Book contents
- Frontmatter
- Contents
- Introduction
- Note to the Reader
- Acknowledgements
- Theory of Parallels — Lobachevski's Introduction
- Theory of Parallels — Preliminary Theorems (1–15)
- Theory of Parallels 16: The Definition of Parallelism
- Theory of Parallels 17: Parallelism is Well-Defined
- Theory of Parallels 18: Parallelism is Symmetric
- Theory of Parallels 19: The Saccheri-Legendre Theorem
- Theory of Parallels 20: The Three Musketeers Theorem
- Theory of Parallels 21: A Little Lemma
- Theory of Parallels 22: Common Perpendiculars
- Theory of Parallels 23: The π-function
- Theory of Parallels 24: Convergence of Parallels
- Theory of Parallels 25: Parallelism is Transitive
- Theory of Parallels 26: Spherical Triangles
- Theory of Parallels 27: Solid Angles
- Theory of Parallels 28: The Prism Theorem
- Theory of Parallels 29: Circumcircles or Lack Thereof (Part I)
- Theory of Parallels 30: Circumcircles or Lack Thereof (Part II)
- Theory of Parallels 31: The Horocycle Defined
- Theory of Parallels 32: The Horocycle as a Limit-Circle
- Theory of Parallels 33: Concentric Horocycles
- Theory of Parallels 34: The Horosphere
- Theory of Parallels 35: Spherical Trigonometry
- Theory of Parallels 36: The Fundamental Formula
- Theory of Parallels 37: Plane Trigonometry
- Bibliography
- Appendix: Nicolai Ivanovich Lobachevski's Theory of Parallels
- Index
- About the Author
Theory of Parallels 19: The Saccheri-Legendre Theorem
- Frontmatter
- Contents
- Introduction
- Note to the Reader
- Acknowledgements
- Theory of Parallels — Lobachevski's Introduction
- Theory of Parallels — Preliminary Theorems (1–15)
- Theory of Parallels 16: The Definition of Parallelism
- Theory of Parallels 17: Parallelism is Well-Defined
- Theory of Parallels 18: Parallelism is Symmetric
- Theory of Parallels 19: The Saccheri-Legendre Theorem
- Theory of Parallels 20: The Three Musketeers Theorem
- Theory of Parallels 21: A Little Lemma
- Theory of Parallels 22: Common Perpendiculars
- Theory of Parallels 23: The π-function
- Theory of Parallels 24: Convergence of Parallels
- Theory of Parallels 25: Parallelism is Transitive
- Theory of Parallels 26: Spherical Triangles
- Theory of Parallels 27: Solid Angles
- Theory of Parallels 28: The Prism Theorem
- Theory of Parallels 29: Circumcircles or Lack Thereof (Part I)
- Theory of Parallels 30: Circumcircles or Lack Thereof (Part II)
- Theory of Parallels 31: The Horocycle Defined
- Theory of Parallels 32: The Horocycle as a Limit-Circle
- Theory of Parallels 33: Concentric Horocycles
- Theory of Parallels 34: The Horosphere
- Theory of Parallels 35: Spherical Trigonometry
- Theory of Parallels 36: The Fundamental Formula
- Theory of Parallels 37: Plane Trigonometry
- Bibliography
- Appendix: Nicolai Ivanovich Lobachevski's Theory of Parallels
- Index
- About the Author
Summary
- Type
- Chapter
- Information
- Lobachevski Illuminated , pp. 28 - 34Publisher: Mathematical Association of AmericaPrint publication year: 2011