Mathematics and Applied Mathematics
October 4, 2021
Euclidean geometry, New foundation, Parallel postulate, Euclid Fifth Postulate, Pythagorean theorem
This book introduces a new basis for Euclidean geometry consisting of 29 definitions, 10 axioms and 45 corollaries with which it is possible to prove the strong form of Euclid's First Postulate, Euclid's Second Postulate, Hilbert's axioms I.5, II.1, II.2, II.3, II.4 and IV.6, Euclid's Postulate 4, the axioms of Posidonius-Geminus, of Proclus, of Cataldi, of Tacquet 11, of Khayyam, of Playfair, Euclid's Postulate 5, and the historical statements proposed in place of Euclid's Postulate 5. The book ends with a chapter that culminates in the proof of the Pythagorean theorem and its converse.