Chén Shìrén 陳世仁
Native of Hǎiníng 海寧 (Zhèjiāng). Born Kāngxī 15 (1676); died Kāngxī 61 (1722). Jìnshì of Kāngxī yǐwèi (1715).
His sole Sìkù-preserved work is the Shǎoguǎng bǔyí 少廣補遺 (KR3f0054) in 1 juàn — a focused-and-original treatment of duīduǒ 堆垜 (heap-and-pile) computation, the calculation of summed series for one-sided pyramidal heaps, square-base pyramidal heaps, triangular-base heaps, hexagonal-base heaps, and related shapes. The work develops 12 distinct procedures, supplemented by chōujī and chōuǒu (drawing odd, drawing even) series-summation procedures.
Chén Shìrén’s contribution is a substantive mathematical innovation in an underdeveloped corner of the Jiǔzhāng Shǎoguǎng tradition. The Sìkù 提要 carefully distinguishes duīduǒ (heap-piling — discrete summation) from the parallel shānggōng solid-geometry tradition: where solids have continuous-and-filled volumes, heaps consist of discrete units with intervening gaps and characteristic external shapes; the two computational methods differ accordingly. The ancient Shǎoguǎng tradition had treated duīduǒ in passing (computing summation given edge-and-layer data) but had not addressed the inverse problem (computing edge-and-layer data given summation). Chén Shìrén’s work systematically addresses the inverse problem, providing 12 distinct method-formulas and applications.
The Sìkù 提要 commends the work as a substantive contribution despite its limited scope: “[Chén Shìrén] specifically takes the various heap-piling shapes and reciprocally derives them from each other, each setting up a method. Although the diagrams-and-explanations are not complete (so as to make the student peep into the meaning of the law-establishment), nevertheless [the work] extends [the application of] the Shǎoguǎng bequeathed methods, drawing-and-applying [them] by analogy — truly aiding mathematics. [It] cannot be slighted on account of [its] one-corner [scope]“. The work is a useful supplement to the Jiǔzhāng tradition.