Qiánkūn tǐyì 乾坤體義
The Substance and Meaning of Heaven and Earth (Treatise on the Cosmos) by 利瑪竇 (Matteo Ricci, Lì Mǎdòu, S.J., 1552–1610, 明, zhuàn 撰)
About the work
Matteo Ricci’s first systematic exposition in Chinese of European cosmography and applied geometry, in 3 juàn. The upper and middle juàn present the cosmological-astronomical doctrine: a spherical Earth divided into the five climatic zones (hánnuǎn wǔdài 寒煖五帶) by latitude, the geocentric nine-celestial-spheres model (the jiǔzhòng tiān 九重天 of Aristotelian-Ptolemaic astronomy as transmitted through the Coimbra Jesuit syllabus), the four classical elements (shuǐhuǒtǔqì 水火土氣 — water, fire, earth, air, replacing the Chinese five-phase scheme); the geometric explanation of solar and lunar eclipses through Earth-shadow; the relative-size ratios of Sun, Moon, the planets, and the Earth; and the theory of atmospheric refraction (yìngméng 映蒙) to explain the apparent enlargement of the rising-and-setting solar and lunar discs. The lower juàn presents elementary practical geometry: line-and-area computations, plane and elliptical figures, mutual containment-and-comparison of figures, treated as a supplement to the classical Chinese fāngtián 方田 (square-field) tradition (juānbǔ gǔ fāngtián zhī suǒ wèijí 補古方田之所未及).
The 提要 — written from the perspective of the Qīng synthetic mathematical tradition that had absorbed and refined the Jesuit material — pronounces an unusually positive verdict: “its words are all verified by actual observation; its methods all carry through completely (qí yán jiē yàn zhū shícè, qí fǎ jiē jù dé biàntōng 其言皆騐諸實測, 其法皆具得變通)“. The editors explicitly trace the genealogy of the KāngxīQiánlóng imperial Shùlǐ jīngyùn 數理精藴 back through Xú Guāngqǐ’s mid-17th-century reform to this very text — shì shū gù yì dàlù zhī chuílún yǐ 是書固亦大輅之椎輪矣 (“this book is indeed the unhewn-spoked wheel of the great Imperial Carriage” — the foundational pre-form of the eventual achievement).
Tiyao
[Sub-classification: 子部, Tiānwén suànfǎ class 1, tuībù sub-category. Edition: WYG.]
Respectfully examined: Qiánkūn tǐyì, 3 juàn, by Lì Mǎdòu of the Míng. Lì Mǎdòu was a Western man; in the Wànlì period he sailed to Guǎngdōng — this is the beginning of Western methods entering China. Lì Mǎdòu had penetrated both Chinese and Western literatures; therefore all the books he authored are in Chinese characters and Chinese language, requiring no second translation.
The book’s upper and middle juàn both treat heavenly phenomena: dividing the inhabited regions of cold-and-warmth into the five [climatic] zones, taking sun, moon, and stars in heaven as nine layers, taking water, fire, earth, and air (qì) as the four great primary phases (sì dà yuánxíng 四大元行); using sun, moon, and earth-shadow — the three things — to determine the eclipse-magnitudes; reaching as far as the constant-stars and the Seven Regulators having ratios-of-doubling [in size] with the earth, and sun-and-moon rising-and-setting each having reflection-and-mist (yìngméng — atmospheric refraction); much disclosing what earlier men did not disclose. Where his many-sided rare similes [are deployed, they] are also all winding-yet-detailed-and-clear.
The lower juàn all treats arithmetic — taking edge-lines and surface-areas, plane-circles and elliptical-circles, mutually containing-and-comparing, supplementing what the ancient Fāngtián did not reach — making a foundation for present-day line, surface, and solid [computation]. Although the fascicles are not many, his words are all verified by actual measurement; his methods all carry through completely. What is called “diction concise but meaning complete” — Our Dynasty’s [imperial] Shùlǐ jīngyùn mostly takes its arguments from [this work] and develops them further. At the time of the late-Míng calendrical-method’s confusion, the Prince-Heir of Zhèng [Zhū] Zàiyù, Xíng Yúnlù, and other men all forcefully refuted the [established] errors, but their learning was not yet sufficient to triumph. Only after Xú Guāngqǐ and others changed to using the new methods did [Chinese mathematical-astronomical understanding] gradually pass from sparse to refined; and in Our Dynasty [the Qīng] [study] has been further deepened, only now beginning to exhaust the subtle. Then this book is indeed the unhewn-spoked wheel of the Great Imperial Carriage.
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: 1605 (the year by which Ricci had completed his major mathematical-cosmographic Chinese publications and was working on integrating the European geometry-and-cosmology curriculum for Chinese readers — Tiānzhǔ shíyì had appeared 1603, Èrshíwǔ yán in 1605) – 1610 (Ricci’s death). The work appears to have circulated in manuscript late in his life; printed editions in continuous circulation from the Chóngzhēn period onward. The Qiánkūn tǐyì’s underlying European source is the standard Coimbra-Jesuit Sphaera mundi tradition derived from Sacrobosco’s Tractatus de sphaera with the Aristotelis Stagiritae De caelo et mundo commentary tradition, transmitted through Christopher Clavius’s lectures at the Roman College where Ricci studied in the 1570s. The geometric material in the lower juàn is preparatory work in the line of Clavius’s geometry textbooks, anticipating the more systematic Jǐhé yuánběn 幾何原本 (Ricci-Xú Guāngqǐ Euclid translation) of 1607.
The work is foundational in two distinct ways:
(a) The geocentric nine-spheres model: the Qiánkūn tǐyì’s presentation of the jiǔzhòng tiān (nine concentric celestial spheres) was the first connected Chinese-language exposition of the Aristotelian-Ptolemaic geocentric universe. Although later Jesuit astronomers (notably Adam Schall von Bell and Ferdinand Verbiest) would shift to the modified Tycho-Brahe geo-heliocentric system in their late-Míng / early-Qīng calendrical writings, the Qiánkūn tǐyì’s geocentric framework was the entry point — and the framework that the Sìkù editors a century-and-a-half later still saw as foundational.
(b) The five climatic zones and round-Earth doctrine: the work’s elementary geographic exposition — five latitudinal zones, antipodal symmetry, atmospheric refraction at the horizon — together with the parallel cartographic project of the Kūnyú wànguó quántú 坤輿萬國全圖 (1602), introduced the round-Earth doctrine to mainstream Chinese intellectual discourse. The Sìkù editors’ position that “Chinese mathematical-astronomical understanding gradually passed from sparse to refined” via Ricci’s foundation is one of the most explicit pieces of late-imperial Chinese acknowledgment of intellectual debt to European science.
The 提要’s narrative arc — late-Míng calendrical breakdown → Zhū Zàiyù and Xíng Yúnlù’s diagnosis but limited remedy → Ricci’s foundational supply of new tools → Xú Guāngqǐ’s mid-century reform → the KāngxīQiánlóng Shùlǐ jīngyùn synthesis as completion — is the standard late-imperial Chinese account of the period 1580–1750 in mathematical astronomy, and the Qiánkūn tǐyì is the indispensable intermediary text in this story.
The work’s status as the first significant Western-mathematical text to be entered into the Sìkù — preceding even the Jǐhé yuánběn itself in the Sìkù arrangement — gives it a peculiar canonical importance. For Ricci’s biography, mission method, and the broader Jesuit-Chinese intellectual project, see the 利瑪竇 person note.
Translations and research
- Engelfriet, Peter M. Euclid in China: The Genesis of the First Chinese Translation of Euclid’s Elements, Books I–VI (Jihe Yuanben, Beijing, 1607) and Its Reception up to 1723, Sinica Leidensia 40, Leiden: Brill, 1998. Standard study of the Ricci-Xú geometric collaboration; treats Qián-kūn tǐ-yì in context.
- Hashimoto Keizō 橋本敬造. Hō Yū-ran: Christian Mission and Calendrical Reform in Late Ming China, Kyoto: Kansai University Press, 1988.
- D’Elia, Pasquale M., S.J. Fonti Ricciane, 3 vols., Roma: La Libreria dello Stato, 1942–1949 (the standard scholarly edition of Ricci’s writings, with Italian translation and apparatus).
- Spence, Jonathan D. The Memory Palace of Matteo Ricci, New York: Viking, 1984. The standard English-language biography.
- Po-chia Hsia, R. A Jesuit in the Forbidden City: Matteo Ricci, 1552–1610, Oxford: Oxford University Press, 2010. Recent scholarly biography.
- Standaert, Nicolas (ed.). Handbook of Christianity in China, vol. 1: 635–1800, Leiden: Brill, 2001.
- Hé Bǐngyù (Ho Peng-Yoke). Li, Qi, and Shu: An Introduction to Science and Civilization in China, Hong Kong: Hong Kong University Press, 1985.
- Wáng Zhòngmín 王重民, “Lì Mǎdòu yǔ Qián-kūn tǐ-yì” 利瑪竇與《乾坤體義》, in Tiān-wén dǎ-tǎn 天問探討 / Tiān-xué chū-hán studies (various reprints from 1930s onward).
Other points of interest
The 提要’s editorial emphasis on Ricci’s dual literary competence — “Lì Mǎdòu had penetrated both Chinese and Western literatures; therefore all the books he authored are in Chinese characters and Chinese language, requiring no second translation” — is a striking late-Qīng acknowledgment of the unusual character of the Ricci texts in the Chinese canonical record: they are the only major Sìkù entries authored de novo in literary Chinese by a foreigner.
The 提要’s complete silence on the religious purpose of Ricci’s work — situating the Qiánkūn tǐyì purely in the Tiānwén suànfǎ (mathematical astronomy) compartment, with no mention of his Christian mission — is consistent with the Qián-lóng-period editorial policy of bracketing Catholic-doctrinal content while preserving the scientific output. (Ricci’s overtly theological Tiānzhǔ shíyì 天主實義 was placed not in the Sìkù but in the Cúnmù 存目 list of titles-known-but-not-included.)