Yuánběn Géxiàng xīnshū (原本)革象新書
Original Recension of the New Treatise on the Reformed Astronomical Image-System by 趙友欽 (Zhào Yǒuqīn, 1271–1335, 元, zhuàn 撰); 王禕 (Wáng Yī, 1322–1373, 明, kāndìng 刊定)
About the work
Zhào Yǒuqīn’s original 5-juan, 32-chapter astronomical-and-optical treatise — one of the most innovative scientific works of the Yuán. The text combines traditional calendrical computation (tuībù), the Chinese-cosmological Gàitiān / Húntiān synthesis, eclipse geometry, and original experimental science. Its most famous chapter, the Xiǎoxì zhī jǐng 小隙之景 (“Image through a Small Aperture”), records Zhào’s systematic camera-obscura experiment: arrays of candles on tables, a perforated board, and a screen, varied in source intensity, aperture size, and screen distance. Zhào established that aperture shape does not determine image shape (the image carries the source’s form, not the aperture’s), that aperture size governs image brightness (not shape), that source intensity scales image brightness, and that screen-distance attenuates brightness — a systematically experimental demonstration unprecedented in pre-modern science of any tradition. Other distinctive contributions include an iterative inscribed-polygon computation of π to high precision (working in the spirit of Liú Huī’s third-century 割圓術 but pushed to higher orders) and an original argument about geographic location and its astronomical correlates (north-pole altitude as latitude, lunar-eclipse timing-difference as longitude). The work was completed during Zhào’s mature life under the Yuán; the 提要 fixes a terminus post quem of 1281 (the inception of the Shòushí lì whose suìcè jiājiǎnfǎ the text takes for granted). Note on textid mapping: the canonical catalog meta assigns title (重修)革象新書 2 卷 to KR3f0005 and (原本)革象新書 5 卷 to KR3f0004, but the actual Kanripo source files under both IDs are swapped (the KR3f0005 directory holds the 5-juan original; the KR3f0004 directory holds the 2-juan abridgment). This work-note describes the work present in the KR3f0005 source directory — i.e. the 5-juan Yuánběn Géxiàng xīnshū.
Tiyao
[Sub-classification: 子部, Tiānwén suànfǎ class 1, tuībù sub-category. Edition: WYG.]
Respectfully examined: Géxiàng xīnshū, 5 juàn, the compiler’s name and surname not recorded. Sòng Lián composed a preface, calling it the work of Master Zhào Yuándū. The Master was a man of Pòyáng who lived in seclusion and concealed himself; his name and style are not known — some say his name was Jìng 敬, zì Zǐgōng 子恭; some say it was Yǒuqīn 友欽 — it cannot be determined in detail. Wáng Yī once revised-and-printed the book; his preface gives the name as Yǒumǒu 友某 (friend-and-something), zì Zǐgōng, and notes that his ancestral lineage in the Sòng held the [imperial-clan] registration. Examining the Sòngshǐ Zōngshì shìxì biǎo 宋史宗室世系表: the Hànwángfáng 漢王房, in its 12th generation, used the character yǒu 友 as the linking-name. The book’s text says: “The suìcè jiājiǎnfǎ (yearly-tabulation addition-and-subtraction method), beginning from the Zhìyuán year xīnsì [1281], has been in use down to the present*“. So this man must come after Guō Shǒujìng — the period also accords [with this]. However, the language is from received tradition and cannot be conclusively settled.
The Dū Qióng Sānyú zhuìbǐ 都卭三餘贅筆 records: “I once saw a miscellaneous book stating that the Master’s name was Yǒuqīn, zì Jìngfū 敬夫, a man of Déxīng 徳興 in Ráo[-zhōu]; that ‘name Jìng, zì Zǐgōng’ and ‘zì Zǐgōng (子公)’ are both wrong” — but it does not say what its source is. Only the surname Zhào is brilliantly clear and beyond doubt.
After the book was pruned-and-polished by Wáng Yī, the recensions in circulation were all from Yī’s recension; Master Zhào’s original was lost. Only the Yǒnglè dàdiǎn preserves [it], and collated against Yī’s recension, the two have variants of difference-and-similarity: we know that at the time of Yáo Guǎngxiào’s compilation [of the Yǒnglè dàdiǎn], the source he relied on was still the old recension. Yī’s preface rather criticizes [the original] as weed-clutter and rough-rude. Yet the shùshù (numerical-arts) tradition is master of measurement-and-computation — it cannot be measured by literary craftsmanship’s skill-or-clumsiness. Furthermore, although Yī also applied his mind to astronomy and stellar pneuma, the Confucian’s combined-versatility ultimately does not match the dedicated specialist’s primary occupation. Therefore the two recensions’ contents likewise have mutual short-and-long: we have recorded both side by side, sufficient to provide for cross-reference.
Within [the original], items such as Rì zhì zhī jǐng (sun-arrival shadow): the Zhōubì 周髀 says: “at summer-solstice the sun is straight at the inner ring; at winter-solstice straight at the outer ring”. China is near below the inner ring; ground-and-horizon meet the inner ring at yínxū 寅戌 [angles] and meet the outer ring at chénshēn 辰申 [angles] — the long-and-short [day-lengths] of the two solstices are bounded by this. Cold-and-heat qì derive from being near or far from the sun. But this book says the day’s length-and-shortness derives from the sun’s high-or-low transit, while the qì’s cold-and-heat derives from accumulated qì much-or-few. — Tiānzhōu suìzhōng (heaven-cycle year-end): heaven left-rotates, its pivot called the Red Pole 赤極; the sun right-rotates, its pivot called the Yellow Pole 黄極; the asterisms also right-rotate, taking the Yellow Pole as their reference, thereby producing precession. But this book says the heaven-body cannot be known — only by means of the asterisms speaking: left-rotation discusses east-west and not north-south; right-rotation discusses north-south and not east-west — radically different views. But this book says: “like a fine and a poor horse: the poor one falls behind the fine one by one circuit, then they meet again at one place”. — Rìdào suìchā (sun-path precession): precession derives from the asterisms’ right-rotation; whenever one examines the winter-solstice sun-position at some star, some degree, some minute, that is one matter. Up to the Shòushí method’s established additions-and-subtractions, called the suìshí xiāozhǎng (yearly-actual diminish-and-grow): with the constant-qì winter-solstice and the fixed-qì winter-solstice, that is again another matter — utterly different things. But this book combines them into one. — Also Tiāndì zhèngzhōng (heaven-and-earth correct-center): when the sun is at heaven’s middle, its form is small; when rising-from-earth or entering-earth, the form is large — this is the [phenomenon] caused by mist-pneuma. But this book says heaven’s zenith is far and the four sides are near. Also: north-south degrees must be measured by the North Pole’s elevation-above-the-earth; east-west degrees must be measured by lunar-eclipse timing — there is no other technique. But this book wishes to use the North Pole to determine east-west declination, and east-west shadow to determine north-south declination. — Dìyù yuǎnjìn (geographic far-and-near): the earth-sphere is fully round, and at every place there is a heaven-zenith. But this book holds to the old doctrine, saying that Yángchéng 陽城 (Sòng-state’s spiritual center) is below the heaven-zenith. Also: the Yuánshǐ records day-and-night clock-divisions for South-and-North seas as each having surplus-and-deficit; but this book holds southern-region day-and-night long-or-short [does] not differ much. Also: clock-divisions follow the equator’s degrees, and shadow movement [follows] the horizon, so morning-and-evening shadow moves slowly, near-noon shadow moves swiftly; the further south, the slower-grows-slower and swifter-grows-swifter. But this book says: westward-deviating means morning slow and evening swift; eastward-deviating means morning swift and evening slow. — Yuètǐ bànmíng (moon-body half-bright): whenever sun-and-moon are mutually facing, [the moon] must be near the eclipse-paths and so enters the dark hollow; far from the eclipse-paths, the earth cannot eclipse it. But this book holds: “divided-by-earth receives light, like a magnet attracting iron”. His arguments all err on the side of looseness-and-incorrectness.
Other [items]: he treats the bó of yuèbó 月孛 as the bó of huìbó 彗孛; says the heaven above the earth is more than the heaven below the earth; says the Yellow Path year-by-year does not follow the old course; says the moon’s mottling is mountains-and-rivers’ shadow; says a lunar eclipse means [the moon] receives much sunlight; says yáng in the extreme returns to kàng; says sun-and-moon’s circumference-and-diameter are double each other; says the dark hollow is not earth’s shadow. Either he adheres to the old methods, or he produces new explanations of his own — at the level of empirical verification he also has many errors-and-failures.
However, his deep-thinking and pursuing-investigation also bring out what earlier men did not bring out. With respect to today’s methods, [his] is loose; with respect to ancient methods, it is already close. Among those who discussed Heaven before the Yuán, he is still among those with original insight. Therefore at the corrupted-erroneous places we have used today’s methods to add notes refuting [him] correctly, while still preserving his statements, in order to retain [him] as one school’s learning.
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: 1281 (the Shòushí lì — the Zhìyuán xīnsì method whose suìcè jiājiǎnfǎ the work cites as already in use — was promulgated this year) – 1335 (Zhào Yǒuqīn’s death). The terminus post quem of 1281 is fixed by the 提要’s careful identification of the calendrical evidence; the terminus ante quem by Zhào’s death. Sòng Lián’s preface — written for Zhāng Rùn’s printing of the original recension at the very end of the Yuán or the beginning of the Míng (Sòng Lián 1310–1381) — confirms a smooth pre-Míng transmission through the disciple-line Zhào → Zhū Huī → Zhāng Rùn.
The text’s transmission is unusual: after Wáng Yī’s 1370s abridgment, the original 5-juan recension dropped out of circulation, and for some four centuries the abridgment was the form known to readers. The Yǒnglè dàdiǎn, however — compiled under Yáo Guǎngxiào 姚廣孝 in the early Míng — preserved Zhào’s original directly from the late-Yuán manuscript tradition rather than from Wáng Yī’s already-pruned recension; on this textual fortuity rests the survival of the original. The Sìkù editors recovered the Yǒnglè dàdiǎn version, collated it against Wáng Yī’s recension to confirm the genuine differences, and printed both in parallel — explicitly invoking the Xīn / Jiù Tángshū precedent.
The 提要’s astronomical critique deserves attention as a document in its own right. Its long catalog of Zhào’s errors — e.g. his geocentric-flat-Earth assumption that Yángchéng (the traditional Chinese geomantic center) lies below the heaven-zenith; his incorrect conflation of the Shòushí’s suìshí xiāozhǎng with the precession-derived suìchā; his magnetic-attraction model of lunar-eclipse light-reception; his incorrect doubling of solar and lunar diameters — is grounded in late-Qián-lóng (1781) astronomical knowledge, which is to say, in Sino-Jesuit synthesis astronomy. The editors’ verdict — “with respect to today’s methods, [his] is loose; with respect to ancient methods, it is already close. Among those who discussed Heaven before the Yuán, he is still among those with original insight” — is a model of historicized scientific judgment: errors are flagged with marginal notes (ànbó 案駁), but the work is preserved as testimony to “one school’s learning”.
The biographical paragraph in the 提要 — collating Sòng Lián’s preface, Wáng Yī’s preface, the Sòngshǐ Zōngshì shìxì biǎo (which fixes the imperial-clan generation by the 友 character), and Dū Qióng’s Sānyú zhuìbǐ (which alternatively gives Zhào’s zì as Jìngfū and his native place as Déxīng) — is the most thorough premodern reconstruction of Zhào Yǒuqīn’s identity and the basis of all later treatments. See the 趙友欽 person note for the consolidated lifedates.
Translations and research
- Volkov, Alexei. “Calculation of Pi in Ancient China: From Liu Hui to Zhao Youqin,” Chinese Science 11 (1993–94): 27–48. The standard study of Zhào’s π method.
- Needham, Joseph (with Wáng Líng), Science and Civilisation in China, vol. 3 (Mathematics and the Sciences of the Heavens and the Earth), Cambridge University Press, 1959; vol. 4.1 (Physics), 1962. Discusses the pinhole-image experiment in the optics section of vol. 4.
- Sivin, Nathan. Granting the Seasons: The Chinese Astronomical Reform of 1280, Sources and Studies in the History of Mathematics and Physical Sciences, New York: Springer, 2009. The standard treatment of the Shòu-shí lì context.
- Bo Shuren 薄樹人. “Zhào Yǒuqīn jí qí Géxiàng xīnshū” 趙友欽及其《革象新書》, Kēxué shǐ jíkān 科學史集刊 12 (1984).
- Hashimoto Keizō 橋本敬造. Joju-reki no kenkyū 授時暦の研究, Kōbe: Tōhō Shoten, 1979 (treats Zhào in the wider context of Yuán astronomical-calendrical reform).
- Cullen, Christopher. Heavenly Numbers: Astronomy and Authority in Early Imperial China, Oxford: Oxford University Press, 2017 (background on Chinese astronomical traditions before Zhào).
Other points of interest
The textid–source mismatch (catalog meta has KR3f0004 = original / 5-juan and KR3f0005 = abridgment / 2-juan; the actual file directories carry the swapped assignment) deserves an editorial note in any future reconciliation of the Kanripo catalog with the source corpus.
The 提要’s biographical excursus is one of the rare cases where the SKQS editors openly use multiple-source reconstruction-of-identity for an author whose name is uncertain — a methodologically interesting moment in Qīng-dynasty Sinological method.