Based on a nineteenth-century Korean mathematical text, Explanation of the detailed sketches in Ceyuan haijing 測圓海鏡 (Haekyŏng sech’ohae 海鏡細草解), this paper examines why and how the author Nam Pyŏng-ch’ŏl 南秉哲 (1817-1863) interpreted the thirteenth-century Chinese mathematical text Ceyuan haijing. He criticized the former researchers or commentators on the Ceyuan haijing for neglecting the ‘sketch’ (cao 草) part and provided a new explanation of the ‘sketch’ part, which was originally full of specific numerical values, with more general formulaic expressions. His new explanation will be analyzed at three levels. First, what terminology and mathematical contents are included, and whether these are consistent. Second, how the explanation interacts with the main Chinese text, and what role it plays. Last, how the explanation correlates with the other Korean mathematical texts at that time, and what features of the nineteenth-century Korean mathematical context it can be said to reflect. For the last analysis, it will be helpful to compare Nam’s text with the Chinese Li Rui’s 李銳(1769-1817) commentary added into Ceyuan haijing in Siku quanshu 四庫全書 during his editing. Also this comparison will show the similarities and differences between Korean and Chinese mathematicians’ attitudes to tianyuan shu 天元術.