Húngài tōngxiàn túshuō 渾蓋通憲圖說
Diagrammatic Treatise on the Comprehensive [Astrolabic] Standard Combining Sphere-Heaven and Cover-Heaven [Cosmologies] by 李之藻 (Lǐ Zhīzǎo, 1565–1630, 明, zhuàn 撰)
About the work
Lǐ Zhīzǎo’s 2-juan synthesis of the Western planispheric astrolabe with the Chinese armillary-and-cover-heaven traditions, published in Wànlì 35 (1607). The work derives its method from the European astrolabium catholicum (the same instrument later treated by Sabatino de Ursis in KR3f0011 Jiǎnpíng yí shuō), but Lǐ Zhīzǎo provides the theoretical framework that locates the instrument within the longer Chinese cosmological-instrumental tradition: the Húntiān 渾天 (Sphere-Heaven) model gives the spherical celestial body, the Gàitiān 蓋天 (Cover-Heaven) model gives the planar projection-onto-the-Earth’s-disc, and the Jiǎnpíng (simplified planar) instrument is the geometric synthesis projecting the sphere onto the plane by stereographic projection from the south celestial pole. The first juàn (shàng) treats the geometric foundations: the placement of the equator as the projecting circle, the placement of the zhòuchángguī 晝長規 (longest-day circle, the tropic of Cancer for the northern observer) as the largest projected circle, and the dependence of all other circles’ projected diameters on their angular distance from the projection-pole. The second juàn (xià) presents the practical applications: the construction of the instrument, the use-procedures, and the derived diagrams. The work is structurally a more theoretical-and-pedagogical companion to de Ursis’s later KR3f0011 (which is more procedural-and-practical), and the two together constitute the foundational late-Wànlì Chinese-language astrolabe corpus.
The 提要 records the early-Qīng mathematician Méi Wéndǐng’s 梅文鼎 important observation that the húngài tōngxiàn instrument’s structure was already to be found in the Yuán-period astronomical instruments of Zhāmǎlǔdīng 札馬魯丁 (Jamāl al-Dīn al-Buhārī, the Iranian astronomer who served the Yuán court in the 1260s) — and Méi’s hypothesis that the instrument represented “lost techniques of the Zhōubì that flowed into the Western lands” (a typical Xīfǎ Zhōngyuán 西法中源 framing). Méi composed a Dìngbǔ 訂補 (correction-and-supplement) in 1 juàn to the Húngài tōngxiàn túshuō and a Xuánjī chǐ jiě 璇璣尺解 to accompany it; the Sìkù editors note that these can be consulted alongside the present text.
Tiyao
[Sub-classification: 子部, Tiānwén suànfǎ class 1, tuībù sub-category. Edition: WYG.]
Respectfully examined: Húngài tōngxiàn túshuō, 2 juàn, by Lǐ Zhīzǎo of the Míng. Zhīzǎo’s Pángōng lǐyuè shū 頖宫禮樂疏 is already catalogued.
This book derives from the Western Jiǎnpíng yí method. For the Húntiān (Sphere-Heaven) and the Gàitiān (Cover-Heaven) are both established as round; whereas the Jiǎnpíng draws the Húntiān as a flat circle: the Húntiān is the full form, the human eye looks at it from outside; the Gàitiān is the half form, the human eye looks at it from inside; the Jiǎnpíng stops at one face — fixing the human eye at a single position and looking-straight-at-it.
The method: supposes the human eye [is] at the south or north pole, viewing the yellow-path (ecliptic), the equator, and the various circles of the longest-day-and-shortest-day; relying on the line-of-sight’s traversed-points, it terminates [their] boundary on a single flat-circle. Next, in accordance with each location’s polar elevation, by the projection-method takes the zenith and the periphery of the horizon, and likewise terminates [their] boundary within the previous flat-circle. Next, in accordance with the equatorial longitude-and-latitude, by the projection-method takes the seven-luminaries [sun-moon-five-planets] and the constant-stars, and likewise takes [these] back to within the previous flat-circle.
The equator is the central circle. Beyond the equator, the closer to the eye [i.e. nearer the south pole, the projection-pole], the larger the circle and the longer its diameter; beyond the equator, the further from the eye, the smaller the circle and the shorter its diameter. Zhīzǎo took the zhòuduǎn guī (shortest-day circle — i.e., the southern tropic) as the largest circle: this is viewing from the south pole, where the zhòuduǎn guī is near the eye and the circle is large. His intent: that the central-Chinese region’s polar elevation, all that lies within 113.5 degrees of the north pole, falls within this great circle.
The book opens with a general discussion of the instrument’s form. The first juàn treats the lower-circles’ day-degree-divisions and clock-divisions, and the construction-and-use methods. The latter juàn’s various diagrams all root in this.
Méi Wéndǐng once made a Dìngbǔ (Correction-and-Supplement) in 1 juàn. His statement: “The húngài instrument uses the gàitiān method to substitute for the húntiān application. Its construction is found in the Yuánshǐ among the instruments used by Zhāmǎlǔdīng. Privately I suspect [it to be] lost techniques of the Zhōubì that flowed into the Western [lands]. However, the present book’s method of dividing the yellow-path into stellar-divisions still lacks half [of the necessary divisions], so this instrument is very rare — there has been no way to obtain its construction. Now [I] have made it complete in what was lacking, and corrected its errors, so that one may make [the instrument] according to method”. He also has a Xuánjī chǐ jiě in 1 juàn; both are sufficient to assist this book in its circulation. With his own views, [these are] in Wéndǐng’s books — here we do not repeat them.
Respectfully collated, Qiánlóng 46, eleventh month [December 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: 1607 (Wànlì 35), the year of publication. Lǐ Zhīzǎo had been collaborating with Matteo Ricci since at least 1601 (his engraving of Ricci’s Kūnyú wànguó quántú world-map dates from 1602); the Húngài tōngxiàn túshuō belongs to the immediately pre-baptism phase of his Catholic-mathematical-astronomical engagement with the Beijing residence (his baptism would follow in 1610, the year of Ricci’s death). The work is the first full Chinese-language exposition of stereographic projection — the underlying mathematical technique of the planispheric astrolabe — and also the first Chinese-language exposition of the European astrolabe instrument as a coherent integrated tool.
The work’s distinctive intellectual contribution is its synthetic framing: rather than presenting the European astrolabe as a foreign import, Lǐ Zhīzǎo articulates it as the resolution of the long-standing Chinese cosmological debate between Húntiān (Sphere-Heaven, the Hàn-period synthesis associated with Zhāng Héng 張衡) and Gàitiān (Cover-Heaven, the older pre-Hàn cosmology preserved in the Zhōubì KR3f0001). The instrument’s name Húngài tōngxiàn — “the standard that comprehensively combines [tōng] Hún and Gài” — explicitly proposes the astrolabe as the geometric reconciliation of the two Chinese cosmological traditions. This framing was probably both apologetic (making the foreign instrument acceptable to Chinese cosmological taste) and historically genuine (the astrolabe’s underlying stereographic projection does in fact effect a planar representation of the celestial sphere from a fixed observation point, formally analogous to what Gàitiān attempted as a representational scheme).
Méi Wéndǐng’s later Dìngbǔ and Xuánjī chǐ jiě — composed in the early Qīng — built on Lǐ Zhīzǎo’s foundation and corrected the missing star-divisional material; the Sìkù editors recognize the LǐMéi sequence as constituting the canonical Chinese-language astrolabe-instrument literature of the late-Míng / early-Qīng. Méi’s Xīfǎ Zhōngyuán hypothesis — that the astrolabe descends from lost Zhōubì techniques transmitted westward — is an instance of the same historiographical framing characteristic of the period (cf. the Zhōubì 提要 KR3f0001 and the Cèliáng fǎyì 提要 KR3f0014). The factual substrate of Méi’s claim is the documented presence of an astrolabe-equivalent instrument among Zhāmǎlǔdīng’s 1267 Yuán-court astronomical instruments; this much is correct. Méi’s larger inference about the original direction of transmission (East-to-West, in the long pre-Islamic past) is unsupported but functionally important as a culturally-acceptable framing for the otherwise-foreign instrument.
The 提要’s note that “the central-Chinese region’s polar elevation, all that lies within 113.5 degrees of the north pole, falls within this great circle” reflects Lǐ Zhīzǎo’s design choice to make the southern-tropic-circle the outer boundary of the instrument’s projection — appropriate for northern-hemisphere astrolabes. This is the standard European convention for medieval-Renaissance astrolabes; Lǐ’s adoption of it without modification reflects his fidelity to the European instrument-design tradition.
For Lǐ Zhīzǎo’s broader Catholic-Chinese intellectual program (the Tiānxué chūhán anthology of 1626, his Tóngwén suànzhǐ of 1614 with Ricci, the Yuánróng jiàoyì of 1614 with de Ursis, the Xīnfǎ suànshū co-directorship), see the 李之藻 person note. For the broader Jesuit-Chinese intellectual context, see 利瑪竇.
Translations and research
- Hashimoto Keizō 橋本敬造. Hō Yū-ran: Christian Mission and Calendrical Reform in Late Ming China, Kyoto: Kansai University Press, 1988.
- Engelfriet, Peter M. Euclid in China, Sinica Leidensia 40, Leiden: Brill, 1998.
- Standaert, Nicolas (ed.). Handbook of Christianity in China, vol. 1, Leiden: Brill, 2001 (Lǐ Zhīzǎo entry).
- D’Elia, Pasquale M., S.J. Galileo in Cina, Roma: Pontificia Universitas Gregoriana, 1947.
- Hé Bǐngyù (Ho Peng-Yoke). Li, Qi, and Shu: An Introduction to Science and Civilization in China, Hong Kong: Hong Kong University Press, 1985.
- Sun, Xiaochun. “Dōng-xī tiān-wén-xué de chuán-bō yǔ jiā-jiē” 東西天文學的傳播與嫁接 (East-West astronomical transmission and grafting), in Zhōng-guó kē-jì shǐ liào 中國科技史料 (Beijing) 23.4 (2002).
- Pan Nai 潘鼐, Zhōng-guó tiān-wén yí-qì shǐ 中國天文儀器史, Shàng-hǎi: Shànghǎi Kē-jì Jiào-yù Chū-bǎn-shè, 2005 (treats Zhā-mǎ-lǔ-dīng’s instruments and the Hún-gài tōng-xiàn synthesis).
Other points of interest
The Húngài tōngxiàn túshuō is one of the relatively few late-Wànlì Jesuit-affiliated mathematical-astronomical works composed by a Chinese author rather than translated from Jesuit oral exposition (cf. the works of de Ursis KR3f0010 KR3f0011 and Dias KR3f0012, all of which are Jesuit-authored). Lǐ Zhīzǎo’s authorial autonomy here — his independent organization, his integration of the European material into the Chinese cosmological framework, his decision to name the work in terms of the HúnGài debate — is characteristic of his role as the senior Chinese-Catholic intellectual partner of his generation and prefigures the more elaborated synthesis that would follow in the Tiānxué chūhán anthology of 1626.
The instrument-name Tōngxiàn 通憲 (literally “comprehensive standard” or “universal canon”) is unusual: xiàn in Chinese astronomical usage typically refers to imperial-administrative standards, and the choice of this term gives the astrolabe the cultural weight of a state-sanctioned canonical instrument. This may have been a deliberate Lǐ Zhīzǎo choice to recommend the foreign instrument to court use — anticipating the calendar-reform memorial of 1611 that he and Xú Guāngqǐ would shortly co-author.