Lobachevski Illuminated
Geometry, Non-Euclidean Parallels (Geometry) MATHEMATICS / Geometry / Non-Euclidean Lobachevskiĭ, N. I sähkökirjat
Cambridge University Press
2011
1st ed.
EISBN 9780883859797
Lobachevski's introduction.
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 [pi]-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.
Appendix: Nicolai Ivanovich Lobachevski's "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 [pi]-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.
Appendix: Nicolai Ivanovich Lobachevski's "Theory of Parallels".
