“视点”与世界几何秩序的构建——托勒密《地理学》制图思想新探

The Visual Point and the Construction of the Geometric Order of the Oikoumene:A New Inquiry into Ptolemy's Cartographic Thought in Geography

托勒密《地理学》是以居住世界为描绘对象,以几何学为基本方法的古代地理制图理论著作。该书继承并实践了埃拉托色尼的“赫尔墨斯视角”,在借鉴古希腊光学传统的基础上,构建了几何意义上的视点,由此将欧氏光学命题、平面几何定理及展平等不同数学方法加以综合,最早在西方地理史上提出了系统的几何制图法。《地理学》对视点的运用反映了托勒密以数学哲学为底色的制图思想。通过假定的视点,居住世界得以被观察和模仿,进而被赋予图像理性意义上的几何秩序。基于视点再现的世界图像,托勒密得以将地理学纳入他宏大的数学世界图景之中。在此过程中,视点也成为托勒密构建世界的几何秩序、实现球面向平面转换的“阿基米德支点”。

Ptolemy's Geography is an ancient opus of cartographic theory with the“oikoumene”(inhabited world)as the object that is described using geometry as the basic method.Based on the“Hermes perspective”from Eratosthenes and the Euclidean optical tradition,Ptolemy constructed a geometrical“visual point”,by which different mathematical methods,such as Euclidean optical propositions,plane geometry theorems and flattening,were integrated,and a systematic geometric mapping method was proposed,the first in the history of Western geography.The employment of the“visual point”in Geography reflects Ptolemy's mathematical philosophy.Through the assumption of the visual point,the oikoumene can be observed and imitated quantitatively,and endowed with a geometric and imagistic order.By way of the world image thus represented,geography was incorporated into Ptolemy's larger world picture of mathematics.In this process,the“visual point”also acts as the“Archimedean fulcrum”for Ptolemy to creatively synthesizedifferent mathematical methods and accomplish transformation from the spherical image to the plane map.