Euclidean Geometry and its Subgeometries

• Main Authors: Specht, Edward John (Author), Jones, Harold Trainer (Author), Calkins, Keith G. (Author), Rhoads, Donald H. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2015.
• Edition: 1st ed. 2015.
• Subjects: Mathematics.; Geometry.; History.; History of Mathematical Sciences.

In this monograph, the authors present a modern development of Euclidean geometry from independent axioms, using up-to-date language and providing detailed proofs. The axioms for incidence, betweenness, and plane separation are close to those of Hilbert. This is the only axiomatic treatment of Eucli...

Table of Contents:

• Preface
• Preliminaries and Incidence Geometry (I)
• Affine Geometry: Incidence with Parallelism (IP)
• Collineations of an Affine Plane (CAP)
• Incidence and Betweenness (IB)
• Pasch Geometry (PSH)
• Ordering a Line in the Pasch Plane (ORD)
• Collineations Preserving Betweenness (COBE)
• Neutral Geometry (NEUT)
• Free Segments of a Neutral Plane (FSEG)
• Rotations about a Point of a Neutral Plane (ROT)
• Euclidean Geometry Basics (EUC)
• Isometries of a Euclidean Plane (ISM)
• Dilations of a Euclidean Plane (DLN)
• Every Line in a Euclidean Plane is an Ordered Field (OF)
• Similarity on a Euclidean Plane (SIM)
• Axial Affinities of a Euclidean Plane (AX)
• Rational Points on a Line (QX).- A Line as Real Numbers (REAL); Coordinatization of a Plane (RR)
• Belineations on a Euclidean/LUB Plane (AA)
• Ratios of Sensed Segments (RS)
• Consistency and Independence of Axioms; Other Matters Involving Models
• References
• Index.