Abstract: The subject of this research in the method of finding proof of theoretical hypotheses based on their content. It demonstrated that historically this method emerged in geometry, and thus is called geometric (by origin) method of analysis and synthesis. Then it was shifted to mechanics by Galileo, and later to other sciences, never obtaining the status of the universal method for confirming theoretical hypotheses. The author conducts gnoseological analysis of this method. First, gnoseological analysis of the three initial forms is carried out on the basis of the three elementary geometric theorems. Then description is given to qualitative transformations that followed its transfer to other sciences. The author discusses the correlation of this method with the classical method of analysis and synthesis, as well as with experimental and hypothetical-deductive method. The main conclusion consists in the thesis that in accordance with its gnoseological status, the method of geometric (by origin) analysis and synthesis is on the same level as the classical method of analysis and synthesis, as well as experimental and hypothetical-deductive method. The author’s special contribution lies in substantiation of the thesis that with the development of science, this method of geometric origin was generalized to the method of finding proof of any theoretical hypotheses. Determination of qualitative changes that occurred in terms of its transfer from geometry to special sciences has an important methodological meaning. The author notes the role of idealization in the process of shifting into theoretical description of researched objects the results of practical actions with them.