The Nine Chapters on the Mathematical Art
The Nine Chapters on the Mathematical Art is the most important mathematical treatise among the 10 ancient books on mathematics that make up the ten Classics of Mathematics,"which appeared in China between the Han (206 B.C. - A.D. 220) and Tang (618-907) dynasties. It can be traced back to around the 1st century, and renowned mathematicians such as Zhang Cang and Geng Shouchang in the early Western Han Dynasty (206 B.C. - A.D. 25) made additions and revisions to it. The version that has been passed down to this day is the annotated edition of "The Nine Chapters on the Mathematical Art" by Liu Hui (c. 225 – 295), an eminent mathematician in the Wei (220-265) and Jin (265-420) dynasties.
the Nine Chapters on the Mathematical Art systematically summarizes the mathematical achievements from the pre-Qin period (770-221 B.C.) to the Eastern Han period (25-220). The book consists of nine chapters – "Field Measurement", "On Millet and Rice", "Distribution by Proportion", "What Width?", "Construction Consultations", "Fair Levies", "Excess and Deficit", "The two-sided reference", and "Base and altitude". It is a how-to manual comprising 246 exemplary problems related to work and daily life, each with answers and steps to the solution. It offered a research model and framework for ancient Chinese mathematics with a focus on computation, practical relevance, and problem-solving. The methods offered in the book for calculating negative numbers and fractions and for solving simultaneous linear equations were mathematical breakthroughs at that time, predating those of India by 800 years and Europe by more than 1,000 years.
A mathematical masterpiece, the Nine Chapters on the Mathematical Art offered concise explanations on effective solutions to problems in applied mathematics. It represented a high water mark for ancient China's understanding of mathematics, placing China on track to lead in the field of classical mathematics. The book was introduced to Korea and Japan during the Sui (581-618) and Tang dynasties before it made its way to India, Arab countries, and Europe, and exerted a great influence on the development of classical mathematics world-wide.
《九章算术》
《九章算术》是中国汉唐之间出现的十部古算书《算经十书》中最重要的一部数学专著，成书于1世纪左右，西汉早期著名数学家张苍、耿寿昌等对它进行过增补删订。现今流传的主要是魏晋时期著名数学家刘徽（约225—约295） 为《九章算术》所作的注本。
《九章算术》系统总结了自先秦时期到东汉时期的数学成就，全书共有九卷，包括方田、粟米、衰分、少广、商功、均输、盈不足、方程、勾股九个章节。全书采用问题集的形式，收录了246个生产、生活实践相关的应用问题，其 中每道题都有答案和解题步骤，确定了中国古代数学以计算为中心、密切联系实际、解决实践问题的研究风格和框架。书中提到的负数、分数计算，联立一次方程解法等都是具有世界领先意义的数学成就，这些成就比印度早800年，比欧洲早1000余年。
《九章算术》是当时世界上最简练有效的应用数学成果，它的出现标志中国古代数学体系的形成，为中国古典数学领先世界奠定了基础。《九章算术》于隋唐时期传入朝鲜和日本，后传至印度、阿拉伯国家和欧洲地区，对世界古典数学发展产生了很大影响。