Liú Héng 劉衡
Style name Jiānshān 兼山. Native of Nánfēng 南豐 (Jiāngxī). Born Qiánlóng 41 (1776); died Dàoguāng 21 (1841). CBDB id 74864 confirms the lifedates (multiple other Liú Héng entries appear in CBDB as homonyms; the dated entry matches the catalog’s “1776-1841” and the man’s known scholarly biography).
Mathematical scholar of the mid-Jiā-qìng to early Dàoguāng decades, working largely outside the Yángzhōu / Sūzhōu metropolitan circles. He is responsible for a substantial run of independent mathematical works preserved in the present KR3fc series — including:
(1) The Jígǔ suànjīng bǔzhù 緝古算經補注 (KR3fc007), a supplementary annotation extending 張敦仁 Zhāng Dūnrén’s xìcǎo of 王孝通 Wáng Xiàotōng’s Jígǔ suànjīng with further procedural notes.
(2) The Liùjiǔ xuān suànshū 六九軒筭書 (KR3fc062) in 3 juàn, the principal collection of Liú’s own mathematical investigations under the studio-name Liùjiǔ xuān.
(3) The Chǐsuàn rìguǐ xīnyì 尺算日晷新義 (KR3fc063) in 3 juàn — a treatise on the sliding-rod sundial.
(4) The Gōugǔ chǐ cèliáng xīnfǎ 勾股尺測量新法 (KR3fc064) in 2 juàn — surveying methods using the right-triangle sighting-rod.
(5) The Chóubiǎo kāizhūchéngfāng jiéfǎ 籌表開諸乘方捷法 (KR3fc065) in 4 juàn — a tabular rapid method for extracting n-th roots.
(6) The Jiègēnfāngfǎ qiǎnshuō 借根方法淺說 (KR3fc066) in 2 juàn — an introductory exposition of the European-derived jiègēnfāng 借根方 (algebraic-equation) method.
(7) The Sìlǜ qiǎnshuō 四率淺說 (KR3fc067) in 2 juàn — an introductory exposition of the rule of three / four-term proportion.
The cluster shows him as both a working algebraist (in the SòngYuán / jiègēnfāng tradition) and a practical surveying-and-instrumentation mathematician. His distinctive contribution was the tabular-aided computation of higher-order root extraction (chóubiǎo method) — pre-figuring the late-Qīng interest in computational tabulation that would culminate in 戴煦 Dài Xù’s KR3fc073 Qiúbiǎo jiéshù and 李善蘭 Lǐ Shànlán’s tabular logarithmic work in the KR3fc078 Zégǔxī zhāi suànxué.
Note: CBDB lists multiple persons named Liú Héng (劉衡, ids 20373, 33376, 51844, 51845, 74864, 111059, etc.); only the entry 74864 with lifedates 1776–1841 matches the mathematical author of the present catalog.