Mínggatu 明安圖 (catalog form 安圖) — Mongol mathematician of the KāngYōngQián era
Mongol name Mínggatu (also romanized Ming’antu); Sinified name 明安圖, often abbreviated 安圖 as in the present catalog. Style sobriquet Xuězhāi 雪齋. Of the Plain-White Mongol Banner (鑲白蒙古旗). Death year c. 1765 (per Bāqí tōngzhì and the closing date of his work at the imperial Bureau of Astronomy); birth year not securely recorded, conventionally placed c. 1692 on the evidence of his initial Bureau-of-Astronomy posting in 1712.
A Mongol-Manchu mathematical scholar who rose through the Kāng-xī-imperial Mathematical Academy (Méngyǎng zhāi 蒙養齋) and the Bureau of Astronomy. His Bureau career spans over fifty years: he is recorded as a Tiānwén shēng 天文生 (Astronomer-student) at the Bureau by 1712 (Kāngxī 51), where he was one of the principal Mongol mathematical scholars recruited under the Kāngxī emperor’s program of Mongol-language astronomical-and-mathematical instruction. He participated in the survey-and-mapping projects culminating in the Kāng-xī-era Huángyú quánlǎn tú 皇輿全覽圖 (the great imperial atlas, completed 1717), and subsequently rose to high Bureau office. Under Qiánlóng he served as Qīntiānjiàn jiānzhèng 欽天監監正 (Director of the Imperial Bureau of Astronomy), the highest astronomical office under the Qīng.
His principal mathematical work is the Gēyuán mìlǜ jiéfǎ 割圏密率捷法 (KR3fc037) in 6 juàn — the systematic Chinese-language exposition of the trigonometric power-series expansions transmitted to him by the Jesuit Pierre Jartoux (Dù Démeǐ 杜德美). The work was incomplete at his death in 1765 and was put through final editing and publication by his pupil 陳際新 Chén Jìxīn and others. The work is the foundational document of Chinese-language analytical mathematics — the first systematic presentation in Chinese of the infinite-series methods (the power-series for sine, cosine, and inverse functions) that constituted the early stages of European calculus.
Mínggatu’s substantive contribution beyond Jartoux’s transmission was (a) the supply of detailed combinatorial proofs (in a style adapted from the 朱世傑 duǒjī figurate-summation tradition) for the series-expansions that Jartoux had stated without proof, and (b) the systematic extension of the series to nine related trigonometric functions, where Jartoux had supplied only three. The work is therefore not merely a translation but a substantive mathematical achievement; it represents the most sophisticated Chinese-language mathematical work of the eighteenth century and a unique fusion of indigenous combinatorial methods with imported analytical techniques.