ELEMENTARY EUCLIDEAN GEOMETRY
CONTENTS POINTS AND LINES THE VECTOR STRUCTURE LINES AND ZERO SETS UNIQUENESS OF EQUATIONS PRACTICAL TECHNIQUES PARAMETRIZED LINES PENCILS OF LINES THE EUCLIDEAN PLANE THE SCALAR PRODUCT LENGTH AND DISTANCE THE CONCEPT OF ANGLE DISTANCE FROM A POINT TO A LINE CIRCLES CIRCLES AS CONICS GENERAL CIRCLES INTERSECTIONS WITH LINES PENCILS OF CIRCLES GENERAL CONICS STANDARD CONICS PARAMETRIZING CONICS MATRICES AND INVARIANTS THE COMPONENT LEMMA CENTRES OF GENERAL CONICS THE CONCEPT OF A CENTRE FINDING CENTRES GEOMETRY OF CENTRES SINGULAR POINTS DEGENERATE CONICS BINARY QUADRATICS REDUCIBLE CONICS PENCILS OF CONICS PERPENDICULAR BISECTORS AXES AND ASYMPTOTES MIDPOINT LOCI AXES BISECTORS AS AXES ASYMPTOTIC DIRECTIONS FOCUS AND DIRECTRIX FOCAL CONSTRUCTIONS PRINCIPLES FOR FINDING CONSTRUCTIONS CONSTRUCTIONS FOR PARABOLAS GEOMETRIC GENERALITIES CONSTRUCTIONS OF ELLIPSE AND HYPERBOLA TANGENTS AND NORMALS TANGENT LINES EXAMPLES OF TANGENTS NORMAL LINES THE PARABOLA 10 1 THE AXIS OF A PARABOLA 10 2 PRACTICAL PROCEDURES 10 3 PARAMETRIZING PARABOLAS THE ELLIPSE 11 1 AXES AND VERTICES 11 2 RATIONAL PARAMETRIZATION 11 3 FOCAL PROPERTIES THE HYPERBOLA 12 1 ASYMPTOTES 12 2 PARAMETRIZING HYPERBOLAS 12 3 FOCAL PROPERTIES OF HYPERBOLAS POLE AND POLAR 13 1 THE POLARS OF A CONIC 13 2 THE JOINT TANGENT EQUATION 13 3 ORTHOPTIC LOCI CONGRUENCES 14 1 CONGRUENCES 14 2 CONGRUENT LINES 14 3 CONGRUENT CONICS 14 4 THE INVARIANCE THEOREM CLASSIFYING CONICS 15 1 ROTATING THE AXES 15 2 LISTING NORMAL FORMS 15 3 SOME CONSEQUENCES 15 4 EIGENVALUES AND AXES DISTINGUISHING CONICS 16 1 DISTINGUISHING CLASSES 16 2 CONIC SECTIONS 16 3 CONICS WITHIN A CLASS UNIQUENESS AND INVARIANCE 17 1 PROOF OF UNIQUENESS 17 2 PROOF OF INVARIANCE