Jiǎnpíng yí shuō 簡平儀說
Treatise on the Simplified Planispheric [Astrolabe] by 熊三拔 (Sabatino de Ursis, S.J., Xióng Sānbá, 1575–1620, 明, zhuàn 撰)
About the work
Sabatino de Ursis’s 1-juàn exposition of the European astrolabium catholicum — the simplified planispheric astrolabe — adapted to Chinese instrumental-and-mathematical conventions. With a preface by Xú Guāngqǐ 徐光啟 dated Wànlì xīnhài autumn (1611) — placing the work at the heart of the calendar-reform debate triggered by the Ministry of Rites’ 1611 memorial. The instrument is a two-disk planar projection of the celestial sphere: the lower disk (xiàpán 下盤, “tiānpán 天盤” — the “heaven board”) carries the equatorial coordinates (the polar line, the equatorial line, the twenty-four seasonal-nodes lines, the twelve hour-lines); the upper disk (shàngpán 上盤, “dìpán 地盤” — the “earth board”), partly transparent, carries the horizontal coordinates (the horizon line, the zenith line, the altitude grid). With the two disks aligned to local polar altitude, the user can read off — for any observed solar altitude — the corresponding hour, season, polar latitude, and azimuth. The text is organized as twelve nomenclature definitions (míngshù shíèr zé 名數十二則) followed by thirteen practical procedures (yòngfǎ shísān shǒu 用法十三首) covering: (1) measuring solar altitude; (2) deriving the sun’s distance from the equator at a given seasonal-node; (3) measuring local solar noon; (4) measuring the local polar elevation (latitude); (5) computing day-and-night length at a given latitude and season; (6) sunrise-and-sunset times; (7) the extraordinary phenomena of the polar regions and the equator; (8) sun-azimuth at sunrise-and-sunset; (9) culmination altitude at noon; (10) sundial construction using the instrument; (11) determining when the sun crosses the zenith; (12) a geometric demonstration that the Earth must be round; (13) the variety of shadow-types observable at different latitudes. The work is the first Chinese-language exposition of an integrated astronomical instrument employing stereographic projection.
Tiyao
[Sub-classification: 子部, Tiānwén suànfǎ class 1, tuībù sub-category. Edition: WYG.]
Respectfully examined: Jiǎnpíng yí shuō, 1 juàn, by the Western-Sea man Xióng Sānbá of the Míng. According to the preface by Xú Guāngqǐ at the head of the volume, [the work] was constantly verified-by-comparison against [the works of] Lì Mǎdòu [Matteo Ricci]. The general purport: by means of [stereographic] projective method (shìfǎ 視法), [the instrument] takes a sphere as a plane, and uses circles to measure the numerical [parameters] of the sphere. There are 12 nomenclature-rules and 13 procedure-rules.
The method uses upper-and-lower two boards. The heaven-board lies below, taking the equatorial longitude-and-latitude — therefore it has the two-pole lines, the equatorial line, the seasonal-node lines, and the hour-divisional lines. The earth-board lies above, taking the horizontal longitude-and-latitude — therefore it has a zenith, a horizon, altitude lines, and horizon-azimuth-degree lines. All [are constructed by] supposing the human eye, from outside the spherical body looking distantly, that what is directly opposite to the great-circle [is projected] as a plane circle; what leans obliquely within is [projected as] an ellipse; what is at the circle-center is [projected as] a straight line; what is parallel to a great-circle, [if] equidistant the small-circle, is also [projected as] a straight line.
The earth-board is hollowed at its plane-circle [region] so that the two boards may be viewed-together. Between the two boards is held a pivot, so they may rotate. In use, fixing the two boards according to the local polar elevation, the equatorial-and-horizontal two longitude-and-latitude [systems] interlock distinctly. All seasonal-nodes, time-divisions, altitude-degrees, and azimuth-degrees can be mutually obtained from each other.
The heaven-board uses a square plate, with a two-eared gnomon set above; the eye sights the shadow. The earth-board’s center [holds] a plumb-line, by which to view degree-and-minute. Setting it up in use, one obtains the solar arc-altitude. Once the solar arc-altitude is obtained, all the time’s other parameters can be derived.
In general, this instrument projects-the-spherical-onto-the-plane like taking a shadow from a candle: although it borrows-an-image, the actual values can be inferred. Spherical-trigonometric (hú sānjiǎo 弧三角) substitution-of-quantity-for-computation truly originates here. Now further deriving from this for measurement: the method is simple and the use is quick — it may be called a sharp instrument of mathematics.
Respectfully collated, Qiánlóng 46, tenth month [November 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.
Original preface (Xú Guāngqǐ 徐光啟, Wànlì xīnhài 1611)
[Yáng] Zǐyún 揚子雲 [Yáng Xióng] did not understand calendrical principles, yet relied on rough method to discuss principle — what principle was that? Shào Yáofū 邵堯夫 [Shào Yōng] did not penetrate the calendrical method, yet wrote private principles and established methods — what method was that?
We do not know that our Confucian study’s transmission has not one character of calendrics (lì) and yet can exhaust the way of Heaven-and-Earth, fully sound the cosmic limits — those who speak of lì cannot escape from this. Confucius said: “the Zéhuǒ [trigram is] gé*” 澤火革. Mèngzǐ said: “if one only seeks its causes” 茍求其故. Gé (revolution): east-west-north-south, year-month-day-hour, where is there nothing that revolves? To speak of method without speaking of revolution — that seems-method-but-is-not-method. Cause (gù): the two-symbols (yīnyáng) and the seven-regulators (sun-moon-five-planets), [with their] precessions-and-recurrences, each have what they are-as-they-are by virtue of (gù). To speak of principle without speaking of cause — that seems-principle-but-is-not-principle.
YáoYú are remote; qīnruò (reverently regulate) and shòushí (impart-the-seasons) — scholar-officials rarely speak of [these things]. The likes of Liú Hóng 劉洪, Jiāng Jí 姜岌, Hé Chéngtiān 何承天, and Zǔ Chōngzhī 祖冲之: every century-or-so one man, every two-or-three centuries one man — there have been none like XīHé 羲和 and ZhòngShū 仲叔 who held ultimate council in a single hall. Therefore on this matter the past three thousand years have been muddled. Guō Shǒujìng was deemed precise-and-marvelous — yet on the meaning of gé (revolution) he is at best partially [adequate], and the ability to speak of what they are-as-they-are by-virtue-of [their] gù — that truly begins from the Western-Tài-Master’s [Ricci’s] entry to China.
The Master once said to me: the Western scholars’ refinement in calendrics has no other clever-trick — for one-or-two thousand at a time, transmitting-and-studying-and-investigating, for three thousand years; “blue [dye] from the indigo-plant becoming bluer-than-the-indigo, water becoming colder-than-water” — at every moment there is some [advance]. Therefore, when speaking of principle, [the discussion grows] subtler and yet more manifest; when establishing method, [the methods grow] more detailed and yet simpler.
I heard his words and sighed: with their thousand-or-two-thousand at a time, transmitting-and-studying-and-investigating for three thousand years — and we, “every century one man, every two-or-three centuries one man” — between this, what comparison of skill-or-clumsiness can be made?
The Master is now dead, granted burial in Yān (Beijing); a decree was further issued to allow his fellow-students, those two-or-three gentlemen, to remain in residence-and-incense-cultivation. The various gentlemen, moved by the imperial grace and seeking to repay it, plan to continue-completing the Lì [Ricci] writings, fully expounding their knowing-Heaven-knowing-Earth, exhausting-principle-investigating-things learning. And it has happened that the Court-mid is just now revising the calendrical method; specifically chosen elder scholars and renowned Confucians have come to oversee its rectification. At that moment, those of the Astronomical Bureau who heard the various gentlemen’s words competed to recommend [the project] above to the Grand Master of Ceremonies, hoping by the precedent of Hóngwǔ rénxū [1382: the Lǐ ChōngWú Bózōng translation of the Huíhuí lì] to translate fully their books for the institutional record. The Grand Master of Ceremonies reported [it] above and [the request] was answered “may be done”. From this point, [in] one moment the calendrical-officer hereditary occupations all summoned valor and sharpened themselves to encourage [the work to] completion — abundant! With Yáo-and-Shùn above and XīHé below, perhaps in the end ultimate council in a single hall [will be possible]?
I hold that of the various gentlemen’s books, when finished, the benefit to the way-of-the-age cannot easily be counted. As for stellar-and-calendrical [matters in particular], when their study is exhausted-to-the-end, [it] will necessarily exceed Guō Shǒujìng several-fold. The smallest [item] is this instrument, that the master Xióng [de Ursis] himself first created and presented to Master Lì [Ricci]; it was what Lì applauded. Incidentally for me he expounded its outline, and [I] in hand received it, drafted it as a chapter — not yet getting into the depths of what is called gù (cause). As for the [discussion of] gé (revolution), this is also one spot of the [legendary] cultivated-leopard’s [pattern]. Master Xióng held it as scant and was unwilling to transmit. I firmly requested that it be put into circulation, as the hāoshǐ (whistling-arrow, [pioneer-marker]) for [the broader project of] discussing calendrical [matters].
Just to exhaust the study, [the books] would still need to number a thousand-or-hundred — this is genuinely not what I can ultimately accomplish. If we must broadly seek scholars of the way-and-arts, with empty-heart raising-and-narrowing, letting their three-thousand-years-of-incremental-cultivation-progress’ work be received, in our years-and-months, all-completed — to manifest-and-illuminate Our Sage-and-Bright [Emperor]‘s coming-to-the-distant grand [accomplishment], and to transmit it to the historical record saying “the calendrical principle becoming perfectly-clear, the calendrical method becoming perfectly-correct, from now and after begun, vastly surpassing the ancient” — also a great delight indeed!
Wànlì xīnhài (1611), autumn-month, Wúsōng [district], Xú Guāngqǐ, xù.
Abstract
Composition: 1611 (Wànlì xīnhài), the date of Xú Guāngqǐ’s preface — a preface that was not retrospective but written at the moment of the work’s first circulation. Internal evidence: Xú Guāngqǐ states that Sabatino de Ursis “first created” the instrument and “presented it to Master Lì [Ricci]” (who “applauded” it) — placing the Jiǎnpíng yí invention sometime between de Ursis’s arrival in Beijing in 1607 and Ricci’s death in May 1610; the written account of the instrument was Xú Guāngqǐ’s draft, with the preface added at publication in 1611. The work thus belongs to the immediate post-Ricci moment, when de Ursis succeeded Ricci as principal Jesuit at the Beijing residence and Xú Guāngqǐ was preparing the technical case for calendar reform that would shortly be memorialized to the throne by the Ministry of Rites.
The work’s instrument-mathematical content makes it the first systematic Chinese exposition of stereographic projection — the geometrical technique by which a spherical surface is projected onto a plane while preserving angles, indispensable to all forms of the astrolabe and ultimately to map-making. The 提要’s recognition that “spherical trigonometric substitution-of-quantity-for-computation truly originates here (* hú sānjiǎo yǐ liàng dài suàn zhī fǎ shí běn yú cǐ *弧三角以量代算之法實本於此)” identifies the work as the foundational entry-point of Western trigonometry into Chinese mathematical practice — predating the more elaborated trigonometric works of the Chóngzhēn lìshū by two decades.
Xú Guāngqǐ’s preface is one of the most consequential documents of late-Míng intellectual history. Its core argument — that European mathematical-astronomical superiority is not the consequence of any particular individual’s genius but rather of the cumulative collective practice of “one-or-two thousand at a time, transmitting-and-studying-and-investigating, for three thousand years” (a strikingly modern formulation of the social character of cumulative scientific practice) — provided the rhetorical-cultural justification for the calendar-reform project that would occupy the next thirty-five years of Chinese mathematical-astronomical institutional life and yield the Chóngzhēn lìshū of 1635 / Shíxiàn lì of 1645. The preface’s other prominent themes — the recoverability of ancient Chinese mathematical-astronomical excellence (XīHé, ZhòngShū) only by means of foreign collaboration; the explicit invocation of the Hóngwǔ Huíhuí lì translation precedent (KR3f0006) to frame the new Jesuit-Chinese collaboration as institutionally orthodox; and the bold prediction that the post-Jesuit reform will “surpass Guō Shǒujìng several-fold” — are all major data points in late-imperial Chinese intellectual history.
Of particular note is the preface’s framing of gé (革, revolution-and-change) and gù (故, cause-and-reason) as the twin missing categories of received Chinese astronomical thought: pre-Jesuit Chinese astronomy could describe but not explain. Xú’s claim that explanatory-causal astronomy “truly begins from the Western-Tài-Master’s entry to China” (* duàn zì XīTàizǐ zhī rù Zhōngguó shǐ *斷自西泰子之入中國始) is one of the most explicit endorsements of foreign intellectual superiority in the entire late-imperial Chinese literature. (The fact that the Qián-lóng-period Sìkù editors preserved this preface intact is itself a significant editorial decision.)
The preface’s somewhat enigmatic reference to the contemporary 1611 calendar-reform proposal — “the Court-mid is just now revising the calendrical method; specifically chosen elder scholars and renowned Confucians have come to oversee its rectification” — refers to the Ministry of Rites’ formal memorial advocating for incorporation of Western methods, a memorial that the throne tabled and that did not produce the institutional reform Xú anticipated. The actual Chóngzhēn lìshū project would only begin in 1629, after a generational delay; Xú himself would lead it, but with the next generation of Jesuit collaborators (Schall, Rho) — de Ursis having been deported in the 1616 anti-Christian persecution.
For Sabatino de Ursis’s broader career and the Jesuit context, see 熊三拔 and 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 (background on the Ricci-de Ursis-Xú collaborative circle).
- Standaert, Nicolas (ed.). Handbook of Christianity in China, vol. 1, Leiden: Brill, 2001 (de Ursis entry).
- D’Elia, Pasquale M., S.J. Galileo in Cina, Roma: Pontificia Universitas Gregoriana, 1947.
- Bertuccioli, Giuliano. “Sabatino de Ursis”, Dizionario Biografico degli Italiani, vol. 39, Roma, 1991.
- Hsia, R. Po-chia. Matteo Ricci and the Catholic Mission to China, 1583–1610, Indianapolis: Hackett, 2016 (background to the de Ursis-Ricci collaboration).
- Jami, Catherine. The Emperor’s New Mathematics: Western Learning and Imperial Authority during the Kangxi Reign (1662–1722), Oxford: Oxford University Press, 2012 (subsequent reception of Jesuit mathematical instruments).
Other points of interest
The 提要’s attribution-of-origin claim — hú sānjiǎo yǐ liàng dài suàn zhī fǎ shí běn yú cǐ 弧三角以量代算之法實本於此 — is technically inaccurate (spherical trigonometry as such was first systematically presented in Chinese in the Cèliàng quányì 測量全義 of the Chóngzhēn lìshū, two decades later) but historically suggestive: the 提要’s editors recognized that European mathematical-astronomical instrument-design (rather than purely textual transmission) was a primary vector by which the new techniques entered Chinese practice.
The 1611 publication date places the Jiǎnpíng yí shuō among the earliest of the post-Ricci Jesuit scientific works in Chinese, predating the Tàixī shuǐfǎ (1612), the Biǎo dù shuō (KR3f0010, 1614), and the Chóngzhēn lìshū project (1629–1635). It is a foundational document in the history of Chinese mathematical astronomy.