Qīzhèng tuībù 七政推步
Computation of the Seven Regulators (Sun, Moon, and Five Planets) by 貝琳 (Bèi Lín, ?–1490, 明, xiūjí 修輯)
About the work
A 7-juan working manual of the Sino-Islamic Huíhuí lì 回回曆 (Islamic-derived calendar) compiled by Bèi Lín, Vice Director of the Nánjīng Imperial Astronomical Bureau (Qīntiānjiān jiānfù), and printed in Chénghuà 13 (1477). The underlying calendrical system is that of the Khwarezmian astronomer Mashā ‘Aytah 馬沙亦黑 (the zǒngmù tíyào emends to 瑪沙伊赫), originally produced for the Yuán court and translated into Chinese in Hóngwǔ 15 (1382) by the Hànlín scholars Lǐ Chōng 李翀 and Wú Bózōng 吳伯宗 in collaboration with the Hùihúi master himself; the Huíhuí lì Bureau-section (Huíhuí lì kē 回回曆科) was thereafter formally instituted within the Qīntiānjiān and the system used in parallel with the indigenous Dàtǒng lì 大統曆 throughout the Míng. But the text remained for nearly a century in manuscript only, increasingly damaged. Bèi Lín’s contribution was the first thorough recension and printed edition: a fresh collation of two surviving copies, completion of damaged tables, supplementation of ten new ready-reckoner lìchéng tables (including the solar-and-lunar mean-longitude tables and the five planets’ mean-motion zhōngxíng tables), the first Sino-Western 277-star concordance, and thirteen ecliptic-coordinate star-charts. The result was the canonical late-Míng working text of the Islamic calendar in Chinese. The Sìkù editors recovered it in two recensions, collated them, and entered the result “to preserve one school of the [astronomical] art and supplement what the Míng shǐ did not provide”.
Tiyao
[Sub-classification: 子部, Tiānwén suànfǎ class 1, tuībù sub-category. Edition: WYG.]
Respectfully examined: Qīzhèng tuībù, 7 juàn, compiled-and-edited by Bèi Lín, Jiànfù of the Míng Nánjīng Qīntiānjiān — that is, the Huíhuí lì of Mashā ‘Aytah 瑪沙伊赫 (originally written 馬沙亦黑; here corrected) recorded in Jiāo Hóng 焦竑’s Guóshǐ jīngjí zhì. According to the Míng shǐ Lì zhì, the Huíhuí lì method was made by Mashā ‘Aytah (originally 馬沙亦黑; corrected), the master Mahmūd of the Western-Region kingdom of Madīnah (originally written 黙狄納 — corrected to 黙德訥 [Mòdénè]). It entered China under the Yuán but was not put into use. In the early Hóngwǔ [period] [its] book was obtained at the Yuán capital. In Hóngwǔ 15 [1382] the Hànlín [scholars] Lǐ Chōng 李翀 and Wú Bózōng 吳伯宗 were ordered to translate the book together with the Huíhuí Master Mashā ‘Aytah and others; the Huíhuí lì Bureau-section was then established and attached to the Qīntiānjiān.
But Bèi Lín’s own colophon further says: “Hóngwǔ 18 [1385], distant barbarians having come to submit, presented the tǔpán (earth-board, i.e. astrolabe-equivalent) method, predicting in advance the Six Luminaries’ encroachments-and-violations, named the Jīngwěidùshí lì (Longitude-Latitude-Time Calendar). The Calendrical Officer Yuán Tǒng 元統 removed the earth-board and translated [it] into Chinese computation, and the book then began to circulate in China”. This is rather inconsistent with what the [Míng] shǐ records.
But examining the book — there is the language: “From the Western-Region pre-year accumulated-years, down to the Hóngwǔ jiǎzǐ year, the accumulated counts are such-and-such”. Jiǎzǐ is Hóngwǔ 17 [1384]; at that time the book was already translated and in circulation. So Lín’s account is incorrect.
The book opens by glossing the numerical units used; then [treats] sun-position; then moon-deviation; then the five-planet computation methods, together with the lunar rising-and-setting times; the línghuà of the five planets; the constant-stars’ degrees-and-minutes. At the end is recorded the computation of solar and lunar eclipses. The remainder are all lìchéng (ready-reckoner) tables. Its method takes the Suí Kāihuáng jǐwèi year [599] as the lìyuán (calendrical-epoch); it does not use intercalary months; it takes Aries, Taurus, and the rest of the twelve zodiacal palaces as the fixed (immobile) months, and the regular 1st-through-12th greater-and-smaller months as the mobile months, each with intercalary days. The fractional eclipse-degrees and shadow-clock-divisions it predicts also at times have discrepancies, but among the Western-Region computational arts, compared with the Jiǔzhí and Wànnián calendars, [its accuracy] is in fact precise.
Méi Wéndǐng 梅文鼎’s Wùān lìsuàn shūjì 勿菴厯算書記 says: “The Huíhuí lì was engraved by Bèi Lín; it lays out the lìchéng by lunar year and takes the jùsuàn (distance-computation) by solar year, ingeniously concealing the root-numbers — even his descendants who held office in the Bureau could not understand it. Yet the Huí calendar is the old Western Transformation rate; the Tàixī originally based itself on the Huí calendar and added refinement to it”. This too is the public verdict. The Míng dynasty throughout used [the Huíhuí lì] in conjunction with the Dàtǒng lì; the Míng shǐ describes its method’s general outline, but the present is the original book and is even more detailed-and-clear.
Only — its method was originally for tabulation by the tǔpán and used the original-country’s book; after early-Míng translation into Chinese, transmission-and-study was rather thin, so there were no places of collation, and the corruption-and-omissions are especially severe. Now we have collated two recensions against each other and recorded [the result], in order to preserve one school of the [astronomical] art and supplement what the Míng shǐ does not provide.
Respectfully collated, Qiánlóng 46, third month [April 1781].
Chief Compilers: (subject) Jì Yún 紀昀, (subject) Lù Xíxióng 陸錫熊, (subject) Sūn Shìyì 孫士毅. Chief Collator: (subject) Lù Fèichí 陸費墀.
Abstract
Composition window: 1477 (the year Bèi Lín completed the recension at the Nánjīng Qīntiānjiān and printed it). The underlying Huíhuí lì technical material, however, is layered: the original Khwarezmian-Islamic system of Mashā ‘Aytah dates to the late-Yuán (received in Hóngwǔ 1 = 1368 from the Yuán capital); the first Chinese translation by Lǐ Chōng and Wú Bózōng was completed in Hóngwǔ 15 (1382); a second wave of Hùihúi astronomical material (the Jīngwěidùshí lì via the tǔpán method, processed by Yuán Tǒng) was added in Hóngwǔ 18 (1385). The 提要 catches Bèi Lín out on a chronological error in his own colophon (he claims the calendar entered circulation only after the 1385 tǔpán episode, but the 1384 jiǎzǐ-dated tabular data within the work itself proves the system was already in use in 1384), and on this basis prefers the Míng shǐ Lì zhì’s account.
The Huíhuí lì used the Suí Kāihuáng jǐwèi year (599 CE) as its calendrical epoch — strikingly, the year of the standard Islamic Hijra (622 CE) does not figure as the epoch in the Chinese transmission. The system uses the twelve zodiacal palaces (Aries, Taurus, etc.) as the fixed months, supplemented by the conventional Chinese twelve lunar months (greater and lesser) as mobile months with intercalary days but without intercalary months — a calendrical structure that combines the Hellenistic-Islamic solar-zodiacal substrate with a Sino-lunar overlay.
Significance: the Qīzhèng tuībù is the principal indigenous-Chinese textual witness to the medieval Islamic mathematical-astronomical tradition’s century of formal incorporation into the Míng official calendrical system (alongside the indigenous Dàtǒng lì — the Yuán Shòushí lì’s direct continuation). It is also the work through which the post-Jesuit Tàixī lì astronomers (Méi Wéndǐng’s “the Tàixī originally based itself on the Huí-calendar and added refinement to it”) could trace the lineage of their own astronomy back through Islamic intermediaries to common ancient sources — a key text in the late-imperial Chinese reception of cross-cultural astronomical contact.
The Huíhuí lì Bureau-section (Huíhuí lì kē) within the Qīntiānjiān — established Hóngwǔ 15 and operated by hereditary Islamic-astronomy families — was abolished only in Chóngzhēn 7 (1634), late in the Míng. The Bèi family of Nánjīng was one of the principal hereditary astronomical lines who maintained the Qīzhèng tuībù tradition; on Bèi Lín’s transmission and family see the 貝琳 person note.
Translations and research
- van Dalen, Benno. “Islamic Astronomical Tables in China: The Sources for the Huihui li”, in M. Folkerts and R. Lorch (eds.), Sic itur ad astra: Studien zur Geschichte der Mathematik und Naturwissenschaften, Wiesbaden: Harrassowitz, 2000, pp. 152–175.
- Yano Michio 矢野道雄. Kūshyār ibn Labbān’s Introduction to Astrology, Tōkyō: Institute for the Study of Languages and Cultures of Asia and Africa (ILCAA), 1997 (covers the Islamic side of the Huí-huí lì’s sources).
- Chén Jiǔjīn 陳久金. Huí-huí tiānwén-xué shǐ yánjiū 回回天文學史研究, Nánníng: Guǎngxī Kēxué Jìshù Chūbǎnshè, 1996.
- Yabuuti Kiyoshi 藪內清, “The Huihui-li and Iranian Astronomy”, in his Chūgoku no temmon-rekihō 中国の天文暦法, Tōkyō: Heibonsha, 1969 (rev. ed. 1990).
- Sivin, Nathan. “Copernicus in China,” Studia Copernicana 6 (1973): 63–122 (background on cross-cultural astronomical contact in late-imperial China).
Other points of interest
The 提要’s careful emendation of the transcription of Islamic personal-and-place names — Mǎshā Yìhēi 馬沙亦黑 → Mǎshā Yīhèi 瑪沙伊赫 (Mashā ‘Aytah / Mashayi Khwaja); Mòdíná 黙狄納 → Mòdénè 黙德訥 (Madīnah); Mǎhāmá 馬哈麻 → Mǎhāmùtè 瑪哈穆特 (Mahmūd) — reflects the Sìkù editors’ programmatic effort to revise older Chinese transliterations of foreign proper names according to the Qīng court’s preferred forms, often (as here) consonant with Manchu-Mongolian transliteration conventions of the Qiánlóng period. These re-transliterations document the late-Qīng Chinese awareness of the historical Islamic provenance of the calendrical material.