Abstract: A new geometric computing theory was proposed. On the definition level of geometric elements, using the Cartesian coordinates ideology as reference, 2D and 3D “geometric algebra elements” (or “geometric elements” for short, which could construct an upperlevel element in the solving sequence) were constructed by geometry algebraization methods. On the processing level of geometries, geometric problems were solved with geometry methods, by which a geometric element solving sequence could be constructed. Directional property was introduced into geometries in this theory and geometries were represented in a unified format. They help to simplify the processing of finding the geometric element solving sequence for a geometry problem. The paper also tried to theoretically find out an integrated solution for geometry ambiguity issues, and established a unified, standardized geometry computing architecture. The Leibniz’s mind——to process geometric objects with geometric language——was implemented in an indirect way!