《五大历数书汇编》中的月亮中心差算法——兼与6世纪之前中国月亮中心差算法比较
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摘要
成书于公元6世纪的《五大历数书汇编》是印度早期一部非常重要的数理天文学著作,几乎汇集了公元6世纪以前印度本土天文学以及传入印度的域外天文学的主要内容。文中详细考察了收录在《五大历数书汇编》中的《太阳历数书》、《宝莉莎历数书》和《罗马伽历数书》中的月亮中心差算法,并与公元6世纪之前的《乾象历》、《景初历》和《元嘉历》等3部中国历法中的月亮中心差算法进行比较,揭示了公元6世纪之前印度和中国天文学家处理月亮不均匀运动的方法的异同。
Paňcasiddhāntikā,which was finished in the Sixth Century,is an important ancient Indian work on mathematical astronomy. This work collected the main content of native astronomy in India and the astronomy introduced into India from other civilizations. In this paper,we discuss the calculation of lunar equation of center in the Saura Siddhānta,Paulis' a Siddhānta and Romaka Siddhānta of Paňcasiddhāntikā and compare them with the calculation of lunar equation of center in the Supernal Emblem System,the Luminous Inception System and the Epochal Excellence System. Based on the discussion and comparison,we reveal the similarities and differences between Indian and Chinese algorithms of lunar equation of center before the Sixth Century.
Paňcasiddhāntikā,which was finished in the Sixth Century,is an important ancient Indian work on mathematical astronomy. This work collected the main content of native astronomy in India and the astronomy introduced into India from other civilizations. In this paper,we discuss the calculation of lunar equation of center in the Saura Siddhānta,Paulis' a Siddhānta and Romaka Siddhānta of Paňcasiddhāntikā and compare them with the calculation of lunar equation of center in the Supernal Emblem System,the Luminous Inception System and the Epochal Excellence System. Based on the discussion and comparison,we reveal the similarities and differences between Indian and Chinese algorithms of lunar equation of center before the Sixth Century.
引文
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[17]TANG Q,QU A J.A comparison of Chinese and Indian solar theories in the Sui and Early Tang Periods(Seventh-Eighth Centuries C.E.)[J].Journal for the History of Astronomy,2018,49(4):472-495.
[18]PINGREE D.History of Mathematical Astronomy in India.Charles Coulston Gillispie.Dictionary of Scientific Biography[M].New York:Charles Scribner's Sons,1978.
[19]VARHAMIHIRA.Pa1casiddhāntikāof Varāhamihira[M].Ed.and Tr.by Neugebauer O and Pingree D.Cobenhagen:Munksgaard,1970.
[20]陈久金.九道术解[J].自然科学史研究,1982,1(2):131-135.
[21]历代天文律历等志汇编[Z].第5册.北京:中华书局,1976:1592-1594.
[22]陈美东,张培瑜.月离表初探[J].自然科学史研究,1987,6(2):135-146.
[23]历代天文律历等志汇编[Z].第6册.北京:中华书局,1976:1592-1594.
[24]赵进义,编著.易照华,修订.天体力学[M].上海:上海科学技术出版社,1983:104.
[25]中国大百科全书·天文卷[M].北京/上海:中国大百科全书出版社,1980:529.
[2]钮卫星.西望梵天:汉译佛经中的天文学源流[M].上海:上海交通大学出版社,2004.
[3]JOSEPH N.Science and Civilization in China:Mathematics and the Sciences of the Heavens and the Earth,Vol.3[M].Cambridge:Cambridge University Press,1959:394.
[4]钮卫星.张子信水星“应见不见”术考释及其可能来源探讨[J].上海交通大学学报(哲学与社会科学版),2009,17(1):53-62.
[5]胡铁珠.大衍历与苏利亚历的五星运动计算[J].自然科学史研究,1990,9(3):219-231.
[6]曲安京.中国古代历法与印度及阿拉伯的关系---以日月食起讫算法为例[J].自然辩证法通讯,2000,22(3):58-68+96.
[7]唐泉,曲安京.希腊、印度、阿拉伯与中国传统视差理论比较研究[J].自然科学史研究,2008,27(2):131-150.
[8]袁敏.古代中印数理天文学比较研究[D].西安:西北大学,2001.
[9]刘丽芳,古代中印晷影测算方法之比较研究[D].天津:天津师范大学,2008.
[10]VARHAMIHIRA.Pa1casiddhāntikā,the astronomical work of Varāhamihira[M].Ed.and Tr.by Thibaut G and Sudhākara Dvivedi Mm.Benares:Medical Hall Press,1889.
[11]VARHAMIHIRA.Pa1casiddhāntikāof Varāhamihira[M].Ed.and Tr.by Neugebauer O and Pingree D.Cobenhagen:Munksgaard,1970.Pt.I.
[12]VARHAMIHIRA.Pa1casiddhāntikāof Varāhamihira[M].Ed.and Tr.by Kuppanna Sastry T S and Sarma K V.Adyar:Madars,1993.
[13]ABRAHAM G.Algebraic formulae for the moon,saturn and jupiter in the Pa1casiddhāntikā[J].Archive for History of Exact Sciences,1982,26(4):287-297.
[14]ABRAHAM G.Theories for the Motion of the Sun in the Pa1casiddhāntikā[J].Archive for History of Exact Sciences,1985,34(3):221-230.
[15]WAERDEN B L V.On the Romaka-Siddhānta[J].Archive for History of Exact Sciences,1988,38(1):1-11.
[16]TANG Q,QU A J.Research on the Motion of Mars in the Sovereign Pole System(A.D.600)[J].Journal for the History of Astronomy,2017,48(4):432-459.
[17]TANG Q,QU A J.A comparison of Chinese and Indian solar theories in the Sui and Early Tang Periods(Seventh-Eighth Centuries C.E.)[J].Journal for the History of Astronomy,2018,49(4):472-495.
[18]PINGREE D.History of Mathematical Astronomy in India.Charles Coulston Gillispie.Dictionary of Scientific Biography[M].New York:Charles Scribner's Sons,1978.
[19]VARHAMIHIRA.Pa1casiddhāntikāof Varāhamihira[M].Ed.and Tr.by Neugebauer O and Pingree D.Cobenhagen:Munksgaard,1970.
[20]陈久金.九道术解[J].自然科学史研究,1982,1(2):131-135.
[21]历代天文律历等志汇编[Z].第5册.北京:中华书局,1976:1592-1594.
[22]陈美东,张培瑜.月离表初探[J].自然科学史研究,1987,6(2):135-146.
[23]历代天文律历等志汇编[Z].第6册.北京:中华书局,1976:1592-1594.
[24]赵进义,编著.易照华,修订.天体力学[M].上海:上海科学技术出版社,1983:104.
[25]中国大百科全书·天文卷[M].北京/上海:中国大百科全书出版社,1980:529.