Abstract
The structure of the Huihui li, a Chinese Islamic calendar originally compiled in A.D. 1383,1 and the basic theory behind it were investigated by Kiyosi Yabuuti in his pioneering works.2 However, we are not yet sure on which Islamic sources the Huihui li was actually based.3
This is a slightly revised version of my paper published in the Memoirs of the International Institute for Linguistic Sciences, Kyoto Sangyo University, No. 1 (March 1999).
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Notes
There are three different recensions of the Huihui li — (1) that recorded in the official Ming Dynastic History which was compiled during the Qing Dynasty, (2) the Qizheng tuibu compiled by Bei Lin in A.D. 1477, and (3) the Korean recension Chiljong san which forms a part of the Sejong sillok compiled during the reign of King Sejong (1419–1450). These recensions are considerably different, especially in the arrangement and order of the explanatory texts and tables. For the difference, see the article by Benno van Dalen in this Volume.
See Part 2, Chapter 3 of Yabuuti’s Chinese Astronomy and Calendrical Sciences (Chûgoku no tenmon rekihô in Japanese), Tokyo (Heibonsha) 1969, 2nd ed. 1990, which was a revision of his earlier paper, published in the Tôhô Gakuhô, Vol. 36 (1964), pp. 611–632 with the title ‘Kaikai reki kai’. This work was recently translated, with some improvements, into English by Benno van Dalen as ‘Islamic Astronomy in China during the Yuan and Ming Dynasties’, Historia Scientiarum, Vol. 7, No. 1 (1997), pp. 11–43.
Recently van Dalen informed me of a very interesting paper which had escaped scholarly attention for long time: A. Wagner, ‘Ueber ein altes Manuscript der Pulkowaer Sternwarte’, Copernicus, Vol. II (1882), pp. 123–129. The author of this paper happened to examine an Arabic manuscript which was brought to the library of the Pulkova observatory by a consul in China. A mere glance at the table of contents and some parameters used in this manuscript is enough to say that this text was the best candidate for the source of the Huihui li. Needham (Science and Civilisation in China, Vol. 3, 1959, p. 372, footnote e), briefly referring to Wagner’s paper, just hoped that ‘they were not destroyed when the Obervatory was burnt during the second world war’ . It is regrettable that no historian of astronomy tried to get access to the Pulkova manuscript. Let us hope that the manuscript survived the recent fire, too.
I thank the Japan Society for Promotion of Science for offering scholarship to Dr. van Dalen and thus making possible our joint project.
My contribution was published as ‘Tables of Planetary Latitute in the Huihui li (I)’ , Current Perspectives in the History of Science in East Asia, ed. by Yung Sik Kim and Francesca Bray, Seoul National University, 1999 (June 30), pp. 307–315, which was followed by van Dalen’s paper.
The unique manuscript is extant in the Bibliothèque Nationale, Paris, arabe 6040. I thank van Dalen who brought a photocopy of this manuscript for my use.
For this very interesting zīj, see Herbert Franke ‘Mittelmongolische Glossen in einer arabischen astronomischen Handschrift’, Oriens 31 (1988), pp. 95–118.
See also Edward S. Kennedy, ‘Eclipse Predictions in Arabic Astronomical Tables Prepared for the Mongol Viceroy of Tibet’, Zeitschrift für Geschichte der arabisch-islamischen Wissenschaften 4 (1987/88), pp. 60–80
and Edward S. Kennedy and Jan Hogendijk ‘Two Tables from an Arabic Astronomical Handbook for the Mongol Viceroy of Tibet’, A Scientific Humanist, Studies in Memory of Abraham Sachs, ed. by Erle Leichty et al., Occasional Publications of the Samuel Noah Kramer Fund, 9, Philadelphia: The University Museum, 1988, pp. 233–242.
I have used the printed edition in 3 vols., Osmania Oriental Publications Bureau, 1956 and a copy of the manuscript from British Library Or. 1997.
See Gerald J. Toomer, Ptolemy’s Almagest, London/New York, 1984.
Otto Neugebauer, Exact Sciences in Antiquity, New York, 1969, p. 200 ff.
In modern expression, when the eccentricity (e) is given, q1 is a function of centrum (y):
Neugebauer, op. cit., p. 201. See also Toomer’s translation of the Almagest, p. 546 and footnote 48.
I have used the Ph.D. dissertation of Willium D. Stahlman, The Astronomical Tables of Codex Vaticanus Graecus 1291, submitted to Brown University in 1959.
See Olaf Pedersen, A Survey of the Almagest, Odense University Press, 1974, p. 320.
The angles are so small that I want to make them clear here: D is at the intersection of EC and the dotted circle of which the centre is E and the radius is R. q1 = ∠OCE, c3 = ∠ODE, and c4 = ∠COD.
Carolo A. Nallino ed. Al-Battani sive Albatenii: Opus astronomicum, 3 vols., Milano, 1903, 1907, 1899. Reprinted from Georg Olms Verlag, Hildesheim•New York, 1977. The first equation for Mercury is in vol.II, pp. 132–137. Al-Battānī’s table for q1 is virtually identical to that in Theon’s Handy Tables. The difference is only 2;4 instead of 2;5 for centrum 138/222 and 1;35 instead of 1;34 for centrum 149/211.
I have used the facsimile edition of Escorial arabe 927 published by F. Sezgin.
Since the tabular values of c3 and c4 are rounded to the unit of minutes, some values of q 1 are different from the sum of c3 and c4 of this table by one minute.
Only two out of 180 values are different, i.e., for centrum 21/339 and 70/290.
Out of 180, only 11 values are different.
The equation tables of Kūšyār ibn Labbān have another special feature of ‘displacement’, in order to avoid negative values.
I thank Toshiaki Kashino for reading this text with me.
For the date of the texts, see Kennedy, A Survey of Islamic Astronomical Tables, Transactions of the American Philosophical Society, Vol. 46, Part 2 (1956). For the date of al-Mumtahan, al-Baghdādī, and Īlkhānī, I acknowledge to Benno van Dalen’s personal communication.
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Yano, M. (2002). The First Equation Table for Mercury in the Huihui li . In: Ansari, S.M.R. (eds) History of Oriental Astronomy. Astrophysics and Space Science Library, vol 275. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9862-0_3
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