Zhǔnwàng jiǎnfǎ / Gēyuán húshǐ bǔlùn / Gōugǔ gēyuán quányì tú / Fāngyuán bǐlì shùbiǎo 準望簡法/割圈弧矢補論/勾股割圈全義圖/方圈比例數表
Four-Work Compendium: Simplified Surveying / Supplementary Discussion of Circle-Arc Functions / Diagrammatic Full Exposition of Right-Triangle Circle-Cutting / Numerical Tables of Square-and-Circle Proportions by 戴震 (撰)
About the work
A four-work compendium by 戴震 Dài Zhèn, transmitted together as a 1-juàn unit complementing the larger KR3fc038 Gōugǔ gēyuán jì. The constituent four works:
(1) Zhǔnwàng jiǎnfǎ 準望簡法 (“Simplified Surveying”). A condensed practical-surveying treatise applying the gōugǔ right-triangle methods to standard surveying problems.
(2) Gēyuán húshǐ bǔlùn 割圈弧矢補論 (“Supplementary Discussion of Circle-Cutting Arc-and-Versed-Sine”). A theoretical supplement to the circle-cutting discussion in Gōugǔ gēyuán jì, treating in particular the arc-and-versed-sine (húshǐ 弧矢) function-relations.
(3) Gōugǔ gēyuán quányì tú 勾股割圈全義圖 (“Diagrammatic Full Exposition of Right-Triangle Circle-Cutting”). The diagrammatic apparatus for the Gōugǔ gēyuán jì’s circle-cutting derivations, separately collected.
(4) Fāngyuán bǐlì shùbiǎo 方圈比例數表 (“Numerical Tables of Square-and-Circle Proportions”). Numerical tables of the ratios between the inscribed/circumscribed polygons and the circle, supporting the circle-cutting π-computations.
Abstract
The four-work compendium is a typical Dài-Zhèn-style scholarly production: a major principal treatise (the KR3fc038 Gōugǔ gēyuán jì) supplemented by a cluster of related shorter pieces treating specific sub-topics and providing the auxiliary apparatus (tables, diagrams, alternative-form treatments). The arrangement is parallel to Dài Zhèn’s philological practice — where his principal philological treatises are likewise accompanied by clusters of shorter related works.
Substantively, the four pieces fill out the Gōugǔ gēyuán jì’s framework:
- The Zhǔnwàng jiǎnfǎ provides the practical-surveying application that the principal treatise leaves implicit.
- The Gēyuán húshǐ bǔlùn expands the trigonometric-function discussion to the húshǐ (arc-and-versed-sine) functions specifically, anticipating the 安圖 Mínggatu power-series treatment in KR3fc037 Gēyuán mìlǜ jiéfǎ.
- The Gōugǔ gēyuán quányì tú provides the geometric-diagrammatic apparatus that the textual treatise leaves embedded in prose.
- The Fāngyuán bǐlì shùbiǎo provides the numerical-tabular apparatus underlying the π-computations.
For Dài Zhèn’s broader project and the Gōugǔ gēyuán jì’s context see KR3fc038.
Dating: the compendium is companion to KR3fc038 and shares its NotBefore / notAfter bracket of 1755–1773.
Translations and research
For Dài Zhèn’s mathematical-historical context see the references at KR3fc038.
- Yü Ying-shih 余英時. 1976. Lùn Dài Zhèn yǔ Zhāng Xuéchéng. Hong Kong: Lóngmén shū-diàn.
- Elman, Benjamin A. 1984. From Philosophy to Philology. Cambridge, Mass.: Council on East Asian Studies, Harvard University.