## Science and Civilisation in China: Volume 3, Mathematics and the Sciences of the Heavens and the EarthAfter 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 |

803 | |

875 | |

### Common terms and phrases

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