Geshu bu 格術補

Geshu bu 格術補 is a book on optics written during the late Qing period 清 (1644-1911) by Zou Boqi 鄒伯奇 (1819-1869). He also wrote the mathematical treatises Celiang beiyao 測量備要 and Chengfang jiefa 乘方捷法 (Chengfang jieshu 乘方捷術). A collection of his writings is called Zou Zhengjun yishu 鄒徵君遺書.

The book of one fascicle, published in 1877, is based on mathematical theory and explains various principles of lenses. According to Chen Li's 陳澧 (1810-1882) preface, the term geshu "the skill of thorough [investigation]" appears in the Mengxi bitan 夢溪筆談, pointing to how a researcher observes the light and shadows of the sun and moon, explores mathematical principles, and delves into the minutest details to understand Western methods of lens-making. The book is thus a supplement (bu 補) to the techniques of ancient Chinese mathematicians.

The author offers a detailed discussion of various mirror shapes and principles, using diagrams to illustrate concepts visually. For instance, when explaining convex lenses (tujing 凸鏡), he states: "When using sunlight to ignite a fire, the focal point represents the nearest limit of convergence. Any discussion of light convergence adheres to this principle. If a convex lens reflects a distant object, the image forms only up to this limit. If the object is nearer, the image appears farther away." Zou introduces the trigonometric calculation method and clarifies this further with a diagram. By employing mathematical methods to calculate the angular distances of lens reflections, the book establishes a solid mathematical foundation for understanding convex mirrors. The author's explanation of telescopes (kuiyuanjing 窺遠鏡) and microscopes (xianweijing 顯微鏡) showcases his precise observations and robust mathematical reasoning. By integrating mathematical calculations into the principles of lens-making, the Geshu bu distinguished itself from conventional knowledge in China at the time. This unique approach received high praise from Qing scholars.

The text is found in the series Zhong-Xi suanxue congshu chubian 中西算學叢書初編 and Baifutang suanxue congshu 白芙堂算學叢書. Is it also included in the Zou Zhengjun yishu.