根；第五章“商功”，研究土石工程、体积计算；第六章“均输”，研究合理摊派赋税；第七章“盈不足”，即双设法问题；第八章“方程”，研究一次方程组问题，介绍正负数概念，进行正负数加减计算；第九章“勾股”，探讨勾股定理、直角三角形属性，研究等边直角三角形问题，介绍二次方程的遁解方法。
The book’s major achievements are as follows:
《九章算术》的数学成就如下：
1. Devising a systemcrtic treatment of arithmetic operations with fractions,1,400 years earlier than the Europeans.
(1)提出用分数进行运算的完整法则，比欧洲早1400多年；
2. Dealing with various types of problems on proportions, 1,400 years earlier than the Europeans.
(2)提出整套的比例理论，比欧洲早了1400多年；
3. Devising methods for extracting square root and cubic root, which is quite similar to today’s method, several hundred years earlier than the Western mathe-maticians.
(3)介绍了开平方、开立方的方法，其程序与现今程序基本一致，比西方早了数百年；
4. Developing solutions for a system of linear equations, about l,600 years earlier than the Western mathematicians.
(4)采用分离系数的方法表示线性方程组，比西方早了1600年；
5. Introducing the concepts of positive and negative numbers, more than 600 years earlier than the West.
(5)提出了正负数，比西方早了6个世纪；
6. Developing a general solution formula for the Pythagorean problems ( prob-lems of Gou gu) , 300 years earlier than the West.
(6)提出了勾股数问题的通解公式，比西方早了3个世纪。
7. Putting forward theories of calculating areas and volumes of different shapes and figures.
(7)提出了各种多边形、圆、弓形等的面积公式。