Xiàng Míngdá 項名達
Style name Méilǚ 梅侶. Native of Rénhé 仁和 (modern Hángzhōu 杭州, Zhèjiāng). Born Qiánlóng 54 (1789); died Dàoguāng 30 (1850). Jǔrén in Dàoguāng 5 (1825); served briefly as district magistrate. CBDB c_personid 84043 confirms the lifedates.
The leading mathematician of the ZhèjiāngHángzhōu mathematical milieu of the second quarter of the nineteenth century, and one of the principal extenders of the Míng Āntú 明安圖 cyclotomic-series tradition. Xiàng Míngdá’s mathematical work is concentrated on (a) the systematic theoretical extension of the cyclotomic infinite-series tradition initiated by 明安圖 Míng Āntú’s Gēyuán mìlǜ jiéfǎ 割圈密率捷法 and continued by 董佑誠 Dǒng Yòuchéng’s KR3fc068 Tújiě; and (b) the procedural reformulation of the gōugǔ 勾股 (right-triangle) and sānjiǎo 三角 (triangle) problem-types.
His principal works preserved in the KR3fc series:
(1) KR3fc069 Xiàngshù yīyuán 象数一原 in 9 juàn — the principal theoretical synthesis of the cyclotomic-series tradition. Posthumously completed and corrected by his student 戴煦 Dài Xù.
(2) KR3fc070 Gōugǔ liùshù 勾股六術 in 2 juàn — systematic six-procedure exposition of the right-triangle problem-types.
(3) KR3fc071 Sānjiǎo héjiào shù 三角和較術 in 4 juàn — systematic exposition of the sum-and-difference methods in triangle geometry, working at the interface of indigenous gōugǔ and European spherical-and-plane trigonometry.
(4) KR3fc072 Kāi zhūchéngfāng jiéshù 開諸乘方捷術 — rapid procedure for higher-order root extraction.
Xiàng Míngdá’s mathematical correspondence with 戴煦 Dài Xù is the principal documentary record of the early-Dào-guāng Zhèjiāng mathematical scene. After Xiàng Míngdá’s death in 1850, Dài Xù completed the Xiàngshù yīyuán and ensured its publication. The Xiàng – Dài lineage is the principal Zhèjiāng counterpart to the Chángzhōu mathematical school of 董佑誠 Dǒng Yòuchéng and 李善蘭 Lǐ Shànlán.