## Non-Euclidean geometry |

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### Contents

THE HISTORICAL DEVELOPMENT | 1 |

FOUNDATIONS | 16 |

POLARITIES | 48 |

Copyright | |

15 other sections not shown

### Common terms and phrases

AB/C absolute polar line affine geometry axioms axis bundle centre circle Clifford parallels Clifford surface Clifford translation collinear points collineation common perpendicular congruent transformation conic conjugate points contains coordinates coplanar coplanar lines correlation cosh cross ratio deduce define definition determined dimensions distance double points elliptic geometry equation equidistant curve Euclid Euclidean geometry flat pencil follows formulae harmonic conjugate harmonic homology Hence horocycle hyperbolic geometry ideal point involution joining Klein length line at infinity lines and planes Lobatschewsky meet metrical non-Euclidean non-Euclidean geometry one-dimensional opposite ordinary line ordinary point pairs permutable point-pairs points and lines points at infinity pole Postulate product of reflections projective geometry Proof quadric quaternion real numbers real projective geometry regulus relation represented respect right angles right parallel rotation segment sides sinh space sphere tangent tetrahedron theorem triangle ABC ultra-parallel vertices