Unidentified Egyptian geometry

The theorems that we will discuss are well-known in mathematics. They are related to the foundations of geometry, to geometry “in the large” and to the history of geometry. Namely, we are dealing with three beautiful ancient theorems whose authors are Archimedes (the theorem on the dropping of a stone), Euclid and an Egyptian writer, Ahmes (problems from Egyptian papyruses). It seems astonishing that the aforementioned theorem of Euclid went unnoticed as a generalization of the fundamental uniqueness theorems of A. Cauchy and H. Minkowski concerning convex closed polyhedra. The three theorems discussed are absolutely flawless, but their theoretical and historical interpretations are still rather inadequate. In our opinion, these theorems belong to the ancient civilizations of Babylon, Egypt and Sumer which were superior to our modern civilization in numerous aspects. This opinion will be supported by generalizations, proofs and a precise reconstruction of ancient theorems.