Wù’ān lìsuàn shūjì 勿菴歷算書記
Hut-of-Not’s Calendrical-and-Computational Book-Notes (Méi Wéndǐng’s bibliographic catalog of his own works) by 梅文鼎 (Méi Wéndǐng, 1633–1721, 清, zhuàn 撰)
About the work
Méi Wéndǐng’s own annotated catalog of his calendrical-and-mathematical writings, in 1 juàn. The work catalogs 62 titles in calendrical-and-observational astronomy and 26 titles in mathematics — 88 titles in all — with a brief explanatory note for each, summarizing what motivated its composition and what its principal arguments are. Although structurally a jiětí mùlù (annotated bibliography), the work is substantively a synthetic statement of Méi Wéndǐng’s intellectual project: by explaining what each work was for, Méi articulates the whole of his Chinese-and-Western synthetic mathematical-astronomical project, identifying the principal source-traditions he drew on and the principal interlocutors he engaged.
The 提要 highlights several key passages:
(a) The opening Gǔjīn lìfǎ tōngkǎo 古今歴法通考 entry presents Méi Wéndǐng’s celebrated genealogical analysis of Chinese calendrical-astronomical traditions from antiquity to the Yuán Shòushí lì, identifying the specific contribution of each major calendrist: “without reading Yēlǚ Wénzhèng [Chǔcái]‘s Gēngwǔ Yuán lì*, one cannot know the* Shòushí ‘s [treatment of the] five planets; without reading the Tǒngtiān lì*, one cannot know the* Shòushí ‘s yearly real diminution-and-growth; without examining Wáng Pǔ’s Qīntiān lì*, one cannot know the principle of oblique-and-straight rising-and-setting…*” — and so on through fifteen named calendrists from Luòxià Hóng (Hàn) through Liú Hóng, Hé Chéngtiān, Zǔ Chōngzhī, Liú Zhuó, Zhāng Zǐxìn, Yī Xíng, Lǐ Chúnfēng, Yēlǚ Chǔcái, and Guō Shǒujìng. The passage is the canonical Méi Wéndǐng statement of the cumulative-and-incremental nature of Chinese calendrical-astronomical history.
(b) The “Western methods broadly nine schools” passage classifies the European-and-foreign astronomical traditions reaching China into nine sub-traditions: (1) Táng Jiǔzhí lì 九執歷 (the 718-CE Indian-derived Buddhist astronomy); (2) Yuán Wànnián lì 萬年歷 (Zhāmǎěrdīng’s 1267 Persian-derived); (3) Míng Huíhuí lì 回回曆 (Mǎshāyīhèi / Mashā ‘Aytah, KR3f0006); (4) Chén Rǎng 陳壤 and Yuán Huáng 袁黄’s Lìfǎ xīnshū 歷法新書; (5) Táng Shùnzhī 唐順之 and Zhōu Shùxué 周述學’s Lìzōng tōngyì and Lìzōng zhōngjīng — these last categorized as “old Western methods” (jiù Xīfǎ 舊西法); (6) Lì Mǎdòu [Ricci]‘s Tiānxué chūhán + Tāng Ruòwàng [Schall]‘s Chóngzhēn lìshū + Nán Huáirén [Verbiest]‘s Yíxiàng zhì + Kāngxī Yǒngnián lì; (7) Mù Ní’gé [Smogulecki]‘s Tiānbù zhēnyuán + 薛鳳祚 Xuē Fèngzuò’s Tiānxué huìtōng; (8) 王錫闡 Wáng Xīchǎn’s Xiǎo’ān xīnfǎ; (9) Jiē Xuān 揭暄’s Xiětiān xīnyǔ + Fāng Zhōngtōng 方中通’s JiēFāng wèndá — these together categorized as “new Western methods” (xīn Xīfǎ 新西法). The classification is the foundational late-imperial Chinese taxonomy of European-derived astronomical traditions; it is repeatedly cited in subsequent Qīng historiographical literature.
(c) The Zhōubì bǔzhù 周髀補註 entry presents the Xīfǎ Zhōngyuán (Western methods originate from the East) thesis: “observing what it [the Zhōubì] says of the lǐchā (longitudinal-difference) method — this is precisely the source from which the Westerners’ theory derives”. The Huíhuí lì bǔzhù entry parallels: “the Huíhuí calendar is precisely the old Western rate; the Tàixī (the European Catholics) are based on the Huí calendar and added refinement”.
The 提要 notes that Méi Wéndǐng’s framing throughout the work is fully synthetic-and-non-factional: “[he] gathers-and-penetrates each one’s essentials, with absolutely no debate-and-faction views”. This judgment captures the methodological posture that made Méi Wéndǐng’s work foundational for the KāngxīQiánlóng synthesis.
Tiyao
[Sub-classification: 子部, Tiānwén suànfǎ class 2, tuībù sub-category. Edition: WYG.]
Respectfully examined: Wù’ān lìsuàn shūjì, 1 juàn, by Méi Wéndǐng of Our Dynasty. Wéndǐng’s Lìsuàn quánshū is already catalogued. This combines [his] already-engraved and not-yet-engraved books, [for] each annotating the meaning of his composition. In all: 62 kinds of step-computation-and-measurement-verification books, and 26 kinds of arithmetic-method books.
Although it is a category of catalog-with-explanations, [its treatment of] the various schools’ source-flow gains-and-losses, one-by-one marking their indication-of-essentials, makes [the] beginnings-and-endings sequenced-and-clear — truly the grand-gathering of the numerical school.
For example, the Gǔjīn lìfǎ tōngkǎo entry says: “[paragraph quoted in the description above]“.
Again [Méi Wéndǐng] says: “The Western methods are roughly of nine schools” — [paragraph quoted in the description above].
The Zhōubì bǔzhù entry says: “observing what it says of the lǐchā method — this is precisely the source from which the Westerners’ theory derives”. The Huíhuí lì bǔzhù entry says: “the Huíhuí calendar is precisely the old Western rate; the Tàixī (Westerners) are based on the Huí calendar and added refinement”.
These all are with the various Chinese-and-Western methods — gathering-and-penetrating, threading-through, one-by-one obtaining their essentials, absolutely without debate-and-faction views. Therefore although the work is with discussion but without method [being expounded in technical detail], [we] still record it [in the] shùshù (numerical-arts) category, as a general-outline of measurement-and-computation.
Respectfully collated, Qiánlóng 46, ninth month [October 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: c. 1700 (when Méi Wéndǐng began the systematic project of cataloging-and-annotating his own writings) – 1721 (his death). The work was kept up-to-date during Méi’s later years; the surviving recension reflects substantially the state of his bibliographic record at the time of his death.
The work’s significance:
(a) The foundational Méi Wéndǐng self-bibliography: as a record of Méi Wéndǐng’s own annotation of his work, the Wù’ān lìsuàn shūjì is the indispensable reference for understanding his project — the only primary-source statement of what each of his works was for and what he himself thought it was about. For modern scholarship on Méi Wéndǐng, the work is the essential reference and starting point.
(b) The classification of Chinese astronomical genealogies: Méi Wéndǐng’s two major taxonomic statements — the genealogy of Chinese calendrists from Luòxià Hóng to Guō Shǒujìng, and the nine-school classification of European-and-foreign astronomical traditions — define the late-imperial Chinese understanding of astronomical history. Through his grandson Méi Juéchéng’s incorporation into the KR3f0018 Lìxiàng kǎochéng, this taxonomic framework entered the imperial Qīng canon.
(c) The Xīfǎ Zhōngyuán foundational statement: the Zhōubì bǔzhù and Huíhuí lì bǔzhù entries provide the most explicit statement of Méi Wéndǐng’s Xīfǎ Zhōngyuán thesis — that the Western methods are refinements of techniques originally Chinese (the Zhōubì’s implicit lǐchā) or Islamic intermediaries of techniques originally Chinese (the Huíhuí lì as preserving the “old Western rate” derived from antique-Chinese astronomy through Persian intermediaries, then refined by the post-Renaissance Europeans). This thesis, articulated in compressed bibliographic form here, would be developed at greater length in many of Méi’s individual works and would shape Qián-lóng-period astronomical historiography (cf. the Xīfǎ Zhōngyuán framings in the 提要 of KR3f0001, KR3f0014, KR3f0015).
(d) Catalog of 88 Méi Wéndǐng titles: the work documents 88 separately-conceived works by Méi Wéndǐng (62 calendrical, 26 mathematical). Many of these did not survive into the Lìsuàn quánshū (which preserves only 29 titles); the Wù’ān lìsuàn shūjì’s catalog therefore preserves the only record of the additional 59 titles that Méi Wéndǐng intended-or-completed but that have not survived. This makes the work an indispensable historical-bibliographic record of late-Kāngxī mathematical scholarship.
The 提要’s verdict — “absolutely without debate-and-faction views” — is a striking characterization. Méi Wéndǐng’s synthesis is presented as the alternative to the ménhù (factional) astronomical disputes that had troubled Chinese astronomical practice from the late Wànlì through the early Kāngxī (Wèi Wénkuí vs. Xú Guāngqǐ; Yáng Guāngxiān vs. Schall; Wáng Xīchǎn’s yímín anti-Western sub-current). Méi’s non-factional synthetic posture is what made his work institutionally absorbable into the imperial Kāngxī mathematical academy.
For the broader Méi Wéndǐng oeuvre, see KR3f0026 Lìsuàn quánshū (the canonical anthology). For the related Dàtǒng lìzhì, see KR3f0027. For the principal author, see 梅文鼎.
Translations and research
- Han Qi 韓琦, Tōng-tiān zhī xué 通天之學, Beijing: Sānlián, 2018 (treats Méi Wéndǐng’s bibliography extensively).
- Liu Dun 劉鈍, Méi Wéndǐng zhuàn 梅文鼎傳 (biographical sequence in various publications).
- Hashimoto Keizō 橋本敬造. Mei Wending and his Wù’ān lì-suàn shū-jì, in Historia Scientiarum (Tōkyō).
- Jami, Catherine. The Emperor’s New Mathematics, Oxford: Oxford University Press, 2012.
Other points of interest
The 提要’s preservation of Méi Wéndǐng’s extended quoted passages — including the full genealogy of fifteen Chinese calendrists and the full nine-school classification of European-and-foreign methods — is one of the most extensive direct-quotation editorial treatments in the Sìkù tíyào corpus for the Tiānwén suànfǎ category. The quotation-extensiveness reflects the editors’ high regard for Méi Wéndǐng’s authoritative formulations.
The work’s brevity (1 juàn) and substantive density (88 work-summaries with extended polemical-framing passages) make it one of the most concentrated technical-bibliographic productions of the high Qīng. Its continued use as primary-source reference for modern Chinese-language history-of-astronomy scholarship is a measure of Méi’s success in compressing his synthetic project into bibliographic form.