Yùzhì lìxiàng kǎochéng 御製歷象考成
Imperially Composed Investigation of the Calendrical Phenomena by 允祿 (Yǔnlù, Héshuò Zhuāng qīnwáng 和碩莊親王, 1695–1767, 清, fèngchì zhuàn 奉敕撰 — by imperial decree) and 何國宗 (Hé Guózōng, ?–1766, 清, fèngchì zhuàn 奉敕撰); with the contributions of Méi Juéchéng 梅㲄成, Wèi Tíngzhēn 魏廷珍, Wáng Lánshēng 王蘭生, Fāng Bāo 方苞, Míngāntú 明安圖, and others as listed in the personnel section
About the work
The Lìxiàng kǎochéng, in 42 juàn (16 + 10 + 16: Upper Edition + Lower Edition + Tables), is the astronomical-calendrical core of the great Kāngxī-Yōngzhèng-period imperial synthesis Lǜlì yuānyuán 律歷淵源 (Foundations of Music and Astronomy, 100 juàn total). Chartered by the Kāngxī emperor in Kāngxī 52 (1713) and completed under Yōngzhèng in Yōngzhèng 2 (1724), the work supersedes the Wànlì-Chóngzhēn-period KR3f0013 Xīnfǎ suànshū — explicitly correcting it on a series of specific technical points — and constitutes the new official-canonical Chinese astronomical-calendrical handbook of the high Qīng. It was the working basis of the Qīntiānjiān (Imperial Astronomical Bureau) until the further revision in KR3f0019 Lìxiàng kǎochéng hòubiān (1742) which introduced Keplerian elliptical orbits.
The work’s tripartite structure:
- Upper Edition (上編 shàngbiān) — Kuítiān chájì 揆天察紀 (“Surveying-Heaven, Examining-the-Calendrical-Threads”): in 16 juàn, the theoretical-physical foundations — celestial geometry, the spherical-trigonometric apparatus, the cosmological framework, the geometric account of solar/lunar/planetary motion.
- Lower Edition (下編 xiàbiān) — Míngshí zhèngdù 明時正度 (“Clarifying-Time, Rectifying-Degrees”): in 10 juàn, the procedural-computational methods — the sequential procedures (bùfǎ 步法) for sun, moon, planets, eclipses, conjunctions.
- Tables (表 biǎo): in 16 juàn, the numerical lìchéng (ready-reckoner) tables.
Front matter includes the Yùzhì Lǜlì yuānyuán xù 御製律歷淵源序 (Yōngzhèng’s preface dated October 1723, the official imperial declaration of the project) and the personnel-list Zhímíng 職名 (with the full Yōngzhèng-2 / 1724 staff roster). The Sìkù 提要 (composed Qiánlóng 49 / 1784) frames the work as Kāngxī’s specifically-commissioned correction of the limitations of the Xīnfǎ suànshū, accomplished against the background of the early-Qīng influx of Western mathematical-astronomical knowledge.
Tiyao
[Sub-classification: 子部, Tiānwén suànfǎ class 1, tuībù sub-category. Edition: WYG.]
Respectfully examined: Yùzhì Lìxiàng kǎochéng, 42 juàn — the Sage Ancestor Benevolent Imperial Ancestor [Kāngxī emperor]‘s imperially-composed Lǜlì yuānyuán’s First Section, [composed in] Kāngxī 52 (1713).
The tuībù (computational-astronomy) art: of ancient methods there is no [reliable] evidence; what can be examined consists of the Hàn Tàichū (104 BCE) and onward, down to the Míng Dàtǒng — and that is all. Since Lì Mǎdòu [Ricci] entered China, the verifications-by-measurement gradually became precise — but the disputations also accordingly arose day by day. Throughout the Míng dynasty, the court’s deliberations clung to factional positions, and [the new methods] were ultimately not put to use.
Our [Qīng] Dynasty’s voice-and-instruction has spread to the limit; the various Western-most countries have all come [to China] across multiple translators, their methods becoming progressively more refined as they are pushed forward. Furthermore — [the new measurements] do not match the Chóngzhēnxīnfǎ [the former Xīnfǎ suànshū]‘s methods, computations, diagrams, and tables. When the Xīnfǎ suànshū was made, the Europeans concealed their learning, [their] doctrinal-statements were obscure-and-deep-and-not-explainable.
The Sage Ancestor Benevolent Imperial Ancestor [Kāngxī emperor] therefore specifically ordered the various ministers to thoroughly investigate the source-of-the-method, and to establish-and-write this book. It is divided into upper and lower two editions: the upper edition called Kuítiān chájì (Surveying-Heaven, Examining-the-Calendrical-Threads), the lower edition called Míngshí zhèngdù (Clarifying-Time, Rectifying-Degrees) — gathering the great unities (dàtóng) of Chinese-and-Western [methods], establishing them on heaven-and-earth without error, [their] subtlety-and-greatness [being] entirely beyond what the bamboo-tube/calabash-shell [narrow] view can fathom.
Now, on what we are able to glance up at: collating with the Xīnfǎ suànshū —
(1) The yellow-path obliquely intersects the equator and emerges within-and-without it; its mutual-distance is the latitude of the sun’s distance from the equator at the two solstices. The Xīnfǎ suànshū used Westerner Tycho [Brahe]‘s measurement, fixing it at 23°31’30”. Now [we], by repeated measurements of the Summer-Solstice midday sun-altitude, obtain the huángchì dàjù (great-distance of yellow-and-red paths) as 23°29’30” — less than what Tycho measured by 2’. Now: the yellow-and-red two paths grow nearer-from-far, [therefore] are necessarily greater in antiquity and lesser at present, gradually shifting — for which subtle reason no clever computation can [foresee them]. Therefore one must measure-densely-by-time-period to conform to the heavens’ motion.
(2) Also: the root of the equation-of-time (shíchā 時差) — its causes are two: one, on account of the sun’s actual motion, the time-divisions thereby advance-and-retreat — [the apsidal gāobēi] is the basis of addition-and-subtraction. The other, on account of the equator’s rising-degrees, the time-divisions thereby grow-and-diminish — [the fēnzhì equinox-and-solstice] is the basis of addition-and-subtraction. The Xīnfǎ suànshū combined the two to establish a single table called rìchā (sun-difference). However, since the gāobēi (apsidal) has motion-divisions per year, the palace-degree index-numbers necessarily cannot be the same. Combining-them-into-one-table, when [used] for many years it necessarily becomes unusable. Now [we] divide them into two tables, doing addition-and-subtraction twice — and as a method this is more precise.
(3) Also: the Xīnfǎ suànshū computes the three solar-eclipse differences (sān chā) using the Huángpíng xiàngxiàn (Yellow-Mean Image-Quadrant) as the basis. However, the three differences all arise from the moon, and the moon’s longitude-and-latitude are the báidào (white-path, lunar-orbit) longitude-and-latitude — [therefore] one ought to use the Báipíng xiàngxiàn (White-Mean Image-Quadrant) as the basis. When the moon is at this degree, there is no east-west difference, and the north-south difference is greatest, equal to the altitude-difference. If [it is] to the east of this degree, [the difference] is early — and there should be a subtraction-difference. If [it is] to the west of this degree, [the difference] is late — and there should be an addition-difference. The addition-and-subtraction sometimes has the same direction as the Huángpíng xiàngxiàn, sometimes the opposite — therefore at the fixed-conjunction-angle (dìngjiāojiǎo) there is the use of reversing (fǎnqí) the addition-and-subtraction.
(4) Also: from antiquity onward, the computation of the lunar-eclipse [parameters of] first-defect and fully-restored and the directional [coordinates of] east-west-north-south have been spoken of with reference to the yellow-path’s longitude-and-latitude — not the horizon’s longitude-and-latitude east-west-north-south. Only when the moon’s real motion’s degree is in the first or sixth lunar-mansion, and the eclipse-time is also at midnight-precisely, do the yellow-path’s longitude-and-latitude east-west-north-south agree with the horizon longitude-and-latitude. Otherwise, the yellow-path rises-and-descends with both straight-and-oblique inclines, and the addition-of-time distance-from-noon is far-or-near; the two longitude-and-latitudes are radically different. The east-west-north-south computed [by the old method] necessarily will not agree with the horizon’s directions. Now [we] actually indicate, on the moon’s body itself, where above-below-left-right is — that the multitude of eyes may all see — which compared to the old method is even more close-and-fitting.
(5) Also: the Xīnfǎ suànshū says that the ancient [planetary] diagrams take the earth as center; the new diagrams take the sun as center. However, in Tycho’s step-computation and equation-numbers, only Mars takes the sun as center; if [one] takes the earth as center to set up [the] computation, the result obtained is identical [with the heliocentric]. We know that Tycho only set up an empty/clever-computation method; the five planets’ actual heaven-orbits all take the earth as center. For Venus and Mercury take the sun as center [only because their] original-wheels (běnlún, deferent), not their original-heavens (běntiān, principal sphere); Saturn-Jupiter-Mars take the sun as center [only as] traces of the next-wheel-position-stars’-motion-distance-from-the-sun, also not their original-heavens.
(6) As for the spherical-trigonometric (hú sānjiǎo 弧三角) method: the Xīnfǎ suànshū’s diagrams-and-explanations are very confused. The zhèngxián (sine) method also lacks the yellow-and-red mutually-derivable method. Now, by abridging the zhèngxián method into opposite-side opposite-angle and vertical-arc-versine three-proportions, then the entire-circle’s longitude-and-latitudes can all be mutually-derived — and operations have their essentials.
These are all the principal items of correcting the Xīnfǎ suànshū. The remainder, in agreement with the Xīnfǎ suànshū, are also pushed-and-extended in precision and density without difference [even] of an accumulated millet-grain. Truly the Great Sage’s composition — for ten-thousand generations none will exceed his [achievement’s] compass.
Respectfully collated, Qiánlóng 49, sixth month [July 1784].
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.
Yōngzhèng’s preface (October 1723)
[Greetings to ancient calendar-and-pitch-pipe traditions: from Yáo’s Xī-and-Hé to Shùn’s HòuKuí to Zhōu’s visit-to-Shāng-Gāo, all dynastic histories carry the calendrical numbers — used to revere Heaven, impart the seasons, communicate with the spirits, harmonize the people. Of this practice the heart is most weighty.]
Our August Father, the Sage Ancestor Benevolent Imperial Ancestor, knew-by-birth, loved-to-study; heaven-bestowed in many capabilities, in his myriad-affairs leisure he gave-his-mind to the calendrical-pitch-pipe and arithmetic methods — accumulating tens of years, broadly examining the multitude-and-complexity, searching the recondite-and-subtle. Cross-collating, he united [it all] in one. He instructed Prince Zhuāng [Yǔnlù] and others to lead-and-direct the literary-officers in compiling at the Méngyǎng zhāi in the inner-palace. Each day [the staff] presented [their drafts]; he personally added corrections. Gathering the result into a book, in total 100 juàn, named Lǜlì yuānyuán. There are three sections, demarcated in editorial-sequence:
The first is called Lìxiàng kǎochéng. Its sections are two: the upper edition, called Kuítiān chájì — discussing the body-of-essence’s images, in order to clarify the principle (lǐ); the lower edition, called Míngshí zhèngdù — densely-applying the use, listing the lìchéng tables, in order to display the method (fǎ).
The second is called Lǜlǚ zhèngyì. Its sections are three: upper edition, called Zhènglǜ shěnyīn (Correcting-Pitches, Examining-Sound) — by which to fix the foot-rule, examine the measurements, seek the pitch-pipe-foundation. Lower edition, called Héshēng dìngyuè (Harmonizing-Sounds, Fixing-Music) — by which by-the-pitch-pipes one makes instruments and examines the eight-sounds. Continuation edition, called Xiéjūn dùqū (Harmonizing-the-Mean, Measuring-Tunes) — by which to exhaust the source of the five-sounds and the two-changes [in their] mutual-harmony-and-mutual-correspondence.
The third is called Shùlǐ jīngyùn. Its sections are two: upper edition, called Lìgāng míngtǐ (Establishing-the-Outline, Clarifying-the-Body) — by which to explain the Zhōubì, explore the HéLuò, expound geometry, clarify proportions. Lower edition, called Fēntiáo zhìyòng (Dividing-the-Categories, Reaching-Use) — by lines, surfaces, and bodies subsuming the Nine Chapters, reaching to jièshuāi (borrowed-decreases) and gēyuán qiútǐ (cutting-the-circle to find solid-bodies), changing-and-transforming on the bǐlì guī, bǐlì shù, jiègēnfāng, and other methods. The tabular-numbers are now complete.
Vast indeed: Our State’s voice-and-spiritual-presence has reached afar; literary-and-administrative tracks are great-unified. From the most-Western Europe, the various countries — each specializing in their hereditary occupations — each presented their techniques at the Chānghé (palace gates) below; classical books and diagrams-and-tables shine-and-completely-await. Our August Father combined-and-synthesized them and decided. Therefore wherever the ancient methods lost transmission over generations [were] selected-but-not-refined, and [wherever] the Western [methods, being like] Zhūlí [the trapping language of borderland barbarians], crooked-and-bent in language, are [merely] spoken without details — all [now] have categorized-clarity, beginning-and-end illuminated. The refined-precision and detailed-completeness — even specialist named-houses cannot peep at one part-in-ten-thousand. What is called “only the Sage can do this” — is this not believable indeed?
Now: principle and number conform-to-the-tally and do not part. Obtaining their numbers, principle is not outside [them]. This is why the Diagram-and-Book opened the prior [foundation] for the Yì-and-Fàn. Using lines and bodies, one categorizes the differences of strings-and-pipes; using arcs and angles, one seeks the degrees of longitudes-and-latitudes. All such items are the refinement of mathematical-method, and the essence of pitch-and-calendar lies here. Therefore the three books mutually serve as inside-and-outside; they regulate the seven regulators (sun, moon, five planets), correct the five sounds, and also necessarily reach into the meaning of the Nine Chapters — by which when tested are without error, when used have effect.
The book having been finished, the various ministers compiling [it] requested that I make a preface and transmit [it]. Reverently considering: the Sage Learning is high-and-deep — how could it be easily approached? But I from early-on have received family-instruction; on this book’s grand purport and subtle meaning, [I] presented my mind in earnest-and-prolonged years. Honoring what I have heard, respectfully I offer this single word of praise. This book — is it only my August Father’s hand-and-bequest’s preservation? Truly: examining antiquity and standardizing the present, it gathers the great-completion. Rising above the prior dynasties, hanging down for a thousand-and-ten-thousand generations as an unchangeable method. Those who would harmonize-the-seasons and rectify-the-day, [bring to] common-rule the measure-weight-and-balance, seek for it in this book — they may then establish heaven-and-earth without contradiction, await the Sage without doubt. Yōngzhèng 1, 10th month, shuò (1st day, October 1723), respectfully written.
Abstract
Composition window: 1713 (Kāngxī 52, the imperial chartering of the Méngyǎng zhāi and the formal beginning of the project) – 1724 (Yōngzhèng 2, the year of completion-and-printing). The principal compilation took place under Kāngxī’s personal direction (1713–1722); the final editorial revision and printing were completed under Yōngzhèng (1722–1724), with Yōngzhèng’s preface dated October 1723.
The work’s significance:
(a) Successor and corrective to the Xīnfǎ suànshū: the Lìxiàng kǎochéng explicitly positions itself as the refinement of the late-Míng KR3f0013 Xīnfǎ suànshū, on the basis of (i) the more accurate measurements made under the early-Qīng Qīntiānjiān (notably the obliquity-of-the-ecliptic measurement of 23°29’30”, reducing Tycho’s value by 2 arcminutes); (ii) the better understanding of the European mathematical-astronomical tradition acquired through the post-1690s influx of Jesuit mathematicians like Antoine Thomas, Joachim Bouvet, Jean-François Gerbillon, and others; and (iii) the methodological maturation of the imperially-sponsored Kāngxī mathematical academy, under which Chinese mathematicians (Méi Wéndǐng’s circle, then his grandson Méi Juéchéng, then Hé Guózōng and Míngāntú) became autonomous interpreters rather than mere transmitters of European material.
(b) The 提要’s six itemized corrections: the 提要’s enumeration of six specific technical corrections to the Xīnfǎ suànshū — the obliquity measurement, the equation-of-time decomposition, the báipíng xiàngxiàn solar-eclipse method, the moon-body coordinate system for lunar-eclipse positions, the geocentric reformulation of Tychonic planetary theory, and the simplified spherical-trigonometric apparatus — is one of the most precise late-imperial Chinese accountings of the progress of mathematical astronomy across one century. The 提要’s careful citation-by-item invites comparison with the immediate-precursor KR3f0013 提要 and frames the Lìxiàng kǎochéng as the realization of the late-Míng project’s potential.
(c) The geocentric vs. heliocentric question: the 提要’s explicit defense of geocentrism — claiming that Tycho’s heliocentric placement of Venus and Mercury was merely “an empty/clever computational method” while the planets in fact orbit the Earth — reflects the standard Jesuit-Chinese consensus of the period. The Jesuit mission’s continuing political-theological commitment to geocentrism (until the 1690s, when papal pressure on the Galileo question briefly relaxed) had constrained what could be transmitted; the Kāngxī court’s mathematicians, working with the materials they had, naturally followed the same geocentric framework. The full transition to heliocentrism in Chinese state astronomy would come only in the 1730s-1740s with the Hòubiān KR3f0019 and its Keplerian elliptical orbits — though even there, formally, the mathematical framework remains compatible with either geocentric or heliocentric interpretation.
(d) The synthetic Lǜlì yuānyuán project: the 100-juan Lǜlì yuānyuán trilogy (Lìxiàng kǎochéng + Lǜlǚ zhèngyì + Shùlǐ jīngyùn) is the most ambitious imperial-scientific synthesis in late-imperial Chinese history. By bringing astronomy, music, and mathematics into a single integrated curriculum — and by explicitly grounding all three in the integration of European-and-Chinese sources — Kāngxī claimed for the imperial throne the role of supreme arbiter-and-synthesizer of natural philosophy. The Yōngzhèng preface’s claim that “even specialist named-houses cannot peep at one part-in-ten-thousand” of the work’s refinement articulates the ideology of the imperial synthesis as transcending all merely partial scholarship.
The work’s institutional life was substantial: it served as the Qīntiānjiān’s working handbook from 1724 until the KR3f0019 Hòubiān of 1742, a period of eighteen years. After the Hòubiān the Lìxiàng kǎochéng was retained as foundational reference work — its tables and procedures continuing to inform Qīng calendrical practice in detail — but the Hòubiān’s elliptical-orbit reform progressively superseded it for the most accurate eclipse-and-planetary computations. The Sìkù-preserved recension is the original 1724 Yōngzhèng-2 imperial printing.
For the broader KāngxīYōngzhèngQiánlóng synthesis-project, see KR3f0019 (the Qián-lóng-period Keplerian revision) and KR3f0020 (the Qián-lóng-period instrument-and-star catalog). For the late-Míng predecessor, see KR3f0013. For the principal authors, see 允祿 and 何國宗.
Translations and research
- Jami, Catherine. The Emperor’s New Mathematics: Western Learning and Imperial Authority during the Kangxi Reign (1662–1722), Oxford: Oxford University Press, 2012. The standard study of the Kāngxī mathematical-astronomical project.
- Han Qi 韓琦, Tōng-tiān zhī xué: Yēsū-huì shì hé tiānwén-xué zài Zhōng-guó de chuán-bō 通天之學: 耶穌會士和天文學在中國的傳播, Beijing: Sānlián, 2018.
- Hashimoto Keizō 橋本敬造. Hō Yū-ran: Christian Mission and Calendrical Reform in Late Ming China, Kyoto: Kansai University Press, 1988 (background to the project).
- Standaert, Nicolas (ed.). Handbook of Christianity in China, vol. 1: 635–1800, Leiden: Brill, 2001.
- Sivin, Nathan. “Copernicus in China”, Studia Copernicana 6 (1973): 63–122.
- Cullen, Christopher. Heavenly Numbers: Astronomy and Authority in Early Imperial China, Oxford: Oxford University Press, 2017.
- Hé Bǐngyù (Ho Peng-Yoke). Li, Qi, and Shu: An Introduction to Science and Civilization in China, Hong Kong: Hong Kong University Press, 1985.
- Lǐ Yán 李儼 and Qián Bǎo-cóng 錢寶琮. Kē-xué shǐ quán-jí 科學史全集, Liáo-níng: Liáo-níng Jiào-yù Chū-bǎn-shè, 1998 (essential reference on Qīng-period mathematics).
Other points of interest
The Kāngxī-period imperial mathematical academy at the Méngyǎng zhāi 蒙養齋 (literally “Studio of Cultivating-the-Young”, the studio in the inner palace where the imperial princes received their education and where Kāngxī himself studied with the Jesuits Antoine Thomas and Joachim Bouvet in the 1680s-1700s) is among the most important institutional innovations of the high Qīng. Its institutional descent — through the Yōngzhèng-period Lǜlì yuānyuán compilation, the Qián-lóng-period Hòubiān and Yíxiàng kǎochéng, and ultimately the late-Qīng Western-mathematics translation projects — constitutes the unbroken institutional thread of imperial Chinese mathematical-astronomical research from the late Míng to the late Qīng.
The 提要’s claim that Tycho’s heliocentric Venus-and-Mercury placement was “an empty/clever computational method” — in the face of straightforward heliocentric astronomical fact — is one of the more pointed examples of the Qián-lóng-period editorial-philosophical posture: when European astronomical doctrines could be reconciled with Chinese cosmological preconceptions (round Earth, geocentric solar-system), they were preserved; when they conflicted (heliocentrism), they were either rejected or — as here — reinterpreted as merely calculational devices.
The Yōngzhèng preface’s framing of the project as Kāngxī’s posthumous monument is consistent with the Qing-period imperial-publication ideology: many of the great works of Kāngxī’s reign — including the Kāngxī zìdiǎn 康熙字典 dictionary (1716) and the Pèiwén yùnfǔ 佩文韻府 rhyming dictionary (1711) — were published under the Yōngzhèng reign with imperial-veneration prefaces. The pattern reflects the political need of the Yōngzhèng regime (which had come to power amid considerable controversy over the succession in 1722) to ground its legitimacy in Kāngxī’s intellectual legacy.