New elements of Euclidean geometry: Solving an old problem from a new perspective

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.