Biǎo dù shuō 表度說
Treatise on Gnomon Measurements by 熊三拔 (Sabatino de Ursis, S.J., Xióng Sānbá, 1575–1620, 明, kǒuyì 口譯 — oral translation); brushed by 周子愚 (Zhōu Zǐyú, 明, bǐlù 筆錄 — literary recording)
About the work
A 1-juàn introductory treatise on the use of the upright gnomon (biǎo 表) to derive solar position, time-of-day, and seasonal markers from shadow measurements — the basic tool of pre-telescopic positional astronomy. Sabatino de Ursis dictated the work in Chinese in 1614 (Wànlì jiǎyín); the Hànlín-affiliated literatus Zhōu Zǐyú polished it. The text opens with five propositions (wǔ tí 五題) on the cosmographic foundations: (1) the daily uniform circular motion of the sun across the heavens implies uniform shadow motion; (2) the Earth lies at the center of the celestial sphere — verified by the equality of day-and-night at the equinoxes; (3) the Earth is small enough relative to the solar sphere to count as a point — the doctrine of KR3f0009 Qiánkūn tǐyì applied here as a presupposition; (4) the Earth is round (dì běn yuántǐ 地本圜體) — proved by the time-zone phenomenon (shíchā 時差) and by lunar eclipses observed simultaneously at different geographic locations; (5) the gnomon-tip serves as the practical proxy for Earth’s center in shadow geometry. The remainder treats the construction of upright (zhíjǐng 直景) and horizontal (dǎojǐng 倒景) gnomons, the use of trigonometric tables to convert shadow lengths to solar altitudes, the determination of the solstices and equinoxes from shadow extrema, the determination of latitude from polar altitude, and the construction of practical sundials (rìguǐ 日晷) — including portable cylindrical and square forms with engraved hour-and-season grids. The work’s diction is unusually pedagogical: de Ursis argues each step before computing it. The 提要 explicitly notes that, in a moment when “the doctrines of the Earth’s roundness and smallness had only just entered the Central Land, and many were astounded on suddenly hearing them”, de Ursis chose to begin with shadow geometry as “the most simple-and-clear thing in the calendrical method”, precisely so that readers might grasp the cosmographic doctrines through demonstrably empirical applications.
Tiyao
[Sub-classification: 子部, Tiānwén suànfǎ class 1, tuībù sub-category. Edition: WYG.]
Respectfully examined: Biǎo dù shuō, 1 juàn, by Xióng Sānbá of the Western Sea, [orally translated] in the Wànlì jiǎyín year [1614] of the Míng. Sānbá’s Tàixī shuǐfǎ 泰西水法 [1612] is already catalogued.
The book’s general purport says: gnomon-measurement (biǎo dù) originated from the tǔguī (earth-gnomon); now further is set forth a quick method, by which one may set up gnomons at will. In general, those wishing to clarify the meaning of gnomon-shadow must first discuss the principle of the sun-disk’s circulating motion and the proportions by which the sun-disk exceeds the earth-globe — for these their method has separately a complete book; here is briefly raised what is essential, divided into five propositions:
— First, the sun-disk’s circuit-of-the-heavens, above toward the celestial-zenith, below toward the horizon, in its rotation over the earth-surface is everywhere uniform; therefore the earth-body’s shadows are also uniform.
— Second, the earth-globe is at the heaven’s center: if one were to suppose the earth-globe not at the heaven’s center, then the earth’s shadow could not follow the sun in circuit-rotation, and slow-and-swift would be unequal. Now at spring-and-autumn equinoxes the sun-disk is six shí above the horizon making day, six shí below the horizon making night — what could this be except being-in-the-true-center?
— Third, the earth is smaller than the sun-disk; viewing the earth-globe from the sun-disk it stops at one point. If the earth were not a [mere] point, then [a person] standing on the earth-surface would not get to see half the heaven-body — the upper half necessarily smaller, the lower half necessarily larger, by being obstructed by the half-earth’s thickness.
— Fourth, the earth is fundamentally a round body; therefore in one day the twelve chén are alternately seen at different places: as where straight-toward-the-sun gets midday, the place straight-back-from-the-sun gets midnight, the place 30 degrees east gets wèi time, the place 30 degrees west gets sì time. If the earth were a square body, then only that under the [direct point of the] sun would have its time correctly placed; left-and-right places would necessarily have unequal long-and-short [times].
— Fifth, the gnomon-tip serves as the earth’s center: in setting up a gnomon to take a shadow, one must on two flat surfaces obtain two kinds of shadow. The first: an upright gnomon, on a level surface forming a right angle with the horizon — the shadow obtained is the upright shadow (zhíjǐng 直景), as for example mountain, tower, and tree shadows on the ground. The second: a transverse gnomon’s shadow is the inverted shadow (dǎojǐng 倒景), as for instance against a sun-facing wall placed transversely on its level surface, with a gnomon set [parallel] to the horizon.
The end speaks of gnomon-form, gnomon-degrees, and the methods of computing the seasonal-nodes, the time-and-clock-divisions, and the drawing of the sundial — all furnished with diagrams-and-text giving evidence that is reliable.
Setting up a gnomon to take a shadow in order to know the clock-divisions and seasonal-nodes is the simplest and clearest item in the calendrical method — and yet without clarity on heaven-and-earth’s circulation and habituation in trigonometric arithmetic (sānjiǎo zhī suànshù 三角之算術), one cannot obtain its precise standard. At this time, the doctrines of the earth’s roundness and smallness had only just entered the Central Land, and many on suddenly hearing them were astounded; therefore [the author] first raised what is most simple-and-clear, in order to display [those doctrines’] credibility.
Abstract
Composition: 1614 (Wànlì jiǎyín), the date stated by the 提要 itself. By this point Sabatino de Ursis had been at the Beijing residence for seven years and had succeeded Ricci as the principal Jesuit voice in mathematical astronomy; he was working in close collaboration with Xú Guāngqǐ 徐光啟 and Lǐ Zhīzǎo 李之藻 on the technical preparations for the calendar-reform initiative formally proposed by the Ministry of Rites in 1611. The Biǎo dù shuō should be read together with its companion piece KR3f0011 Jiǎnpíng yí shuō (1611, with Xú Guāngqǐ’s preface) as the elementary entry-point to the European mathematical-astronomical curriculum that de Ursis was making available to the Chinese reform party.
The work’s argumentative strategy — beginning with what is empirically demonstrable (gnomon shadows, easily measured) and reasoning from these to the doctrinally controversial (round Earth, geocentric universe, small Earth) — is the standard Jesuit pedagogical method, and the 提要 captures the strategy precisely. The Sìkù editors, writing 167 years after the work, were of course working within a Chinese mathematical-astronomical tradition that had long since accommodated round-Earth doctrine (their reference to “trigonometry” — sānjiǎo zhī suànshù 三角之算術 — would have been incomprehensible to early Wànlì readers but was self-evident to Qián-lóng-period editors).
The 提要’s classification of the Earth-roundness-and-smallness doctrines as having “only just entered the Central Land” (chū rù Zhōngtǔ 初入中土) at the time of the work is a careful piece of intellectual-historical periodization: the editors recognize that pre-Jesuit Chinese astronomy, even at its highest (Guō Shǒujìng’s Shòushí lì), had operated within a broadly flat-Earth-and-large-Earth framework. The Biǎo dù shuō is thus situated as one of the foundational propaedeutic texts of the 1610s Jesuit-Chinese astronomical encounter.
Practical content: the work supplies (a) explicit construction directions for upright and transverse gnomons; (b) the trigonometric tables needed to convert shadow length to solar altitude (twelve-fold subdivision of the gnomon length, sixty-fold subdivision of each unit, giving 720-place precision); (c) latitude tables for major Míng cities (Beijing 40°+, Nánjīng 32.5°, Shāndōng 37°, Shānxī 38°, Shǎnxī 36°, Hénán 35°, Zhèjiāng 30°), with the editors’ candid note that these were measured directly only for Nánjīng-Beijing-Jiāngxī-Guǎngdōng and only estimated from maps for the rest; and (d) construction directions for cylindrical and square portable sundials with seasonal grids.
For the broader Jesuit context (Ricci’s mission, de Ursis’s career, the calendar-reform initiative), see 利瑪竇 and 熊三拔.
Translations and research
- Engelfriet, Peter M. Euclid in China, Sinica Leidensia 40, Leiden: Brill, 1998 (background on the Ricci-de Ursis-Xú collaborative circle).
- Hashimoto Keizō 橋本敬造. Hō Yū-ran: Christian Mission and Calendrical Reform in Late Ming China, Kyoto: Kansai University Press, 1988.
- Standaert, Nicolas (ed.). Handbook of Christianity in China, vol. 1, Leiden: Brill, 2001 (entries on de Ursis and the Beijing residence).
- D’Elia, Pasquale M., S.J. Galileo in Cina, Roma: Pontificia Universitas Gregoriana, 1947 (treats de Ursis among the post-Ricci Jesuit astronomers).
- Bertuccioli, Giuliano. “Sabatino de Ursis”, in Dizionario Biografico degli Italiani, vol. 39, Roma: Istituto della Enciclopedia Italiana, 1991.
Other points of interest
The 提要’s editorial attention to the passage between Chinese and Western scientific cultures — its explicit recognition that the round-Earth doctrine “only just entered the Central Land” in the late Wànlì and that the work’s empiricist pedagogy was a deliberate response to that novelty — is one of the more historically self-aware moments in the Sìkù tíyào’s treatment of Western scientific texts.
The work’s first proposition — the sun’s uniform daily circulation — is presented as a Ptolemaic-Aristotelian doctrine, but de Ursis carefully avoids the specifically heliocentric implications of post-1543 Copernican astronomy. The Jesuits’ political-theological commitment to geocentrism (until the 1690s) shaped what could and could not be transmitted; the Biǎo dù shuō’s presentation here is fully orthodox by the Jesuit standards of 1614.