Solid geometry

Baker, Henry Frederick

Bibliographic data

Volume

Persistent identifier:: 871728818

Author:: Baker, Henry Frederick

Title:: Solid geometry

Sub title:: quadrics, cubic curves in space, cubic surfaces

Scope:: XIX, 228 Seiten

DOI:: 10.14463/GBV:871728818

Year of publication:: 1923

Place of publication:: Cambridge

Identifier (digital):: 871728818

Illustration:: Diagramme

Signature of the source:: Mr.I 326(3)

Language:: English

Publisher of the original:: University Press

Usage licence:: Public Domain Mark 1.0

Publisher of the digital copy:: Technische Informationsbibliothek Hannover

Place of publication of the digital copy:: Hannover

Year of publication of the original:: 2016

Document type:: Volume

Collection:: Mathematics

Index

Title:: INDEX

Document type:: Volume

Structure type:: Index

INDEX 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 confocals, 93, 98; of a develop able, 133 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 ; quadratic complex, tetrahedral com plex, 99 Cone, quadric, defined, 4, 17 ; cone of revolution, 81 Confocal paraboloids, 95 Confocal quadric surfaces, 91 if.; the three through a point not always distinct, 92; touching a line, 109; as dual of quadrics with a common curve, 119; leading to Poncelet’s porism, 116 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; 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, tangents belong to a linear complex, 68 ; generated by points of contact of tangent planes of confocals through a line, 107. General consideration of cubic curve in space, 125 if. ; drawn through five points of a quadric, 129; four tangents meet a line, 132; outpolar to a quadric, 146; constructed to satisfy six conditions, 129, 139-142; constructed to meet each of four lines in a pair of an involution given thereon, 145 Cubic developable, dual to a cubic curve, 130, 135 Cubic surface, general account, 159 ff.; theorem of coresiduation for curves upon, 181; curves upon, 191; equations of, 203-208; determined by six arbitrary points in a plane, 194; leading to a plane quartic curve, 196; Hessian of, 208; cubic surface with four double points, 214 Cubo-cubic transformation in space, 143 Curves of intersection of a quadric with confocals projected into con focal conics, 113 Cuspidal edge of a developable, 131 Cylinder, 81 Dandelin, 44 Deformation of quadric with rigid generators, 114

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