Science and Civilisation in China: Volume 3, Mathematics and the Sciences of the Heavens and the Earth

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Cambridge University Press, 1959 - Body, Mind & Spirit - 877 pages
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After two volumes mainly introductory, Dr Needham now embarks upon his systematic study of the development of the natural sciences in China. The Sciences of the Earth follow: geography and cartography, geology, seismology and mineralogy. Dr Needham distinguishes parallel traditions of scientific cartography and religious cosmography in East and West, discussing orbocentric wheel-maps, the origins of the rectangular grid system, sailing charts and relief maps, Chinese survey methods, and the impact of Renaissance cartography on the East. Finally-and here Dr Needham's work has no Western predecessors-there are full accounts of the Chinese contribution to geology and mineralogy.
 

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Contents

List of Illustrations page
xvii
List of Tables
xxxv
Authors Note
xli
MATHEMATICS page i
5
A Geometry
91
2 The theorem of Pythagoras p
95
3 Treatment of plane areas and solid figures p
97
4 Evaluation of n p
99
k Mathematics and science in China and the West p
150
THE SCIENCES OF THE HEAVENS
169
ASTRONOMY page 17
171
b Definitions p
178
c Bibliographical notes
182
ii Chinese and Japanese literature p
185
d Ancient and medieval cosmological ideas p
210
e The polar and equatorial character of Chinese astronomy
229

5 Conic sections p
102
6 Yang Hui and the coming of Euclid p
103
7 Coordinate geometry p
106
8 Trigonometry p
108
9 Problems and puzzles p
111
i Algebra p
112
1 Simultaneous linear equations p
115
2 Matrices and determinants
117
4 Indeterminate analysis and indeterminate equa tions p
119
5 Quadratic equations and the method of finite differences p
123
6 Cubic and higher equations
125
7 Numerical higher equations p
126
8 The Thien Yuan notation
129
9 Binomial theorem and the Pascal triangle p
133
10 Series and progressions
137
11 Permutation and combination p
139
12 Calculus p
141
j Influences and transmissions p
146
The naming cataloguing and mapping of stars p
263
g The development of astronomical instruments p
284
spheres p
342
h Calendrical and planetary astronomy p
390
Records of celestial phenomena p
409
j The time of the Jesuits p
437
k Summary p
458
METEOROLOGY page
462
GEOGRAPHY AND CARTOGRAPHY page
497
c A note on Chinese explorers p
522
GEOLOGY and Related Sciences page
591
SEISMOLOGY page
624
MINERALOGY page
636
ADDENDA page
681
GENERAL INDEX page
803
Table of Chinese Dynasties
875
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