This paper presents certain aspect of intuitive reasoning in mathematics called the 'intuitive analysis of concepts' along some schemes of that kind of intuitive analysis. The method of the intuitive analysis of concept of polyhedra based on the historical findings as presented by Lakatos in 'Proofs and Refutations' is described. Some important consequences for phenomenology as well as philosophy and history of mathematics follow. Mathematical knowledge seems to be created within the 'hermeneutical horizon' distinct for ancient and modern mathematics.
Financed by the National Centre for Research and Development under grant No. SP/I/1/77065/10 by the strategic scientific research and experimental development program:
SYNAT - “Interdisciplinary System for Interactive Scientific and Scientific-Technical Information”.