Introduction |
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1 | (12) |
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Part I Western learning and the Ming-Qing transition |
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Chapter 1 The Jesuits and mathematics in China, 1582-1644 |
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13 | (22) |
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1.1 Mathematics and literati culture in China c. 1600 |
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14 | (8) |
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1.2 Mathematics in the Society of Jesus |
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22 | (2) |
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1.3 Teaching and translating |
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24 | (7) |
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1.4 Jesuit science, `practical learning' and astronomical reform |
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31 | (4) |
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Chapter 2 Western learning under the new dynasty (1644-1666) |
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35 | (22) |
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2.1 Dynastic transition in Beijing: a new calendar for new rulers |
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36 | (2) |
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2.2 Adam Schall, imperial astronomer |
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38 | (3) |
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2.3 Jiangnan scholars and the Jesuits |
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41 | (3) |
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2.4 Number and magnitude expanded: a scholar's mathematics |
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44 | (5) |
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2.5 Schall's defeat: the 1664 impeachment |
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49 | (8) |
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Part II The first two decades of Kangxi's rule |
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Chapter 3 The emperor and his astronomer (1668-1688) |
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57 | (25) |
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3.1 Kangxi's takeover and the rehabilitation of Jesuit astronomy |
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57 | (8) |
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3.2 Ferdinand Verbiest, imperial astronomer and tutor |
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65 | (8) |
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3.3 Kangxi, student of Chinese and Western learning |
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73 | (5) |
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3.4 Philosophy, `fathoming the principles' and orthodoxy |
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78 | (4) |
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Chapter 4 A mathematical scholar in Jiangnan: the first half-life of Mei Wending |
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82 | (20) |
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4.1 Mei Wending's early career |
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83 | (3) |
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4.2 Integrating Chinese and Western mathematics |
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86 | (4) |
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4.3 The Discussion of rectangular arrays: restoring one of the `nine reckonings' |
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90 | (3) |
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4.4 Writing mathematics: purpose, structure and style of the Discussion of rectangular arrays |
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93 | (9) |
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Chapter 5 The `King's Mathematicians': a French Jesuit mission in China |
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102 | (18) |
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5.1 Setting up a scientific expedition to China |
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102 | (6) |
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5.2 From Brest to Beijing |
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108 | (4) |
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112 | (4) |
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5.4 Travels and observations in China |
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116 | (4) |
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Chapter 6 Inspecting the southern sky: Kangxi at the Nanjing observatory |
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120 | (19) |
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121 | (6) |
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6.2 Li Guangdi's recollection |
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127 | (4) |
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131 | (2) |
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6.4 Imperial investigation of the Old Man Star |
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133 | (6) |
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Part III Mathematics for the emperor |
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Chapter 7 Teaching `French science' at the court: Gerbillon and Bouvet's tutoring |
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139 | (21) |
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7.1 Chronology of the lessons |
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141 | (3) |
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7.2 The Academie, the Moderns and the way to God |
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144 | (4) |
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7.3 A typical lesson: 10 April 1690 |
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148 | (3) |
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7.4 The imperial workshop and instruments |
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151 | (5) |
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7.5 Chinese, Manchu and the control of Western science |
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156 | (4) |
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Chapter 8 The imperial road to geometry: new Elements of geometry |
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160 | (20) |
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8.1 Changing the textbook |
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160 | (2) |
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8.2 Pardies' Elemens de geometrie: the pedagogy of geometry in seventeenth-century France |
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162 | (4) |
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8.3 The double translation |
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166 | (3) |
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8.4 Diamonds and pearls: ratios in the new Elements |
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169 | (4) |
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173 | (3) |
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8.6 The emperor's role in the composition of the new Elements |
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176 | (4) |
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Chapter 9 Calculation for the emperor: the writings of a discreet mathematician |
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180 | (34) |
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9.1 Antoine Thomas (1644-1709) and his Synopsis mathematica |
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180 | (4) |
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9.2 The Outline of the essentials of calculation |
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184 | (7) |
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9.3 Practical geometry and tables |
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191 | (4) |
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9.4 The foundations of calculation: back to Euclid |
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195 | (5) |
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9.5 Cossic algebra: the Calculation by borrowed root and powers and its summary |
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200 | (10) |
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9.6 Symbolic linear algebra: a treatise within the treatise |
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210 | (4) |
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Chapter 10 Astronomy in the capital (1689-1693): scholars, officials and ruler |
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214 | (25) |
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10.1 Mei Wending in Beijing |
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214 | (4) |
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10.2 A patron's commission: the Doubts concerning the study of astronomy |
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218 | (4) |
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10.3 Three solar eclipses |
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222 | (7) |
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10.4 An imperial pronouncement on mathematics and classical scholarship |
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229 | (4) |
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10.5 The officials' responses |
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233 | (6) |
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Part IV Turning to Chinese scholars and Bannermen |
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Chapter 11 The 1700s: reversal of alliance? |
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239 | (21) |
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11.1 Locating the Beijing Jesuits c. 1700 |
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240 | (5) |
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11.2 The mathematical sciences in history |
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245 | (8) |
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11.3 From favour to distrust: the papal legation |
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253 | (2) |
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11.4 The Jesuits as imperial cartographers |
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255 | (2) |
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11.5 Assessing mathematical talent: Chen Houyao's interview |
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257 | (3) |
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Chapter 12 The Office of Mathematics: foundation and staff |
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260 | (24) |
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12.1 The Summer solstice of 1711 |
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260 | (2) |
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12.2 Selecting talented men |
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262 | (3) |
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12.3 The mathematical staff at the emperor's sixtieth birthday |
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265 | (2) |
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12.4 An editorial project in the mathematical sciences |
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267 | (6) |
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12.5 The imperial princes |
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273 | (4) |
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12.6 Mathematicians, astronomy and cartography |
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277 | (3) |
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12.7 The mathematical sciences in examinations |
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280 | (4) |
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Chapter 13 The Jesuits and innovation in imperial science: Jean-Francois Foucquet's treatises |
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284 | (31) |
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13.1 Foucquet in Beijing: from the Book of Change to astronomy |
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284 | (3) |
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13.2 The Dialogue on astronomical methods: a reform proposal? |
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287 | (7) |
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13.3 Foucquet's writings on mathematics |
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294 | (6) |
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13.4 Symbols in the New method of algebra |
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300 | (5) |
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13.5 The Jesuits and the Office of Mathematics |
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305 | (4) |
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13.6 Tables and the standardisation of mathematical sciences |
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309 | (6) |
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Part V Mathematics for the Empire |
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Chapter 14 The construction of the Essence of numbers and their principles |
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315 | (25) |
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315 | (5) |
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320 | (3) |
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14.3 The historical narrative of mathematics |
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323 | (4) |
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14.4 The structure of imperial mathematics |
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327 | (3) |
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14.5 Rephrasing the Jesuits' textbooks |
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330 | (3) |
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14.6 Vocabulary and classification |
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333 | (7) |
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Chapter 15 Methods and material culture in the Essence of numbers and their principles |
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340 | (24) |
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15.1 Problems and their genealogy: Master Sun and Hieron |
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341 | (4) |
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15.2 Inkstones and brushes |
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345 | (3) |
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15.3 Weighing up the difficulty of problems |
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348 | (4) |
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15.4 Algebra and the problems of the `Line Section' |
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352 | (2) |
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15.5 The remainder problem |
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354 | (2) |
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15.6 The construction and use of instruments |
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356 | (2) |
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358 | (6) |
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Chapter 16 A new mathematical classic? |
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364 | (21) |
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364 | (4) |
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16.2 Harmonics and astronomy |
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368 | (5) |
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373 | (5) |
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16.4 Supplements to the Origins of pitchpipes and the calendar |
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378 | (4) |
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16.5 The study of mathematics in mid-Qing China |
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382 | (3) |
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385 | (8) |
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393 | (2) |
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395 | |
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1 Mathematical and astronomical manuscripts from the Kangxi court |
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395 | (2) |
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2 Editions used for main other Chinese works on mathematics, astronomy and harmonics |
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397 | (1) |
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397 | (3) |
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400 | (21) |
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421 | |