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| Baker H.F. — Principles of Geometry. Volume 3 |
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| Предметный указатель |
Absolute conic, and plane 70
Apolar form, apolar to a system of binary forms of the same order 136
Apolar linear complexes 66
Associated points, eight 148 154 157
Axes of confocal system of quadrics 98—100
Axis of a plane in regard to a system of a developable 133
Axis of a plane in regard to a system of confocals 93 98
Beltrami 208 224
Bertini 223
Bitangents of a plane quartic curve 199
Burnside 168
Carslaw 224
Castelnuovo 223
Cayley 212 214 223 224
Central systems 11 184
Centre of a quadric 79
Centres of similitude of two spheres 78
Chasles 54 67 69 111
Chords, ten, common to two cubic curves in space 141
circles 72
Circular sections of a quadric 79
Clebsch 170 194 203 208
Coaxial system of spheres 74
Complex, linear, of lines 56 61
Complex, quadratic complex, tetrahedral complex 99
Cone, cone of revolution 81
Cone, quadric, defined 4 17
Confocal paraboloids 95
Confocal quadric surfaces 91ff.
Confocal quadric surfaces as dual of quadrics with a common curve 119
Confocal quadric surfaces leading to Poncelet’s porism 116
Confocal quadric surfaces, the three through a point not always distinct 92
Confocal quadric surfaces, touching a line 109
Congruence, linear, of lines 65
Conics, meeting eight lines 150
Conjugate lines, in regard to a quadric 34 59
Conjugate points and planes, in regard to a quadric 32
Contact cones, for a cubic surface, leading to contact conics for a plane quartic curve 198
Coordinates of a line 56
Coresidual sets of points on a plane curve 179
Coresiduation, theorem of, for plane curves 179
Coresiduation, theorem of, for surfaces 181
Correspondence between generators of a quadric determining cubic curve 135
Corresponding points of the Hessian surface 209
Cremona 206 208
Cubic curve in a plane, determination of the ninth intersection of two when eight are given 156 178 217
Cubic curve, constructed to meet each of four lines in a pair of an involution given thereon 145
Cubic curve, constructed to satisfy six conditions 129 139—142
Cubic curve, drawn through five points of a quadric 129
Cubic curve, four tangents meet a line 132
Cubic curve, general consideration of cubic curve in space 125ff.
Cubic curve, outpolar to a quadric 146
Cubic curve, tangents belong to a linear complex 68
Cubic curve, tangents generated by points of contact of tangent planes of confocals through a line 107
Cubic developable, dual to a cubic curve 130 135
Cubic surface, cubicsurface with four double points 214
Cubic surface, curves upon 191
Cubic surface, determined by six arbitrary points in a plane 194
Cubic surface, equations of 203—208
Cubic surface, general account 159ff.
Cubic surface, Hessian of 208
Cubic surface, leading to a plane quartic curve 196
Cubic surface, theorem of coresiduation for curves upon 181
Cubo-cubic transformation in space 143
Curves of intersection of a quadric with confocals projected into confocal conics 113
Cuspidal edge of a developable 131
Cylinder 81
Dandelin 44
Deformation of quadric with rigid generators 114
Developable 103
Developable of common tangent planes of confocals 118
Developable, cubic 130 133 135
Diagonal cubic surface 170
Director sphere of quadric 86
Dixon, A.C. 202
Dixon, A.L. 118
Dobriner 158
Double tangents of plane quartic curve 199
Double-six of lines 159ff.
Double-six of lines, determined by five arbitrary points 168
Dual character of a quadric 4 5 30 32
Elliptic quartic curve, eight tangents meet any line 69 151
Enveloping cones drawn from a point to confocals 110
Equation of a quadric 7
Feuerbach 221
Focal conics 92 95
Focal distance property of conics, generalised 96
Focal lines of contact cones drawn to confocal quadrics 109
Focal system 61ff. 135
Four curves in space, number of lines meeting 184
Four lines, condition they are tangent lines of a cubic curve 145
Freedom of a system of curves on a surface 194
Gabbatt 223
Gaskin's theorem in three dimensions 89
Generator of a developable 131
Generators of a quadric 5 7
Generators of a quadric at right angles 90
Generators of a quadric, through the umbilici 80
Genus of a curve in space 194
Geodesics 112
Gordan 208
Grassmann 208
Hesse 44 154 158
Hessian pair of three points of a cubic curve in space 137
Hessian pair of three points of a cubic curve in space, Hessian of a cubic surface 181 187 188 208
Hexad, self-conjugate 48 50 146
Hierholzer 151
Hudson 224
Inflexional curves of Steiner’s quartic surface 222
Inflexional curves of the cubic surface with four double points 216
Inflexional lines at any point of a cubic surface 197
Inpolar, or outpolar, quadric 52 88
Intersection of two quadrics 123
Invariant of two linear complexes 66
Invariant of two lines 58
Involution, general, of sets of four points of a cubic curve in space 139
Ivory’s theorem 118
Jessop 223
kronecker 223
Kummer’s surface 221
Laguerre 221
Lie — Scheffers 149
Lie — Scheffers, Lie 221
Limiting points of two spheres 74
| Linear complex 56 61 62 66
Linear complex, linear congruence 65
Lines of a quadric 1
Lines of a quadric, coordinates of a line 56
Lines of a quadric, invariant of two 58
Lines of a quadric, lines and planes at right angles 70
Lueroth 151
Middle point 70
Milne 203
Moebius and focal systems 69
Moebius tetrads 67 137 138
Morley 221 224
Neuberg 221
Normals at right angles to a given line, locus of 106
Normals of a quadric 86
Normals of confocals, through a point 104
Normals of three confocals through a point are focal lines of enveloping cone 109
Null system 69
Osculating plane of cubic curve 127
Outpolar, cubic curve, to a quadric 146
Outpolar, or inpolar, quadric 52 88
Parabola in a plane touched by axes of confocals 98
Paraboloid 83
Parallel lines and planes 70
Parallel tangent planes of confocals have their points of contact on a conic 108
Parametric expression of a quadric 7
Pascal 44
Pentad, self-conjugate 37 50 147 177
Pentagon, skew, determines a focal system 68
Perpendicular lines and planes 70
Plane sections of a sphere 73
Plane, equation of 1
Pluecker 102
Point-pair of Hessian surface expressed by six point-pairs 188
Polar line of a line in regard to a quadric 28 58 69
Polar lines of a line in regard to confocals, locus of 106
Polar plane of a quadric from the equation 22 23
Polar plane of a quadric, defined descriptively 27
Polar point of a plane in regard to a quadric 29 30 31
Polar quadric, in regard to a cubic surface 182
Polar reciprocal in regard to a quadric 93
Pole and polar, in a focal system 61 64
Poncelet 10
Poncelet, porism for conics deduced from theory of confocal surfaces 116
Principal planes of a quadric 79
Principal planes of enveloping cones drawn to confocals 109
Quadric polynomial reduced to sum of squares 15
Quadric polynomial reduced to sum of squares, representing a cone 18
Quadric polynomial reduced to sum of squares, representing a repeated plane 20
Quadric polynomial reduced to sum of squares, representing two planes 19
Quadric surface defined as representing a plane with two fundamental points 13
Quadric surface defined by its lines 2
Quadric surface defined by two conics and a line 7
Quadric surface defined by two related central systems 11
Quadric surface, possible intersection of two quadric surfaces 123
Quadric surface, self-polar tetrad of two 152
Quadric surface, three intersect in eight points 153 154
Quartic curve, elliptic, intersection of two quadrics 69 151
Quartic curve, plane, derived from cubic surface 196
Quartic curve, rational 85 150 222
Quartic surface, containing umbilicar generators of a quadric 93
Quartic surface, determined by normals of quadric at points of plane section 105
Quartic surface, determined by tangents of a cubic curve 132
Quartic surface, Steiner’s 221
Radical plane of two spheres 74
Rational curve in general 149
Rational quartic curve 85 150 222
Residual set of points on a plane curve 179
Revolution, cone of 81 82
Reye 49 206 211
Right angles, lines and planes at 70
Right circular cone 81 82
Right circular cone, circumscribing a quadric, locus of vertex 95
Roth 203
Schroeter 158
Schur quadrics 162 168 177 187 200 211
Screw 69
Section of a quadric by plane at right angles to a focal conic 95
Segre 158 208
Self-conjugate hexad 48 50 146
Self-conjugate pentad 37 50 147 177
Self-polar figure, a general 40
Self-polar tetrad in regard to a quadric 33 50 52
Serret, P. 49
Servais 221
Sextic curve in space 154 198
Similitude, centres of, for two spheres 78
Spheres 72
Spheres, cutting at right angles 76
Squares, expression of a quadric by five 38 39
Squares, expression of a quadric by six 49
Squares, quadric polynomial reduced to 16
Star-systems, related 11 184
Steiner points, for Pascal figure 44
Steiner system of bitangents of a plane quartic curve 200
Steiner, trihedral pairs 164 174 203 208
Steiner’s quartic surface 221
Stenfors 168
Striction, line of, on a quadric 84
Sturm 208
Sylvester 64 66 206 208 210
Tangent cone, or enveloping cone, of a quadric 26
Tangent of a cubic curve 127 132
Tangent of a cubic curve, tangent plane of a cubic surface 197
Tangent plane of a quadric 23 27
Tangential equation of a quadric 25
telling 148
Tetrad of points whose opposite joins are conjugate points in regard to a quadric 35
Tetrad of which opposite joins are at right angles 78
Tetrad, self-polar 33 50 52 145
Tetrad, two related by reciprocation 41 53
Tetrad, two tetrads in perspective 37
Tetrahedral complex 99 134
Thomson and Tait 132
Transformation, cubo-cubic, in space 141
Trihedral 164 174 203
Umbilicus of a paraboloid 83
Umbilicus of a quadric 80
Umbilicus, umbiliear generators of a quadric lie on a quartic surface 93
Veronese 223
Von Staudt 158 168
Wakeford 148
Weddle’s surface 154
Wilton 224
Zeuthen 158
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