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Tables of Contents for The Nine Chapters on the Mathematical Art
Chapter/Section Title
Page #
Page Count
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