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Neutral and Non-Euclidean Geometries
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Contents
List of Figures
Proposition
Proposition
Pasch's Triangle
Crossbar Theorem
Isosceles triangles
Segment subtraction
Theorem
Angle subtraction
Alternate interior angles
Exterior angle theorem
Side-Angle-Angle
Segment midpoint
Triangle inequality
Saccheri-Legendre Theorem
Right triangle with defect 0
Rectangles
Defect 0 for all right triangles
Parallel lines in the Klein model
Length in the Klein model
Measuring angles in the Poincaré Half-Plane Model
A
p
-line in the Poincaré disk model
Angle measure in the Poincaré Disk Model
Construction of the
p
-line through
A
and
B
Limiting Parallel Rays
Hyperparallel Lines
Horoparallel Lines
Lambert Quadrilateral
Saccheri Quadrilateral
SAS in the Poincaré Model
Angle of Parallelism
Central Projection from
N
The Saccheri quadrilateral
associated
with
A horocycle in the Poincaré model
Concentric horocycles in the Poincaré model
A hypercycle in the Poincaré model
Horocyclic Sector in the Poincaré model
Tractrix curve
Graphs of hyperbolic functions
Hyperbolic Circle
Saccheri Quadrilateral
Complementary Segments
Engel's Theorem
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