## Introduction to higher geometry |

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### Contents

CHAPTER I | 1 |

Homogeneous Linear Equations | 3 |

Proportionality Linear Dependence | 8 |

Copyright | |

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### Common terms and phrases

affine affine transformations analytic angle arbitrary axis coaxal coefficients collineation complete quadrangle complex concurrent conjugate conjugate-imaginary cross ratio definition degenerate determined diagonal distinct points dual elements EXERCISES Find the equation finite line finite point fixed points four points given circles given line given point harmonic set Hence homogeneous coordinates hyperbola identical involution isotropic lines line at infinity line conies line coordinates line geometry linear combination linear transformation linearly dependent lines joining locus mutually inverse necessary and sufficient nondegenerate conic null circle orthogonal parabola pencil of lines perpendicular PiP2 plane point at infinity point conic point coordinates point curve point of intersection points Pi pole projective coordinates projective geometry projective transformation proof proper circles properties Prove Theorem quadric range of points real points real trace regulus respect rigid motions self-conjugate Show sides singular point solution straight line triangle vertex vertices zero