JinMathematicsComplete格物

海岛算经

Haidao Suanjing

About This Work

The Sea Island Mathematical Manual, written by Liu Hui in 263 CE, is the first Chinese treatise dedicated to surveying and remote measurement. It uses the method of double differences—paired observations from two stations using a sighting pole—to calculate inaccessible distances and heights through proportional reasoning, solving trigonometric problems without explicit trigonometric functions.

Contents · 内容

Problem 1: Height of a sea island from shore今有望海岛

Problem 2: Height of a pine tree on a hill今有望松生山上

Problem 3: Distance to a walled city across a river今有南望方邑

Problem 4: Depth of a valley今有望深谷

Problem 5: Height of a tower on a hilltop今有登山望楼

Problem 6: Distance to a river mouth from the sea今有东南望波口

Problem 7: Width of a river from a bank今有望清渊

Problem 8: Height and distance of a wall seen from above今有登山临邑

Problem 9: Height of a mountain viewed across a river今有登山望津

Why This Matters

This text is part of the living archive of Chinese intellectual achievement — a tradition that produced systematic astronomical observation, mathematical innovation, medical frameworks still in clinical use, and engineering at continental scale, centuries before comparable developments in Europe.

The question "did ancient China have science?" misunderstands what science is. Science is not a single cultural tradition — it is the systematic observation of nature, the rigorous documentation of phenomena, the testing of ideas against evidence, and the building of knowledge across generations. By every one of these measures, the works in this catalogue are scientific. They used different conceptual frameworks — correlative rather than mechanistic, systemic rather than reductionist — but these frameworks produced real knowledge: accurate star catalogues, effective medical treatments, precise calendar computations, and technologies that transformed civilization.