Shùxué 數學
Mathematical-Astronomical Studies by 江永 (Jiāng Yǒng, 1681–1762, 清, zhuàn 撰)
About the work
Jiāng Yǒng’s 8-juan critical extension of 梅文鼎 Méi Wéndǐng’s mathematical-astronomical synthesis (the KR3f0026 Lìsuàn quánshū and related works), with an appended supplementary 1-juan Xù lìxué 續歷學 (“Continued Calendrical Studies”). Composed in mid-life under the new authority of the KR3f0018 Yùzhì lìxiàng kǎochéng (1724), Jiāng Yǒng works systematically through Méi Wéndǐng’s positions, extending arguments, refining technical details, and where necessary correcting Méi where Jiāng Yǒng believes the master to have been mistaken — but always within the broadly Méi-tradition methodological framework.
Each of the 8 juàn has its own xiǎoxù 小序 (small preface) and treats a specific topic:
(1) Lìxué bǔlùn 歷學補論 — supplementary calendrical exposition extending Méi Wéndǐng on points he had not addressed.
(2) Suìshí xiāozhǎng 嵗實消長 — on the secular variation of the annual real-year. Méi Wéndǐng held that the suìshí gradually shrinks as the apsidal point approaches the winter-solstice and lengthens as it passes; Jiāng Yǒng holds that the suìshí is fundamentally invariant, with the apparent variation due entirely to the motion of the apsidal point and the variation of the small-orbit-circle, with the seasonal-nodes-distance to apsidal-point producing slight surplus near apsidal-point and slight deficit near apogee.
(3) Héngqì zhùlì 恒氣註厯 — on whether to use constant-seasonal-nodes (héngqì) or fixed-seasonal-nodes (dìngqì) in calendar annotation. Méi Wéndǐng had been inconsistent (using dìngqì for the winter-solstice computation but recommending héngqì for general calendar annotation); Jiāng Yǒng argues that consistency requires using dìngqì for all seasonal-nodes if one uses it for the winter-solstice.
(4) Dōngzhì quándù 冬至權度 — on the historical winter-solstice records, building on Méi Wéndǐng’s Chūnqiū dōngzhì kǎo but going further to identify systematic errors in the dynastic-history calendrical-record.
(5) Qīzhèng yǎn 七政衍 — on the geometry of the seven-regulators’ motions, especially on the question of which celestial spheres rotate left-or-right and which move with-or-against the Lǐxiàng kǎochéng model. Jiāng Yǒng provides explicit diagrams to clarify the KR3f0018 Lìxiàng kǎochéng’s model where Méi Wéndǐng had given only verbal description.
(6) Jīnshuǐ fāwēi 金水發微 — on the question of whether Venus and Mercury have separate annual-orbit and apparent-and-disappearance circles. Méi Wéndǐng had originally held them to be the same; later (under the influence of his student Liú Yǔngōng 劉允恭) he concluded they are different (Venus and Mercury have their own annual orbits, with the fújiàn lún being their around-sun apparent figure). Yáng Xuéshān 楊學山 had subsequently questioned the revised position; Jiāng Yǒng defends Méi Wéndǐng’s revised position with explicit diagrams.
(7) ZhōngXī héfǎ nǐcǎo 中西合法擬草 — on Xú Guāngqǐ’s 徐光啟 late-Míng synthetic position (using Chinese conventions for some elements and Western for others). Jiāng Yǒng identifies confusions in the Xú Guāngqǐ position (the use of dìngqì mid-month points as the imperial-ritual guògōng zodiacal-passage times; the inconsistent application of 12-palace nomenclature) and offers corrections, mostly drawing on Méi Wéndǐng’s later refinements.
(8) Suànshèng 算賸 — extending the Méi Wéndǐng trigonometry by adding shortcut methods for spherical triangles, especially for the right-spherical-triangle (zhènghú sānjiǎo 正弧三角) computation.
The supplementary 1-juan Zhènghú sānjiǎo shūyì 正弧三角疏義 supplements the Suànshèng with additional spherical-trigonometry exposition.
The 提要’s verdict is highly favorable: Jiāng Yǒng “following-the-precedent and adding [refinement] — the more pushed-and-extended the more dense — in measurement-verification can also be said to deeply have discoveries”.
Tiyao
[Sub-classification: 子部, Tiānwén suànfǎ class 2, tuībù sub-category. Edition: WYG.]
Respectfully examined: Shùxué, 8 juàn with continued 1 juàn, by Jiāng Yǒng of Our Dynasty. Yǒng’s Zhōulǐ yíyì jǔyào is already catalogued.
This compilation [is] based on Méi Wéndǐng’s Lìsuàn quánshū, [for which it] makes clarifications-and-rectifications, and [is] uniformly aligned with the Imperially-determined Lìxiàng kǎochéng, mediating its same-and-different.
[The 提要 then describes each of the 8 juàn — see the description above.]
[Méi] Wéndǐng’s calendrical-arithmetic is recognized as supreme art (tuī wéi juéjì 推為絶技); this [Jiāng Yǒng work] further proceeds from what is already supplied, obtains what is not detailed — 踵事而増愈推愈密 (following-precedent and adding [refinement] — the more pushed-and-extended the more dense). In measurement-verification, [Jiāng Yǒng] can also be said to deeply have discoveries.
Respectfully collated, Qiánlóng 46, eleventh month [December 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: c. 1730 (after the Lìxiàng kǎochéng publication and Méi Wéndǐng’s death; Jiāng Yǒng was approximately 50) – 1762 (Jiāng Yǒng’s death; the work was certainly substantially complete by the early-Qián-lóng period). The exact composition span is uncertain; Jiāng Yǒng appears to have worked on the topics over many years.
The work’s significance:
(a) Continuation-and-improvement of the Méi Wéndǐng synthesis: Jiāng Yǒng’s posture toward Méi Wéndǐng is one of critical-extension within a shared tradition — he is not a critic in the sense of opposition but in the sense of refinement-and-correction. The work is the principal mid-Qián-lóng demonstration that the Méi Wéndǐng tradition is open to ongoing scholarly elaboration rather than a closed canon.
(b) Integration of KR3f0018 Lìxiàng kǎochéng into the Méi tradition: Jiāng Yǒng’s explicit alignment of his work with the imperial Lìxiàng kǎochéng — using the imperial work as the standard against which Méi Wéndǐng’s positions are evaluated — demonstrates the early-Qián-lóng synthesis of the imperial and the private mathematical-astronomical traditions. The Lìxiàng kǎochéng itself draws on Méi Wéndǐng (through Méi Juéchéng); Jiāng Yǒng’s work uses the imperial recension to refine the original Méi positions.
(c) The specific technical contributions: several of Jiāng Yǒng’s substantive arguments — particularly on the alternative-account of suìshí secular variation (juàn 2), the consistency-requirement for dìngqì usage (juàn 3), and the systematic spherical-trigonometric shortcuts (juàn 8) — represent genuine technical advances over the Méi tradition. The 提要’s assessment that Jiāng Yǒng’s work is “more pushed-and-extended, the more dense” captures the cumulative-progressive character of his contribution.
(d) Bridge between Méi tradition and Dài Zhèn: Jiāng Yǒng was the principal teacher of Dài Zhèn 戴震 (1724–1777), the leading philosopher of mid-late-Qīng kǎojù scholarship and one of the principal mathematical-astronomical scholars of the late Qiánlóng period. Through Dài Zhèn’s later works and through other Jiāng Yǒng students, the Jiāng Yǒng synthesis became a central component of high-Qīng mathematical-and-astronomical practice.
For Jiāng Yǒng’s biographical context, see 江永. For the foundational Méi Wéndǐng works that this engages with, see KR3f0026 Lìsuàn quánshū and KR3f0027 Dàtǒng lìzhì. For the imperial tradition Jiāng Yǒng aligns with, see KR3f0018 Lìxiàng kǎochéng and KR3f0019 Hòubiān.
Translations and research
- Han Qi 韓琦, Tōng-tiān zhī xué 通天之學, Beijing: Sānlián, 2018.
- Hashimoto Keizō 橋本敬造, Mei Wending and his Successors (in various journal publications).
- Sun, Xiaochun. Calendrical Astronomy and Imperial Authority in Qing China (in various journal publications).
Other points of interest
The work’s continued treatment of the Suìshí xiāozhǎng problem — with Jiāng Yǒng departing from Méi Wéndǐng’s account — is one of the more interesting cases of high-Qīng intra-tradition technical disagreement. The resolution would later be achieved in the KR3f0019 Hòubiān’s adoption of Keplerian elliptical orbits, which obviates both Méi Wéndǐng’s and Jiāng Yǒng’s geometric models in favor of a more analytically-precise framework.