**acute**- Measure of Angles and
**Alternate "Interior Angle Theorem**- Alternate Interior Angles
**alternate interior angles**- Alternate Interior Angles
**angle**- Euclid's Mathematical System
**"parallelism**- Angle of Parallelism
**acute**- Measure of Angles and
**addition**- Congruence Theorems
**construction****Poincaré**- Constructions in the Poincaré

**Euclid's definition**- The Origins of Geometry
**exterior**- Weak Exterior Angle Theorem
**fan**- Fan Angles | Strange New Triangles | Constructions in the Poincaré
**interior**- Betweenness Axioms
**measure****degree**- Measure of Angles and
**Poincaré model**- The Poincaré Half-Plane Model | The Poincaré Disk Model | The Poincaré Disk Model
**radian**- Constructions in the Poincaré | Hyperbolic Trigonometry

**measure****measure****measure****measure****measure****obtuse**- Measure of Angles and
**parallelism**- Hyperparallel Lines | Constructions in the Poincaré | Angle of Parallelism | Hypercycles and Horocycles
**remote interior**- Weak Exterior Angle Theorem
**right**- The Origins of Geometry | Euclid's Mathematical System
**sides**- Euclid's Mathematical System
**subtraction**- Congruence Theorems

**Angle-Angle-Angle (AAA)**- Similar Triangles
**angles****corresponding**- Alternate Interior Angles
**summit**- Saccheri
**supplementary**- Euclid's Mathematical System

**antipodal**- Spherical Geometry
**Archimedes' Axiom**- Euclid's Mathematical System | Axioms of Continuity
**area****elliptic geometry**- The Pseudosphere
**function**- The Uniqueness of Hyperbolic
**hyperbolic**- Requirements for an Area to The Uniqueness of Hyperbolic | Hyperbolic Trigonometry
**hyperbolic circle**- Circumference and Area of
**hyperbolic geometry**- The Uniqueness of Hyperbolic | The Pseudosphere

**axis**- Hypercycles and Horocycles
**base****Saccheri quadrilateral**- Saccheri
**triangle**- Preliminaries

**base line**- Hypercycles and Horocycles
**Beltrami-Klein model***see*Klein "model**betweenness****undefined term**- Euclid's Mathematical System

**Betweenness Axioms**- Euclid's Mathematical System
**biconditional**- Biconditionals and Combinations of
**Bolyai****Já nos**- The Origins of Geometry
**János**- The Hyperbolic Axiom and

**chord**- The Beltrami-Klein Model
**circle**- Euclid's Mathematical System
**great***see*great circle**inversion**- Inversion in Euclidean Circles

**circle of inversion**- Inversion in Euclidean Circles
**circles****orthogonal**- Inversion in Euclidean Circles | The Poincaré Disk Model

**Circular Continuity Principle**- Euclid's Mathematical System | Axioms of Continuity
**circumference****hyperbolic circle**- Circumference and Area of

**collinear**- Incidence Geometry
**complementary****segments***see*segments, complementary

**concurrent**- Incidence Geometry
**conditional**- Sentence Connectives
**conformal**- The Beltrami-Klein Model
**congruence****undefined term**- Euclid's Mathematical System

**Congruence Axioms**- Euclid's Mathematical System
**conjunction**- Sentence Connectives
**Continuity Axioms**- Euclid's Mathematical System
**contradiction****proof***see*Proof by Contradiction

**contrapositive**- Proving Conditionals
**coordinates****axial**- Coordinate Geometry in the | Coordinate Geometry in the
**Beltrami**- Coordinate Geometry in the | Coordinate Geometry in the
**Lobachevsky**- Coordinate Geometry in the | Coordinate Geometry in the
**Poincaré**- Coordinate Geometry in the | Coordinate Geometry in the
**polar**- Coordinate Geometry in the
**Weierstrauss**- Coordinate Geometry in the

**corresponding points**- Hypercycles and Horocycles
- Hyperbolic Trigonometry
**Crossbar Theorem**- Betweenness Axioms
**trilateral**- Strange New Triangles

**curvature**- The Pseudosphere
**cut****Dedekind**- Axioms of Continuity

**Dedekind "cut***see*cut,Dedekind**Dedekind's Axiom**- Euclid's Mathematical System | Axioms of Continuity
**Deduction Theorem**- Proving Conditionals
**defect**- The Defect of a
**dilation**- Inversion in Euclidean Circles
**disjunction**- Sentence Connectives
**distance****Klein**- The Beltrami-Klein Model
**Poincaré**- The Poincaré Disk Model

**Elementary Continuity Principle**- Euclid's Mathematical System | Axioms of Continuity
**emanate**- Euclid's Mathematical System
**endpoint**- Euclid's Mathematical System
**equidistant****points**- Hyperparallel Lines

**equidistant curve***see*hypercycle**Euclid**- The Origins of Geometry to The Origins of Geometry
**Exterior Angle Theorem**- Weak Exterior Angle Theorem
**trilateral**- Strange New Triangles

**fan angle***see*angle, fan**finite decomposition**- Preliminaries
**For all***see*quantifieruniversal**For each***see*quantifieruniversal**For every***see*quantifieruniversal**Formula****Bolyai-Lobachevsky**- Angle of Parallelism
**Fundamental**- Hyperbolic Trigonometry

**Gauss****Carl Fredreich**- The Hyperbolic Axiom and
**Carl Friedrich**- The Origins of Geometry

**geodesic**- The Pseudosphere
**geometry****Bolyai-Lobachevsky**- The Hyperbolic Axiom and
**hyperbolic****analytic**- Hyperbolic Analytic Geometry

**great circle**- Spherical Geometry
**half-plane**- Betweenness Axioms
**horocycle**- Hypercycles and Horocycles | Hypercycles and Horocycles | Hypercycles and Horocycles to Hypercycles and Horocycles
**chord**- Hypercycles and Horocycles
**radius**- Hypercycles and Horocycles
**tangent to**- Hypercycles and Horocycles

**horocycles****codirectional**- Hypercycles and Horocycles

**horoparallel***see*parallel, "limiting**hyperbolic plane**- The Hyperbolic Axiom and
**hypercycle**- Hypercycles and Horocycles
**hyperparallel**- Hyperparallel Lines
**ideal point**- Proof of Claim and | Strange New Triangles
**ideal points**- The Beltrami-Klein Model
**IFF***see*biconditional**iff-string**- Proving Biconditionals
**incidence****undefined term**- Euclid's Mathematical System

**Incidence Axioms**- Euclid's Mathematical System
**Indiana**- The Origins of Geometry
**indirect proof***see*Proof by Contradiction**induction****mathematical**- Mathematical Induction

**inverse**- Inversion in Euclidean Circles
**isometric**- The Pseudosphere
**Klein model**- The Beltrami-Klein Model to The Beltrami-Klein Model
**length****absolute unit**- Similar Triangles
**spherical**- Spherical Geometry

**limiting curve***see*horocycle**line****construction****Poincaré**- The Poincaré Disk Model

**equidistant**- Hypercycles and Horocycles
**Euclid's definition**- The Origins of Geometry
**of enclosure**- Inversion in Euclidean Circles | Constructions in the Poincaré
**undefined term**- Euclid's Mathematical System

**line separation property**- Betweenness Axioms
**lines****parallel**- Euclid's Mathematical System
**perpendicular**- Euclid's Mathematical System

**Lobachevsky****Nicolai Ivanovich**- The Origins of Geometry | The Hyperbolic Axiom and

**lune**- Spherical Geometry | Spherical Geometry
**negation**- Sentence Connectives
**obtuse**- Measure of Angles and
**opposite sides**- Incidence Geometry
**ordering****angle**- Congruence Theorems
**segment**- Congruence Theorems

**parallel**- limiting(
**asymptotically***see*parallel, "limiting**divergently***see*hyperparallel**limiting**- Limiting Parallel Rays to Limiting Parallel Rays

**Pasch's Theorem**- Betweenness Axioms
**trilateral**- Strange New Triangles

**pencil of lines**- Fan Angles
**perpendicular***see*lines,perpendicular*see*angle, "parallelism**plane**- Euclid's Mathematical System
**Plane Separation Axiom**- Betweenness Axioms
**Playfair's Postulate**- The Origins of Geometry
**Poincaré Model**- The Poincaré Disk Model to The Poincaré Disk Model
**point****Euclid's definition**- The Origins of Geometry
**undefined term**- Euclid's Mathematical System

**pole**- Inversion in Euclidean Circles | The Beltrami-Klein Model
**power**- Inversion in Euclidean Circles | Inversion in Euclidean Circles
**projection****orthogonal**- Isomorphism of Models
**stereographic**- Isomorphism of Models | Isomorphism of Models

**proof****formal**- Proof

**Proof by Cases**- Proof by Cases
**Proof by Contradiction**- Proof by Contradiction
**pseudosphere**- The Pseudosphere
**Pythagorean Theorem****Hyperbolic**- Hyperbolic Trigonometry
**Spherical**- Spherical Geometry

**quadrilateral****Lambert**- Saccheri | More on Quadrilaterals
**Saccheri**- Saccheri | Preliminaries | More on Quadrilaterals
**altitude**- Saccheri
**associated**- Preliminaries | Preliminaries

**quantifier****existential***see*existential quantifier**universal**- Quantifiers

**radius**- Euclid's Mathematical System
**ray**- Euclid's Mathematical System
**rays****limiting "parallel**- Limiting Parallel Rays
**opposite**- Euclid's Mathematical System

**rectangle**- The Defect of a
**reductio ad absurdum***see*Proof by Contradiction**right angle***see*angle, right**Rule of Conditional"Proof***see*Deduction Theorem**Rules of Logic**- Rules of Reasoning
**Rules of Reasoning**- Introduction
**Saccheri-Legendre Theorem**- Saccheri-Legendre Theorem
**same side**- Incidence Geometry
**segment**- Euclid's Mathematical System
**Segment "Subtraction**- Congruence Theorems
**segments****complementary**- More on Quadrilaterals

**side****same**- Incidence Geometry

**Side-Angle-Angle (SAA)**- Weak Exterior Angle Theorem
**Side-Side-Side (SSS)**- Congruence Theorems
**sides****opposite**- Incidence Geometry
**Saccheri quadrilateral**- Saccheri

**Sine Theorem****Spherical**- Spherical Geometry

- Hyperbolic Trigonometry
**statement**- Sentences and Statements
**summit****Saccheri quadrilateral**- Saccheri

**supplementary "angles***see*angles,supplementary**system****mathematical**- Mathematical Systems

**theorem**- Proof
**There exists***see*quantifierexistential**tractrix**- The Pseudosphere | The Pseudosphere | The Pseudosphere
**transversal**- Alternate Interior Angles
**triangle****congruent**- Congruence Theorems
**exterior**- Betweenness Axioms
**interior**- Betweenness Axioms
**singly "asymptotic***see*trilateral**singly asymptotic**- Proof of Claim and

**Triangle Inequality**- Elementary Continuity Principle | Measure of Angles and
**triangulation**- Preliminaries
**trilateral**- Strange New Triangles | Hypercycles and Horocycles
**equiangular**- Hypercycles and Horocycles

**trilaterals****congruent**- Strange New Triangles

**ultraideal points**- The Beltrami-Klein Model
**variable**- Sentences and Statements
**vertex**- Euclid's Mathematical System
**Wallis**- Similar Triangles

david.royster@uky.edu