Dǒng Yòuchéng 董佑誠
Style name Fānglì 方立. Native of Yánghú 陽湖 (modern Chángzhōu 常州, Jiāngsū). Born Qiánlóng 56 (1791); died Dàoguāng 3 (1823) at age 33. The Chángzhōu mathematical school of the early nineteenth century — formed around 李兆洛 Lǐ Zhàoluò and including Dǒng Yòuchéng and his brother Dǒng Jīn 董金 — was one of the principal Jiāqìng to Dàoguāng mathematical lineages outside the Yáng-zhōu-centred 阮元 Ruǎn Yuán circle. CBDB does not have an entry for the mathematician under this name.
Dǒng Yòuchéng’s principal mathematical contribution is the Gēyuán liánbǐlì shù tújiě 割圈連比例術圖解 (KR3fc068) — the geometric-illustrative exposition of the cyclotomic continued-proportion method, an indigenous Chinese rediscovery of the infinite-series expansions for trigonometric functions. The method derives from 明安圖 Míng Āntú’s Gēyuán mìlǜ jiéfǎ 割圈密率捷法 (1730s, posthumously edited and published 1839), which itself is a Chinese transformation of the trigonometric infinite-series identities communicated to the Imperial Mathematics Bureau by the Jesuit Jartoux. Dǒng Yòuchéng’s contribution is the systematic geometric explanation of why the continued-proportion procedures yield the correct series — providing a derivation in indigenous Chinese geometric terms of what European mathematics derives from the calculus of differences.
Dǒng’s Gēyuán liánbǐlì shù tújiě was an important reference for the next generation of Chángzhōu mathematicians, especially 項名達 Xiàng Míngdá and 戴煦 Dài Xù, both of whom extended the cyclotomic-series tradition further (cf. KR3fc069–KR3fc073). Dǒng’s early death at 33 cut short what would likely have been a major mathematical career.