Jiāliàng suànjīng 嘉量算經
Mathematical Canon of the [Imperial] Measure by 朱載堉 (撰)
About the work
朱載堉 Zhū Zàiyù’s (1536–1611) mathematical treatise on the imperial jiāliàng 嘉量 — the standard measuring-vessel cited in the Hàn shū Lǜlì zhì — in 9 juàn. The jiāliàng is the canonical Hàn-imperial measure of volume, comprising the hú 斛, dǒu 斗, shēng 升, gě 合 and yuè 龠 nested measures; its dimensions had become a focal philological problem for MíngQīng scholars seeking the underlying acoustic-and-volumetric basis of the imperial-canonical system of weights, measures, and pitches.
Abstract
The work belongs to Zhū Zàiyù’s vast project of mathematical-philological recovery of the ancient lǜlǚ 律呂 (pitch-pipe) and dùliànghéng 度量衡 (weights-and-measures) systems. Where his more famous works treat the acoustic side of the project — the KR3i… Lǜxué xīnshuō 律學新説 (1584) on equal-temperament, etc. — the Jiāliàng suànjīng treats the volumetric side. Zhū Zàiyù’s central concern is the reconstruction of the dimensions of the imperial jiāliàng vessel from the verbal description in the Hàn shū Lǜlì zhì (compiled by Bān Gù 班固 in the late 1st century CE, drawing on the lost Sānwáng lǜshū of Liú Xīn 劉歆) — a problem that requires mathematical reconciliation of multiple cross-referenced dimensions stated in disparate units.
The work systematizes:
(1) The arithmetic of cubic measure and the relations among the canonical volumetric units (hú, dǒu, shēng, etc.).
(2) The reconstruction of the jiāliàng vessel dimensions, including the inscription details (the jiāliàng míng 嘉量銘 of Liú Xīn) that constrain the geometry.
(3) The relation between the volumetric jiāliàng and the acoustic-pitch system: the huángzhōng 黃鐘 pitch-pipe, whose length and bore determine the basic unit volume of the yuè 龠 (the smallest unit). This is the mathematical foundation of the Hàn-canonical tónglǜ dùliànghéng (uniform pitches-weights-measures-and-volumes) system.
(4) Comparison of the reconstructed dimensions with the Wáng Mǎng jiāliàng 王莽嘉量 vessel preserved in the imperial collection (the famous bronze vessel cast by Wáng Mǎng’s regime in 9 CE, on which Liú Xīn’s specifications were authoritatively realized) — including detailed measurements of the surviving vessel and Zhū Zàiyù’s reconciliation of the textual specifications with the surviving physical artifact.
The work is one of the principal documentary records of late-Míng mathematical-antiquarianism. Zhū Zàiyù’s approach combines technical mathematical competence with serious historical-philological scholarship — characteristic of his entire mathematical project. His reconstruction of the jiāliàng dimensions became the standard reference for subsequent Qīng lǜlǚ and dùliànghéng scholars; the work was repeatedly cited in the Kāng-xī-era imperial reference compendia and in the QiánJiā evidential-scholarship literature on the ancient measurement-systems.
Dating: the work belongs to Zhū Zàiyù’s mature productive period, notBefore 1582 (after the closing of his initial Lǜxué xīnshuō phase) and notAfter 1603 (the date by which his collected Yuèlǜ quánshū had absorbed the work). The companion calendrical-mathematical Lǜlì róngtōng 律厯融通 (1595, KR3f0007) by Zhū Zàiyù provides the parallel calendrical-mathematical exposition.
Translations and research
- Cullen, Christopher. 1990. “The Suàn-shù shū 筭數書 ‘Writings on Reckoning’.” Needham Research Institute Working Papers. — Provides context for the jiā-liàng problem in the comparative early-Chinese metrological literature.
- Cullen, Christopher, and Anne S. C. Farrer. 1983. “On the Term ‘Hsüan Chi’ and the Flanged Trilobate Jade Discs.” Bulletin of the School of Oriental and African Studies 46.1: 52–76.
- Needham, Joseph (with Wang Ling). 1959. Science and Civilisation in China, vol. 3. Cambridge: Cambridge University Press. — Treats Zhū Zàiyù’s mathematical-metrological work.
- Goodrich, L. Carrington, and Chaoying Fang, eds. 1976. Dictionary of Ming Biography. New York: Columbia University Press. — Standard biography of Zhū Zàiyù.
Links
- Companion works by same author: KR3f0007 Lǜlì róngtōng; the broader Yuèlǜ quánshū corpus
- Tradition: the Hàn-canonical Lǜlì zhì of the Hàn shū