The Nine Chapters on the Mathematical Art Companion and Commentary

by Shen Kangshen; Crossley, John N.; Lun, Anthony W. -C.

• ISBN13: 9780198539360
• ISBN10: 0198539363
• Format: Hardcover
• Copyright: 2000-01-20
• Publisher: Oxford University Press

Summary

The Nine Chapters on the Mathematical Art is a classic text: the most important mathematical source in China during the past 2000 years, and comparable in significance to Euclid's Elements in the West. This volume contains the first complete English translation of the Nine Chapters, togetherwith two commentaries written in the 3rd and 7th centuries AD, and a further commentary by the translators. The Nine Chapters contains 246 problems and their solutions, which fall into nine categories that are firmly based on practical needs. There are methods for solving problems in areas such asland measurement, construction, agriculture, commerce, and taxation. The Chinese commentators provided the algorithms needed to solve the problems, and explanations of how the algorithms work. The translators' commentary provides clear and accessible background material for the Western reader,explanations of technicalities, and notes on the treatment of similar or identical mathematical problems in other countries. The Nine Chapters quickly acquired a distinguished reputation, and was the standard mathematics textbook in China and the surrounding regions until Western science wasintroduced in about 1600. This English translation gives the reader an idea of the distinctive style and important contributions of traditional Chinese mathematics.

Table of Contents

Introduction	1	(52)
Liu Hui's commentaries	1	(5)
The content of the Nine Chapters	1	(2)
Liu Hui	3	(3)
Metrological Systems	6	(11)
Metrological Systems and Calculation Devices in the Qin and Han Dynasties (c.2nd century BC to 2nd century AD)	6	(5)
Counting Rods and Rod Arithmetic	11	(6)
Influence on Traditional Mathematics	17	(5)
Master Sun's Mathematical Manual and Zhang Qiujian's Mathematical Manual (Zhang Qiujian Suanjing)	18	(1)
Continuation of Ancient Mathematics (Jigu Suanjing)	19	(1)
The Appended Rules (Zhuishu) and Detailed Solutions on Problems in Huangdi's Nine Chapters (Huangdi Jiuzhang Suanjing Xicao)	19	(1)
Works in the Song, Jin and Yuan Dynasties	19	(2)
The Systematic Treatise on Arithmetic (Suanfa Tongzong, 1592)	21	(1)
Euclid's Elements in Chinese	21	(1)
Collected Works on the Calendar and Mathematics (Meishi Lisuan Congshu)	22	(1)
Mei Wending
The Productive Late Qing Period	22	(1)
The Cradle of Western Mathematics	22	(5)
Egypt	23	(1)
Babylon	23	(1)
Greece	24	(3)
Mathematical Culture along the Silk Road	27	(6)
India	27	(2)
The Arab World	29	(1)
Arabian Mathematics	30	(1)
The Middle Ages	31	(2)
European Mathematics	33	(5)
Systems of Numbers	35	(1)
Four Operations	36	(1)
Formulae and Rules	36	(1)
Geometrical Figures	37	(1)
Celebrated Mathematical Problems	38	(1)
Traditional Japanese Mathematics	38	(3)
Seki Takakazu and his school	39	(1)
Influences on Hesuan from traditional Chinese mathematics	40	(1)
Research on the Nine Chapters outside China	41	(8)
Asia	41	(2)
Europe	43	(4)
America	47	(1)
Australasia	48	(1)
How the present work was accomplished	49	(3)
Liu Hui's Preface to his Running Commentary on the Nine Chapters	52	(508)
Field Measurement	59	(75)
Summary	59	(2)
Types of problem	59	(1)
Pedagogy	60	(1)
Other countries	60	(1)
Translation and Annotation	61	(73)
Millet and Rice	134	(23)
Summary	134	(7)
Types of problems	134	(1)
Pedagogy	134	(1)
Other countries	135	(2)
Ancient China	137	(2)
The Qilu Rule and the Inverse Qilu Rule	139	(1)
The Qilu Rule	139	(1)
The Inverse Qilu Rule	139	(1)
Variations on the Rules	140	(1)
Translation and Annotation	141	(16)
Distribution by Proportion	157	(18)
Summary	157	(2)
Types of problems	157	(1)
Standard proportionality problems	157	(1)
Other countries	158	(1)
Pedagogy	158	(1)
Translation and Annotation	159	(16)
Short Width	175	(76)
Summary	175	(21)
Types of problems	175	(1)
Ancient China	176	(1)
Techniques	176	(8)
The Celestial Element Rule	184	(10)
The Short Width Rule	194	(1)
Other countries	195	(1)
Translation and Annotation	196	(55)
Construction Consultations	251	(56)
Summary	251	(3)
Types of problems	251	(1)
Pedagogy	251	(1)
Practical roots	252	(1)
Other countries	252	(2)
Translation and Annotation	254	(53)
Fair Levies	307	(42)
Summary	307	(3)
Types of problems	307	(1)
Pedagogy	308	(1)
Other countries	309	(1)
Translation and Annotation	310	(39)
Excess and Deficit	349	(37)
Summary	349	(9)
Types of problems	349	(1)
Other countries	350	(1)
Rule of Double False Position	351	(4)
Excess and Deficit Rule	355	(2)
Linear approximations	357	(1)
Pedagogy	358	(1)
Translation and Annotation	358	(28)
Rectangular Arrays	386	(53)
Summary	386	(13)
Types of problems	386	(1)
Other countries	386	(2)
Ancient China	388	(2)
Traditional Chinese Examples	390	(8)
Pedagogy	398	(1)
Translation and Annotation	399	(40)
Right-angled Triangles	439	(79)
Summary	439	(19)
Types of problems	439	(1)
Chinese Mathematics before 300 AD	440	(1)
Traditional Chinese Mathematics after 300 AD	440	(16)
Questions about the Origin of the Gougu Rule	456	(2)
Translation and Annotation	458	(60)
Sea Island Mathematical Manual	518	(42)
Summary	518	(21)
Overview	518	(1)
The instruments and methods	519	(5)
Liu Hui's views	524	(1)
Surveying	525	(7)
A comparison of corresponding work in the West before the early nineteenth century	532	(3)
Solstice shadow measurement	535	(3)
Works on the Sea Island	538	(1)
Translation and Annotation	539	(21)
Afterword	560	(3)
Shen Kangshen
Note on the References	563	(1)
References	564	(19)
Index	583