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- 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