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 Zhèjiāng-Hángzhōu 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.