This paper examines how Hong Taeyong (1731–1783), a literatus in the eighteenth-century Korea, presented problems concerning astronomical measurements in his mathematical manual, and how these efforts extended the scope of traditional mathematical problems into the realm of cosmology under the influence of Western mathematical knowledge. The Chuhae suyong, his only work on mathematics, is unique in the history of East Asian mathematics. Unlike other mathematical works, which were limited to the calculations of mundane affairs, such as commercial exchanges, taxation, and land surveys, this book devoted its concluding chapter to measurements of the celestial bodies, especially their size and distance from the earth. Previous studies have focused on his more famous cosmological work, Ǔisan mundap, in which he advanced radical cosmological ideas, such as those of an infinite universe and the diurnal rotation of the earth, while the relation between these two works has not been studied. By examining the structure of his mathematical manual, this paper argues that Hong strived to understand the physical shape of heaven and earth, and that his book contained the mathematical knowledge that served this purpose. He applied to astronomical measurements the rule of three and basic trigonometry that he learned from the Shuli jingyun, the official Qing mathematical text compiled under the auspice of the Kangxi emperor (1662–1722). The insights that Hong acquired from solving the astronomical measurement problems, this paper suggests, laid the foundation to Hong’s critique of astrology, as expounded in his cosmological work.