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.
《九章算術》
《九章算術》是中國漢唐之間出現的十部古算書《算經十書》中最重要的一部數學專著，成書于1世紀左右，西漢早期著名數學家張蒼、耿壽昌等對它進行過增補刪訂。現今流傳的主要是魏晉時期著名數學家劉徽（約225—約295） 為《九章算術》所作的注本。
《九章算術》系統總結了自先秦時期到東漢時期的數學成就，全書共有九卷，包括方田、粟米、衰分、少廣、商功、均輸、盈不足、方程、勾股九個章節。全書采用問題集的形式，收錄了246個生產、生活實踐相關的應用問題，其 中每道題都有答案和解題步驟，確定了中國古代數學以計算為中心、密切聯系實際、解決實踐問題的研究風格和框架。書中提到的負數、分數計算，聯立一次方程解法等都是具有世界領先意義的數學成就，這些成就比印度早800年，比歐洲早1000余年。
《九章算術》是當時世界上最簡練有效的應用數學成果，它的出現標志中國古代數學體系的形成，為中國古典數學領先世界奠定了基礎。《九章算術》于隋唐時期傳入朝鮮和日本，后傳至印度、阿拉伯國家和歐洲地區，對世界古典數學發展產生了很大影響。
