## Elementary Geometry in Hyperbolic SpaceThe series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 35 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. Please submit any book proposals to Niels Jacob. Titles in planning include Flavia Smarazzo and Alberto Tesei, Measure Theory: Radon Measures, Young Measures, and Applications to Parabolic Problems (2019) |

### Contents

Preliminaries | 1 |

Notes to Chapter I | 16 |

Orthogonality | 31 |

The Isometry Group of Hyperbolic Space | 44 |

The spherical and cylindric surfaces | 60 |

Lines | 61 |

Notes to Chapter V | 78 |

Determination of a hexagon by three of its sides | 93 |

Notes to Chapter VI | 138 |

27 | 155 |

Notes to Chapter VII | 174 |

Linear families of spherical surfaces | 191 |

2223F | 201 |

Area and Volume | 202 |

Volume of some bodies of revolution | 209 |

Notes to Chapter IX | 220 |