## An Introduction to the Geometry of N Dimensions |

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### Contents

CHAPTER I | 1 |

Definitions and axioms of geometry | 2 |

The axioms of incidence | 3 |

141 other sections not shown

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### Common terms and phrases

ABCD absolute polar assemblage axes axioms cells centre Cn _ co-ordinates completely orthogonal completely parallel condition configurational numbers conjugate Consider contains convex corresponding cross-ratio cube curve cuts degrees of freedom denoted determine dihedral angle dimensional divided dodecahedron edges elliptic elliptic geometry equation euclidean Euler's face-constituents faces four dimensions geometry given lines half-orthogonal hedra hedron Hence hexahedra homogeneous homogeneous co-ordinates honeycomb hyper hypercone hyperplane at infinity hypersphere i)-flat intersect isomorphic line at infinity linear space Math matrix non-euclidean geometry normal number of flats octahedra octahedron orthotope parallelotope pass pentahedron perpendicular plane point at infinity point in common poly polygon polyhedra polyhedron polytope Po)n prism prismoid projection pyramid quadric quadrilateral r-boundary r-flat ratio reciprocal regular polytopes represented Schlegel diagram second species Similarly simplex simplex-polycorypha Sn _ sphere spherical straight line surface-content tetrahedron three dimensions triangles trihedral vertex vertex-edge vertices