362:
267:
1193:
335:) denotes the unknown x, so the numerals on that line mean 18x. The line below is the constant term (-316) and the line above is the coefficient of the quadratic (x) term. The system accommodates arbitrarily high exponents of the unknown by adding more lines on top and negative exponents by adding lines below the constant term. Decimals can also be represented. Later, the line order was reversed so that the first line is the lowest exponent.
289:
and a square. They often involve two people who walk on straight lines until they can see each other, meet or reach a tree in a certain spot. The purpose of book was to study intricate geometrical relations with algebra and provide solutions to equations.
338:
Li does not explain how to solve equations in general, but shows it with the example problems. Most of the equations can be reduced to the second or sometimes third order. It is often assumed that he used methods similar to
319:
313:
239:, writing official histories. However, he had a political fallout and resigned after a few months, again citing ill health. He spent his final years teaching at his home near Feng Lung mountain in Yuan,
116:
who was also named Li Zhi, removing one stroke from his original name to change the character. His name is also sometimes written as Li Chih or Li Yeh. His literary name was
Renqing (
983:
Chan, Hok-Lam. 1997. “A Recipe to
Qubilai Qa'an on Governance: The Case of Chang Te-hui and Li Chih”. Journal of the Royal Asiatic Society 7 (2). Cambridge University Press: 257–83.
436:, similar in shape to the heavens but smaller in size, arguing that it could not be square since that would hinder the movement of the heavens and celestial bodies.
1224:
410:, while the heavens were spherical in shape, along with celestial bodies such as the sun and moon (described by 1st-century AD polymathic scientist and statesman
935:
Cullen, Christopher. (1993). "Appendix A: A Chinese
Eratosthenes of the Flat Earth: a Study of a Fragment of Cosmology in Huainanzi", in Major, John. S. (ed),
376:) is a work of more basic mathematics written soon after Li Ye completed Ceyuan haijing, and was probably written to help students who could not understand
297:, "coefficient array method" or literally "method of the celestial unknown". The method was known before him in some form. It is a positional system of
1012:
2123:
1438:
2042:
1766:
1705:
1597:
1212:
653:
1894:
1432:
235:, Kublai twice offered Li government positions, but Li was too old and in ill health. In 1264, Li finally accepted a position at the
2133:
597:
1073:
2138:
2006:
2143:
1907:
1334:
1319:
1306:
1271:
1236:
1207:
720:
2128:
1339:
1103:
1005:
944:
923:
902:
881:
860:
839:
818:
794:
773:
752:
728:
631:
1981:
1329:
1219:
676:
Lam Lay-Yong; Ang Tian-Se (September 1984). "Li Ye and his Yi Gu Yan Duan (old mathematics in expanded sections)".
1061:
418:
bullet and ball, respectively). However, the idea of a flat earth was criticized by the Jin dynasty astronomer
1867:
1165:
1056:
318:
1365:
1034:
998:
380:. Yigu yanduan consists of three volumes dedicated to solving geometrical problems on two tracks, through
285:) is a collection of 170 problems, all related to the same example of a circular city wall inscribed in a
2148:
1826:
1357:
1353:
1279:
1251:
1030:
1192:
1241:
1051:
274:, that all the problems use. It shows a circular city wall, inscribed in a right triangle and a square.
181:
1113:
958:
293:
Many of the problems are solved by polynomial equations, which are represented using a method called
1689:
1444:
1098:
1066:
553:
455:
of the globe. The flat Earth theory in
Chinese science was finally overturned in the 17th-century.
1951:
1720:
1295:
1128:
460:
113:
361:
1545:
1093:
592:
1314:
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456:
916:
Science and
Civilization in China: Mathematics and the Sciences of the Heavens and the Earth
895:
Science and
Civilization in China: Mathematics and the Sciences of the Heavens and the Earth
874:
Science and
Civilization in China: Mathematics and the Sciences of the Heavens and the Earth
853:
Science and
Civilization in China: Mathematics and the Sciences of the Heavens and the Earth
832:
Science and
Civilization in China: Mathematics and the Sciences of the Heavens and the Earth
811:
Science and
Civilization in China: Mathematics and the Sciences of the Heavens and the Earth
787:
Science and Civilization in China: Mathematics and the Sciences of the Heavens and the Earth
766:
Science and Civilization in China: Mathematics and the Sciences of the Heavens and the Earth
745:
Science and Civilization in China: Mathematics and the Sciences of the Heavens and the Earth
2118:
2113:
1961:
1450:
1170:
384:
and geometry. It also contained algebraic problems, but with slightly different notations.
173:
439:
However, the idea of a spherical earth was not accepted in mainstream Chinese science and
8:
2000:
1840:
1229:
1175:
588:
503:
481:
440:
302:
85:
312:
1976:
1936:
1143:
1138:
693:
266:
26:
648:
80:), was a Chinese mathematician, politician, and writer who published and improved the
2015:
1855:
1850:
1787:
1324:
1148:
1133:
1123:
1118:
1078:
940:
937:
Heaven and Earth in Early Han Thought: Chapters Three, Four, and Five of the Huananzi
919:
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1926:
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40:
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93:
21:
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in 1230 at the age of 38, and was administrative prefect of Jun prefecture in
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1992:
1986:
1971:
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548:
381:
344:
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81:
70:
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1021:
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369:
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232:
214:
109:
17:
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Identifiants et Référentials pour l'enseignement supérieur et la recherche
422:(fl. 307-345 AD), who suggested a rounded shape as an alternative. In his
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1931:
1921:
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1872:
1762:
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1485:
1412:
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689:
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990:
1902:
1811:
1756:
1750:
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1539:
1533:
1521:
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1427:
1390:
1380:
472:
464:
623:
Li, Qi and Shu: An Introduction to Science and Civilization in China
2063:
2051:
2032:
1956:
1845:
1805:
1677:
1653:
1630:
1587:
1569:
1395:
717:
Vita mathematica: historical research and integration with teaching
626:(unabridged ed.). Courier Dover Publications. pp. 89–96.
415:
135:
918:, vol. 3, reprint edition. Cambridge: Cambridge University Press.
897:, vol. 3, reprint edition. Cambridge: Cambridge University Press.
876:, vol. 3, reprint edition. Cambridge: Cambridge University Press.
855:, vol. 3, reprint edition. Cambridge: Cambridge University Press.
834:, vol. 3, reprint edition. Cambridge: Cambridge University Press.
813:, vol. 3, reprint edition. Cambridge: Cambridge University Press.
789:, vol. 3, reprint edition. Cambridge: Cambridge University Press.
768:, vol. 3, reprint edition. Cambridge: Cambridge University Press.
747:, vol. 3, reprint edition. Cambridge: Cambridge University Press.
2069:
2057:
1946:
1701:
1479:
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1400:
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1108:
1088:
723:
Notes. Vol. 40. Cambridge University Press. pp. 89–90.
570:
1683:
1624:
1606:
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168:(now Beijing). His father was a secretary to an officer in the
88:
of one variable. Along with the 4th-century Chinese astronomer
217:, ordered Li to give advice on science. In 1259, Li completed
108:
Li Ye was born Li Zhi, but later changed his name to Li Ye to
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1714:
419:
240:
203:
177:
100:
before the advances of European science in the 17th century.
89:
1799:
805:
803:
675:
459:
also introduced the spherical Earth model advanced by
243:. Li told his son to burn all of his books except for
800:
586:
640:
387:
308:For example, 2x + 18x − 316 = 0 is represented as
451:periods, with the advent of evidence of European
2105:
939:. Albany: State University of New York Press.
184:. He then lived in poverty in the mountainous
1006:
684:(3). Berlin / Heidelberg: Springer: 237–266.
427:
397:
326:
222:
193:
1439:Along the River During the Qingming Festival
654:Complete Dictionary of Scientific Biography
231:), also a mathematics text. After becoming
1013:
999:
188:. In 1248 he finished his most known work
961:. St. Paul, Minn.: Minnesota Public Radio
2025:
360:
265:
33:Chinese scientist and writer (1192–1279)
1020:
598:MacTutor History of Mathematics archive
580:
565:
563:
443:until the 17th century during the late
152:
130:
53:
2106:
2007:Collected Cases of Injustice Rectified
1932:Endless power transmitting chain drive
957:Baran, Madeleine (December 16, 2009).
914:Needham, Joseph; Wang, Ling. (1995) .
893:Needham, Joseph; Wang, Ling. (1995) .
872:Needham, Joseph; Wang, Ling. (1995) .
851:Needham, Joseph; Wang, Ling. (1995) .
830:Needham, Joseph; Wang, Ling. (1995) .
809:Needham, Joseph; Wang, Ling. (1995) .
785:Needham, Joseph; Wang, Ling. (1995) .
764:Needham, Joseph; Wang, Ling. (1995) .
743:Needham, Joseph; Wang, Ling. (1995) .
613:
601:. University of St Andrews in Scotland
994:
985:https://www.jstor.org/stable/25183352
956:
950:
710:
678:Archive for History of Exact Sciences
577:(French). Accessed 19 February 2018.
560:
2124:13th-century Chinese mathematicians
704:
571:Li, Ye (1192-1279) 李, 冶 (1192-1279)
432:), Li Ye echoed Yu's idea that the
13:
977:
959:"Historic map coming to Minnesota"
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646:
619:
14:
2160:
547:Breard, Andrea. (Jan 01, 2021). "
378:Sea mirror of circle measurements
283:Sea mirror of circle measurements
272:Sea mirror of circle measurements
255:
245:Sea mirror of circle measurements
200:Sea mirror of circle measurements
1191:
713:"Enigmas of Chinese Mathematics"
388:Astronomy and shape of the earth
317:
311:
2134:Medieval Chinese mathematicians
929:
908:
887:
866:
845:
824:
779:
350:
92:, Li Ye proposed the idea of a
1433:Great Bodhisattva of Zhengding
758:
737:
406:stipulated that the earth was
250:
1:
2139:Politicians from Shijiazhuang
1868:Southern Song dynasty coinage
649:"Li Chih, also called Li Yeh"
519:
2144:Song dynasty science writers
715:. In Ronald Calinger (ed.).
549:Li Ye: Chinese mathematician
7:
1280:Department of State Affairs
557:. Accessed 7 February 2021.
492:
10:
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1242:Bureau of Military Affairs
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1114:Alliance Conducted at Sea
1104:Song–Viet war (1075–1077)
1029:
657:. Charles Scribner's Sons
428:
398:
365:Problem 8 in Yigu yanduan
327:
223:
194:
174:civil service examination
143:
121:
77:
66:
44:
1445:Four Great Books of Song
554:Encyclopaedia Britannica
374:New steps in computation
229:New steps in computation
1296:Secretariat-Chancellery
202:). Li then returned to
182:Mongol invasion in 1233
159:
103:
1927:Early Bessemer process
1895:Science and technology
1094:Nong Zhigao rebellions
647:Ho, Peng Yoke (2008).
620:Ho, Peng Yoke (2000).
366:
275:
1315:Ministry of Personnel
1220:Imperial examinations
884:, p. 498; footnote i.
711:Swetz, Frank (1996).
666:Via encyclopedia.com.
364:
270:The master figure in
269:
172:army. Li passed the
1451:Dongjing Meng Hua Lu
1225:Administrative units
1099:Song–Tibet relations
1074:Song–Đại Cồ Việt war
589:Robertson, Edmund F.
424:Jingzhai gu zhin zhu
303:polynomial equations
86:polynomial equations
2001:Forensic entomology
1962:Watertight bulkhead
1841:Joint-stock company
1335:Ministry of Justice
1320:Ministry of Revenue
1230:Sixteen Prefectures
842:, pp. 216-218, 227.
587:O'Connor, John J.;
504:Chinese mathematics
482:Kunyu Wanguo Quantu
434:Earth was spherical
322:in Arabic Numbers.
180:province until the
84:method for solving
61:; 1192–1279), born
2149:Writers from Hebei
1937:Astronomical clock
1144:Treaty of Shaoxing
690:10.1007/BF00348622
593:"Li Zhi Biography"
367:
316:which is equal to
276:
164:Li Ye was born in
114:third Tang emperor
2101:
2100:
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2016:Dream Pool Essays
1908:Gunpowder weapons
1821:
1820:
1348:
1347:
1340:Ministry of Works
1325:Ministry of Rites
1272:Three Departments
1109:Fang La rebellion
1089:Wang Ze rebellion
591:(December 2003).
499:Chinese astronomy
471:and presented in
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1770: 1174–1189
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1709: 1050–1080
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1408:Longquan celadon
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404:celestial sphere
402:) theory of the
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1977:Horner's method
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1044:Chenqiao mutiny
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978:Further reading
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489:China in 1602.
408:flat and square
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186:Shanxi province
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110:avoid confusion
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94:spherical Earth
34:
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926:, pp. 498-499.
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776:, pp. 44, 129.
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341:Ruffini's rule
287:right triangle
279:Ceyuan haijing
262:Ceyuan haijing
260:Main article:
257:
256:Ceyuan haijing
254:
252:
249:
237:Hanlin Academy
213:, grandson of
190:Ceyuan haijing
161:
158:
138:was Jingzhai (
105:
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76:(Chinese:
65:(Chinese:
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1993:Yingzao Fashi
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947:, p. 269-270.
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72:
71:courtesy name
64:
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29:
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2088:Guo Shoujing
2075:
2014:
2005:
1991:
1982:Architecture
1967:Fishing reel
1942:Movable type
1912:
1882:
1776:Zhou Jichang
1727:Zhang Zeduan
1576:Zhou Bangyan
1468:Fan Zhongyan
1449:
1437:
1423:Yaozhou ware
1418:Qingbai ware
1252:New Policies
1057:Southern Han
1048:Unification
1022:Song dynasty
963:. Retrieved
952:
936:
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797:, pp. 44-45.
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603:. Retrieved
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487:Ming-dynasty
480:
477:Matteo Ricci
469:Eratosthenes
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370:Yigu yanduan
368:
357:Yigu yanduan
351:Yigu yanduan
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299:rod numerals
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219:Yigu yanduan
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215:Genghis Khan
208:
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73:
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35:
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18:Chinese name
2119:1279 deaths
2114:1192 births
2090:(1231–1316)
2084:(1202–1261)
2082:Qin Jiushao
2078:(1192-1279)
2072:(1186–1249)
2066:(1031–1095)
2060:(1020–1101)
2054:(1010–1070)
2039:Zhang Sixun
1884:Zhu Fan Zhi
1873:Champa rice
1837:(1021–1086)
1814:(1235–1305)
1808:(1222–1307)
1802:(1210–1269)
1796:(1199–1295)
1790:(1190–1230)
1784:(1178–1249)
1763:Lin Tinggui
1759:(1140–1210)
1753:(1120–1182)
1747:(1100–1197)
1741:(1096–1119)
1739:Wang Ximeng
1735:(1094-1172)
1729:(1085–1145)
1723:(1082–1135)
1717:(1051–1107)
1698:(1049–1106)
1692:(1036–1093)
1686:(1020–1090)
1680:(1019–1079)
1674:(1000–1064)
1639:(1170–1231)
1633:(1140–1207)
1627:(1130–1200)
1621:(1127–1206)
1615:(1126–1193)
1613:Fan Chengda
1609:(1125–1209)
1590:(1085–1144)
1584:(1084–1155)
1582:Li Qingzhao
1578:(1056–1121)
1572:(1047–1126)
1566:(1045–1105)
1560:(1039–1112)
1554:(1037–1101)
1548:(1033–1107)
1542:(1032–1085)
1536:(1022–1077)
1530:(1019–1086)
1524:(1019–1083)
1518:(1017–1073)
1512:(1012–1067)
1506:(1011–1077)
1500:(1009–1066)
1494:(1007–1072)
1488:(1002–1060)
1486:Mei Yaochen
1413:Cizhou ware
1290:Chancellery
1285:Secretariat
1213:Family tree
1171:Diaoyucheng
965:19 February
605:21 December
509:Qin Jiushao
441:cartography
251:Mathematics
211:Kublai Khan
136:appellation
134:) and his
74:Li Jingzhai
22:family name
2108:Categories
2035:(972–1051)
1952:Pound lock
1878:Nanhai One
1835:Wang Anshi
1733:Su Hanchen
1696:Li Gonglin
1666:Zhao Chang
1662:(970–1053)
1660:Xu Daoning
1656:(960–1030)
1637:Zhao Rukuo
1619:Yang Wanli
1528:Sima Guang
1516:Zhou Dunyi
1492:Ouyang Xiu
1482:(998–1061)
1476:(991–1055)
1470:(989–1052)
1201:Government
661:2009-12-21
573:" IdRef:
520:References
514:Zhu Shijie
473:world maps
447:and early
412:Zhang Heng
153:Ching-chai
148:Wade–Giles
131:Jen-ch’ing
126:Wade–Giles
49:Wade–Giles
2026:Inventors
1903:Gunpowder
1812:Qian Xuan
1778:(12th c.)
1757:Liang Kai
1751:Zhao Boju
1690:Wang Shen
1672:Yi Yuanji
1668:(10th c.)
1540:Cheng Hao
1534:Zhang Zai
1522:Zeng Gong
1510:Cai Xiang
1504:Shao Yong
1428:Jian ware
1391:Guan ware
1381:Ding ware
1176:Xiangyang
1052:Later Shu
905:, p. 498.
698:120593520
465:Philolaus
209:In 1257,
112:with the
2064:Shen Kuo
2052:Jia Xian
2033:Bi Sheng
1957:Dry dock
1846:Banknote
1806:Gong Kai
1678:Wen Tong
1654:Fan Kuan
1647:Painters
1631:Xin Qiji
1588:Zhu Bian
1570:Cai Jing
1546:Cheng Yi
1396:Jun ware
1366:Religion
1237:Military
1208:Emperors
1139:Yancheng
1124:Jingkang
1035:Timeline
821:, p. 45.
755:, p. 40.
493:See also
475:such as
463:such as
416:crossbow
98:flat one
16:In this
2070:Song Ci
2058:Su Song
1947:Compass
1827:Economy
1788:Li Song
1702:Cui Bai
1480:Song Qi
1474:Yan Shu
1461:Writers
1401:Ru ware
1386:Ge ware
1358:Society
1354:Culture
1159:Caizhou
1149:Tangdao
1031:History
414:like a
394:huntian
170:Jurchen
140:Chinese
118:Chinese
41:Chinese
1856:Guanzi
1851:Jiaozi
1684:Guo Xi
1625:Zhu Xi
1607:Lu You
1594:Zhu Yu
1558:Su Zhe
1552:Su Shi
1498:Su Xun
1371:Poetry
1154:Caishi
1024:topics
943:
922:
901:
880:
859:
838:
817:
793:
772:
751:
727:
696:
630:
166:Daxing
150::
142::
128::
120::
63:Li Zhi
56:Li Yeh
51::
43::
20:, the
2076:Li Ye
1861:Huizi
1745:Li Di
1715:Mi Fu
1181:Yamen
1134:De'an
694:S2CID
429:敬齋古今注
420:Yu Xi
241:Hebei
204:Hebei
178:Henan
90:Yu Xi
37:Li Ye
1922:Coke
1800:Muqi
1356:and
967:2018
941:ISBN
920:ISBN
899:ISBN
878:ISBN
857:ISBN
836:ISBN
815:ISBN
791:ISBN
770:ISBN
749:ISBN
725:ISBN
628:ISBN
607:2009
467:and
449:Qing
445:Ming
392:The
343:and
333:yuan
325:The
233:Khan
224:益古演段
195:測圓海鏡
160:Life
104:Name
2043:fl.
1767:fl.
1706:fl.
1598:fl.
721:MAA
686:doi
551:".
479:'s
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78:李敬斋
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399:渾天
347:.
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247:.
227:,
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198:,
146:;
144:敬斋
124:;
122:仁卿
67:李治
47:;
45:李冶
27:Li
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