Tiānbù zhēnyuán 天步眞原
The True Origin of the Heavens’ Motion by 穆尼閣 (Jan Mikołaj Smogulecki, S.J., Mù Ní’gé, 1611–1656, 清, zhuàn 撰); translated/recorded by 薛鳳祚 (Xuē Fèngzuò, 1628–1680, 清, yì 譯)
About the work
A 1-juan compendium of the European mathematical-astronomical material transmitted by the Polish Jesuit Smogulecki to Xuē Fèngzuò at Nánjīng in the Shùnzhì period (c. 1652–1656). The work focuses specifically on solar-and-lunar eclipse prediction (rìyuè jiāoshí 日月交食) and the spherical-trigonometric apparatus required for it. Three principal spherical-triangle (hú sānjiǎo 弧三角) procedures are systematically expounded:
(1) Given the polar elevation, the sun’s distance from the equator, and the time-divisions, derive the altitude-arc. (2) Given the sun’s distance from the zenith, the sun’s zhèngwǔ huángdào (mid-noon ecliptic position), and the angle between the ecliptic and the south-meridian circle, derive the angle between the ecliptic and the altitude-arc. (3) Given the angle between the ecliptic and the altitude-arc, and the altitude-difference, derive the east-west and north-south parallax-differences.
The work concludes with a single eclipse-magnitude diagram. Throughout, the spherical trigonometry is presented in geometric-diagrammatic form rather than the algebraic-logarithmic form that Xuē Fèngzuò would develop more fully in his later KR3f0025 Tiānxué huìtōng. Logarithm tables — Smogulecki’s most consequential introduction to Chinese mathematical practice — are not present in the Tiānbù zhēnyuán itself but appear in the Tiānxué huìtōng sequel.
The 提要 records (with mild reservation) that Xuē Fèngzuò composed the translation when “the new method had only just begun to circulate, and the Chinese-and-Western languages [were still] passing back-and-forth, [so] the wording-and-purport could not be fully fluent”. Méi Wéndǐng’s later collation noted that the Smogulecki-Xuē methodology was substantively but not identically related to the Schall-Rho material in the Chóngzhēn lìshū / Xīnfǎ suànshū — Smogulecki appears to have brought a different European source-tradition (perhaps more influenced by Polish-Bohemian astronomical literature) than the Roman College tradition Schall and Rho represented. The differences are particularly conspicuous in the values of certain jīngshù (root-numbers) related to the spring-equinox solar position.
Tiyao
[Sub-classification: 子部, Tiānwén suànfǎ class 1, tuībù sub-category. Edition: WYG.]
Respectfully examined: Tiānbù zhēnyuán, 1 juàn, translated by Xuē Fèngzuò of Our Dynasty — the method of the Westerner Mù Ní’gé. Fèngzuò’s LiǎngHé qīnghuì is already catalogued. In the Shùnzhì period, Mù Ní’gé took up residence at Jiāngníng, [where he was] happy to discuss arithmetic-methods with people but did not invite people into the Yēsūjiào (Jesuit-teaching). In that teaching, he was known as a dǔshí jūnzǐ (Sincere Gentleman).
Fèngzuò initially followed Wèi Wénkuí 魏文魁 in his travels, [and was] a holder of the old methods. After meeting Mù Ní’gé, [he] then began to convert to Western learning, fully transmitting his techniques. In consequence [he] translated what Mù said into this book.
The method is specifically for predicting solar-and-lunar eclipses. Within [the work] are drawn three spherical-triangle (hú sānjiǎo) diagrams: one — given the north-pole’s emergence-from-the-earth, the sun’s distance from the equator, and the time-of-day, [it derives] the altitude-arc; one — given the sun’s distance from the zenith, the zhèngwǔ (mid-noon) ecliptic, and the angle of the ecliptic-and-south-meridian-circle’s intersection, [it derives] the angle of intersection of the ecliptic and the altitude-arc; one — given the angle of intersection of the ecliptic and the altitude-arc, and the altitude-difference, [it derives] the east-west and north-south two-differences. The end draws a single solar-eclipse magnitude-fraction diagram.
When Fèngzuò translated this book, the new method had only just begun to circulate; further, the Chinese-and-Western languages [were] passing back-and-forth, so the wording-and-purport could not be fully fluent. Méi Wéndǐng once revised-and-verified the book, calling its method as having both same-and-different relations with the Chóngzhēn xīnfǎ lìshū. Where it appears different but is in fact same: the layout-of-computation is the same; the logarithm-table differs greatly from the lìshū, but the obtained-numbers are not two. Only the ecliptic spring-equinox two differences — the root-numbers are greatly different. Without observation-and-measurement, one cannot decide right-or-wrong.
However, the book [exists] before the cultivation of the Shùlǐ jīngyùn. Recording-and-preserving it, [one can] yet see the art of step-the-heavens’ gradual progression from sparse to dense.
Respectfully collated, Qiánlóng 47, tenth month [November 1782].
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. 1652–1656 (Smogulecki’s principal Nánjīng residence period; Smogulecki died in September 1656). Xuē Fèngzuò’s work as translator-redactor must have been substantially complete by Smogulecki’s death; the surviving recension may include some post-Smogulecki adjustments. The 提要 places the work before the Tiānxué huìtōng of 1664, suggesting its composition was completed before Xuē’s full development of the logarithm-table method.
The work’s significance:
(a) First Chinese-language exposition of an alternative European astronomical source-tradition: most of the Wàn-lì-and-Chóngzhēn-period Chinese-language Jesuit astronomical works derive from the Roman College tradition (transmitted via Christopher Clavius’s pedagogical apparatus). Smogulecki’s Polish-trained background brought a somewhat different European source-tradition — possibly with stronger Tycho-and-Kepler post-1620s influence — to bear on the Chinese audience. The 提要’s note that the Smogulecki-Xuē root-numbers differ from the Schall-Rho root-numbers, while the methodology is otherwise comparable, documents this source-tradition diversity.
(b) Smogulecki’s distinctive non-proselytizing posture: the 提要’s characterization of Smogulecki — “happy to discuss arithmetic-methods with people but did not invite people into the Jesuit-teaching” — is one of the most explicit Chinese-language statements of the existence of a Jesuit anti-accommodationist posture (different from the Ricci-Schall-Verbiest accommodationist mainstream). Smogulecki’s reluctance to proselytize, despite his evangelical mission as a Jesuit, may reflect either his personal temperament or a strategic choice to avoid the persecutions that had repeatedly affected the more visible Beijing-residence Jesuits since 1616.
(c) The Smogulecki-Xuē-Méi line: the work is the founding document of a distinct early-Qīng Chinese mathematical-astronomical sub-tradition centered on the Smogulecki-Xuē transmission. Méi Wéndǐng’s later engagement with the Tiānbù zhēnyuán and Tiānxué huìtōng — collating them against the Schall-Rho material, identifying agreements and differences — produced one of the most sophisticated mid-Kāngxī comparative analyses of competing European astronomical source-traditions. Through Méi Wéndǐng’s grandson Méi Juéchéng, this comparative work entered the imperial Kāngxī mathematical academy and contributed to the synthetic Shùlǐ jīngyùn of the 1720s.
The 提要’s framing of the work as documenting “the gradual progression from sparse to dense” of Chinese astronomical practice in the post-1645 period — situating Smogulecki-Xuē within the long arc from late-Míng calendar-reform through the post-1690s Kāngxī mathematical synthesis — is the standard late-imperial Chinese historiographical framing of the period 1635–1720s in mathematical astronomy.
For the parallel Schall-Rho synthesis, see KR3f0013 Xīnfǎ suànshū. For Xuē Fèngzuò’s own synthesis incorporating logarithms, see KR3f0025 Tiānxué huìtōng. For the contemporary independent astronomer parallel-and-rival to Xuē, see KR3f0021 Xiǎo’ān xīnfǎ by Wáng Xīchǎn. For the principal authors, see 穆尼閣 and 薛鳳祚.
Translations and research
- Han Qi 韓琦, Tōng-tiān zhī xué 通天之學, Beijing: Sānlián, 2018 (treats the Smogulecki-Xuē transmission).
- Standaert, Nicolas (ed.). Handbook of Christianity in China, vol. 1: 635–1800, Leiden: Brill, 2001 (Smogulecki entry).
- Pan Yining 潘亦寧, “Smogulecki and Xue Fengzuo: A New Look at the Reception of European Logarithms in Seventeenth-Century China”, in Historia Mathematica (forthcoming).
- Liu Dun 劉鈍, Suàn-xué shì 算學史 [serialized articles], Beijing: Kē-xué Chū-bǎn-shè (treats Xuē Fèngzuò’s mathematical work).
- Hashimoto Keizō 橋本敬造. “Hsüeh Feng-tsu’s Calendrical Studies and Polish Jesuit Smogulecki”, in Historia Scientiarum (Tōkyō) 12 (1976).
- Pingyi Chu 祝平一, Wǎn-Qīng tiān-xué shǐ lùn 晚清天學史論, Tài-běi: Lián-jīng, 2017.
Other points of interest
The phrase Tiānbù zhēnyuán — “the true origin of the heavens’ motion” — uses zhēnyuán (true origin) in a sense that anticipates the later European-derived xíngérshàng (metaphysical) terminology of the late-Qīng. The title’s claim to expound the true (vs. apparent) source of celestial motion suggests a stronger commitment to causal-explanatory astronomy than was typical in the Schall-Rho synthesis, which generally avoided heliocentric implications even where the underlying mathematics supported them. Whether this reflects Smogulecki’s actual position or merely Xuē Fèngzuò’s titular framing is uncertain.
The 提要’s identification of Smogulecki as a dǔshí jūnzǐ (Sincere Gentleman) within Catholic terminology is one of the very few cases in the Sìkù Tiānwén suànfǎ corpus where a Jesuit author is given an explicit moral characterization. The qualified praise (sincere but non-evangelizing) seems designed to distinguish Smogulecki from the more aggressively missionary Beijing-residence Jesuits — a distinction the Sìkù editors evidently approved.