Proof of Euclid’s fifth postulate and the establishment of the metaphysical foundations of the so-called space (metametry)

Euclid’s fifth postulate has been accepted as a theorem since the time of ancient Greece. The efforts to prove it have been going on for nearly 2 000 years. Non-Euclidean geometry, based on its rejection, emerged in the first half of the 19th century. The author of the present article returns to the problem by addressing the metaphysical foundations of physics. The author has found the ideal instrument for analyzing infinity to be an infinitely small unit, which cannot be divided further. With the help of this instrument, the fundamental properties of the so-called space were found. It was concluded that there are no oblique or curved lines on the basic level. The apparent curved and oblique lines are stairs with negligibly fluent changing or constant steps, correspondingly. Hence, the refutation of non-Euclidean geometries and seeking a new proof of the postulate. Inter alia, it was found that the requirement to conclude the proof from Euclid’s other four axioms only diverted the attention of mathematicians from the true problem. The author proved the fifth postulate on a plane. Its application to a pair of skew lines is considered. In conclusion, the author describes the basic properties of the so-called space

Axiom · Calculus (dental · Epistemology · Euclidean geometry · Euclidean space · Geometry · Ideal (ethics · Metaphysics · Oblique case · Physics · Plane (geometry · Pure mathematics · Theoretical physics · Advanced Theoretical and Applied Studies in Material Sciences and Geometry · Engineering Technology and Methodologies · History and Theory of Mathematics · Mathematics · Philosophy

• What is Living and What is Dead in Indian Philosophy

  Dale Riepe, Debiprasad Chattopadhyaya•Philosophy and Phenomenological…•1977

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