Science and civilisation in China, volume 3, Mathematics and the sciences of the heavens and the earth

Title page......Page 3
List of Illustrations......Page 14
List of Tables......Page 31
List of Abbreviations......Page 33
Acknowledgments......Page 35
Author's Note......Page 37
a) Introduction......Page 44
b) Numeral notation, place-value, and zero......Page 48
c) Survey of the principal landmarks in Chinese mathematical literature......Page 61
1) From antiquity to the San Kuo period (+3rd century)......Page 62
2) From the San Kuo to the beginning of the Sung (+l0th century)......Page 76
3) The Sung, Yuan and Ming periods......Page 81
1) Elementary theory of numbers......Page 97
2) Magic squares......Page 98
1) The four basic processes......Page 105
2) Roots......Page 108
f) Mechanical aids to calculation......Page 111
1) Counting-rods......Page 113
2) Graduated counting-rods......Page 115
3) The abacus......Page 117
1) Fractions......Page 125
2) Decimals, metrology, and the handling of large numbers......Page 126
4) Negative numbers......Page 134
1) The Mohist definitions......Page 135
2) The theorem of Pythagoras......Page 139
3) Treatment of plane areas and solid figures......Page 141
4) Evaluation of Pi......Page 143
5) Conic sections......Page 146
6) Yang Hui and the coming of Euclid......Page 147
7) Co-ordinate geometry......Page 150
8) Trigonometry......Page 152
9) Problems and puzzles......Page 155
i) Algebra......Page 156
1) Simultaneous linear equations......Page 159
3) The rule of false position......Page 161
4) Indeterminate analysis and indeterminate equations......Page 163
5) Quadratic equations and the method of finite differences......Page 167
6) Cubic and higher equations......Page 169
7) Numerical higher equations......Page 170
8) The Thien Yuan notation......Page 173
9) Binomial theorem and the 'Pascal' triangle......Page 177
10) Series and progressions......Page 181
11) Permutation and combination......Page 183
12) Calculus......Page 185
j) Influences and transmissions......Page 190
k) Mathematics and science in China and the West......Page 194
THE SCIENCES OF THE HEAVENS......Page 213
a) Introduction......Page 214
b) Definitions......Page 221
i) European literature......Page 225
ii) Chinese and Japanese literature......Page 228
i) The 'official' character of Chinese astronomy......Page 229
ii) Ancient calendars......Page 237
iii) Astronomical writings from the Chou to the Liang (+6th century)......Page 239
iv) Astronomical writings from the Liang to the beginning of the Sung (+10th century)......Page 244
v) Sung, Yuan and Ming......Page 249
1) The Kai Thien theory (a hemispherical dome)......Page 253
2) The Hun Thien school (the celestial sphere)......Page 259
3) The Hstian Yeh teaching (infinite empty space)......Page 262
4) Other systems......Page 267
5) General notions......Page 270
e) The polar and equatorial character of Chinese astronomy......Page 272
1) Circumpolar stars and equatorial mark-points......Page 275
2) The development of the system of the hsiu......Page 285
3) The origin of the system of the hsiu......Page 297
4) The pole and the pole-stars......Page 305
1) Star catalogues and star co-ordinates......Page 309
2) Star nomenclature......Page 319
3) Star maps......Page 324
4) Star legend and folklore......Page 334
1) The gnomon and the gnomon shadow template......Page 336
2) Giant instruments in masonry......Page 347
3) The sundial (solar time indicator)......Page 361
i) Portable equinoctial dial-compasses......Page 375
4) The clepsydra (water-clock)......Page 379
i) Clepsydra types; from water-clock to mechanical clock......Page 381
ii) Clepsydras in history......Page 385
iii) Combustion clocks and the equation of time......Page 399
5) The sighting-tube and the circumpolar constellation template......Page 403
6) The armillary sphere and other major instruments......Page 411
i) The general development of armillary spheres......Page 414
ii) Armillary instruments in and before the Han......Page 426
iii) The invention of the clock-drive......Page 431
iv) The invention of the equatorial mounting......Page 439
7) Celestial globes......Page 462
h) Calendrical and planetary astronomy......Page 470
1) Motions of the sun, moon and planets......Page 473
2) Sexagenary cycles......Page 477
3) Planetary revolutions......Page 479
4) Duodenary series, p......Page 483
5) Resonance periods......Page 487
1) Eclipses......Page 490
i) Eclipse theory......Page 491
ii) Extent, reliability and precision of the records......Page 498
iii) Eclipse prediction......Page 501
iv) Earth-shine and corona......Page 503
2) Novae, supernovae, and variable stars......Page 504
3) Comets, meteors, and meteorites......Page 511
4) Solar phenomena; sun-spots......Page 517
j) The time of the Jesuits......Page 520
1) China and the dissolution of the crystalline spheres......Page 521
2) The imperfect transmission......Page 525
3) 'Western' science or 'New' science?......Page 532
4) The integration of Chinese astronomy into modern science......Page 540
k) Summary......Page 547
b) Climate in general......Page 551
c) Temperature......Page 554
d) Precipitation......Page 556
e) Rainbows, parhelia and spectres......Page 562
f) Wind and the atmosphere......Page 567
g) Thunder and lightning......Page 570
h) The aurora borealis......Page 572
i) Sea tides......Page 575
THE SCIENCES OF THE EARTH......Page 587
a) Introduction......Page 588
1) Ancient writings and official histories......Page 591
2) Anthropological geographies......Page 599
3) Descriptions of southern regions and foreign countries......Page 601
4) Hydrographic books and descriptions of the coast......Page 605
5) Local topographies......Page 608
6) Geographical encyclopaedias......Page 612
c) A note on Chinese explorers......Page 614
1) Introduction......Page 617
2) Scientific cartography; the interrupted European tradition......Page 618
3) Religious cosmography in Europe......Page 620
4) The role of the navigators......Page 627
5) Scientific cartography; the continuous Chinese grid tradition......Page 632
i) Origins in Chhin and Han......Page 633
ii) Establishment in Han and Chin......Page 636
iii) Development in Thang and Sung......Page 643
iv) Climax in Yuan and Ming......Page 655
6) Chinese sailing charts......Page 660
7) The role of the Arabs......Page 667
8) Religious cosmography in East Asia......Page 673
e) Chinese survey methods......Page 678
f) Relief and other special maps......Page 688
g) The coming of Renaissance cartography to China......Page 694
h) Comparative retrospect......Page 698
i) The return of the rectangular grid to Europe......Page 701
a) Introduction; geology and mineralogy......Page 702
1) Pictorial representations......Page 703
2) The origin of mountains; uplifting, erosion, and sedimentary deposition......Page 709
3) Caves, underground waters, and shifting sands......Page 717
4) Petroleum, naphtha, and volcanoes......Page 720
c) Palaeontology......Page 723
1) Fossil plants......Page 724
2) Fossil animals......Page 726
a) Earthquake records and theories......Page 736
b) The ancestor of all seismographs......Page 738
b) The theory of chhi and the growth of metals in the earth......Page 748
c) Principles of classification......Page 753
d) Mineralogical literature and its scope......Page 756
e) General mineralogical knowledge......Page 760
1) Aetites......Page 765
2) Alum......Page 766
3) Sal ammoniac......Page 767
4) Asbestos......Page 768
5) Borax......Page 775
6) Jade and abrasives......Page 776
7) Precious stones, including the diamond......Page 784
8) The touchstone......Page 787
1) Geological prospecting......Page 788
2) Geobotanical and bio-geochemical prospecting......Page 790
Israel and Khazaria......Page 796
Korea......Page 797
BIBLIOGRAPHIES......Page 800
Abbreviations......Page 801
A. Chinese books before +1800......Page 808
B. Chinese and Japanese books and journal articles since +1800......Page 839
C. Books and journal articles in Western languages......Page 859
GENERAL INDEX......Page 918
Table of Chinese Dynasties......Page 990
Errata to Volumes 1 and 2......Page 991
Romanisation Conversion Table......Page 993