Gù Yìngxiáng 顧應祥
Style name Wéixián 惟賢, sobriquet Ruòxī 箬溪. Native of Chángxìng 長興 (in modern Zhèjiāng). Born Chénghuà 19 (1483); died Jiājìng 44 (1565). Jìnshì of Hóngzhì 18 (1505).
A Míng-period official-scholar whose mathematical interests took him into engagement with the SòngYuán mathematical tradition that had been largely forgotten by his time. His successive offices reached Yúnnán Tàishí (Provincial Provincial Examiner). His official-historical work is the Réndài jìyào 人代紀要 (catalogued separately in the Sìkù).
His mathematical works are mostly attempts to explain or supplement SòngYuán mathematical classics that had become difficult of comprehension by the late Míng:
(1) The Cèyuán hǎijìng fēnlèi shìshù 測圓海鏡分類釋術 (KR3f0043), in 10 juàn — his attempt to expound Lǐ Yě’s KR3f0042 Cèyuán hǎijìng. The Sìkù 提要 of KR3f0043 is sharply critical: Gù Yìngxiáng received Lǐ Yě’s book from Táng Shùnzhī 唐順之, but could not understand the lì tiānyuányī 立天元一 method that is the foundation of Lǐ Yě’s work. Gù therefore removed the tiānyuányī sections from his exposition, replacing them with elementary computational procedures. The 提要: “[Gù Yìngxiáng] removed the detailed-procedures and exclusively elaborated the calculation-methods, claiming this was for the benefit of the elementary student. He utterly failed to recognize that the marvel of lì tiānyuányī is precisely its ability to enable [the solution of] what other methods cannot solve. If [the cǎo-procedure] is absent, then even [Lǐ] Yě [himself] would not have been able to obtain the methods, while [Gù Yìngxiáng] sticks merely to the addition-subtraction-and-extraction-of-roots numbers — this can be called: ‘following the branches and leaves but losing the root’“. Táng Shùnzhī’s letter to Gù about this exposition (preserved in the 提要) is the foundational late-Míng documentation of the forgetting of tiānyuányī.
(2) The Húshǐ suànshù 弧矢算術 (KR3f0045), in 1 juàn — on circle-segment (arc-and-arrow) computations.
Despite the Sìkù 提要’s sharp critique of Gù’s failure to understand tiānyuányī, his works represent an important late-Míng attempt at reviving SòngYuán mathematical scholarship, and his elementary-computational expositions found readers who would not have engaged with Lǐ Yě’s more demanding original. Through Gù Yìngxiáng’s transmission, at least the geometric problems and final-answers of the Cèyuán hǎijìng circulated in the late Míng, even though the underlying methodology had been lost.