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Название: Principles of Geometry (vol. IV)
Автор: Baker H.F.
Аннотация:
The present volume, the first written and the most revised, of the book, for which indeed, mostly, the earlier volumes were undertaken, still bears many marks of the difficulty of compressing the matter into brief compass. But the writer hopes that it may seem to the reader as remarkable as it does to him, that it should be possible to comprehend under one point of view, and that so simple, the introduction to nearly all the surfaces ordinarily studied in the geometry of three dimensions, as well as the usual line geometry. Chapters v, vi, vii seek to make clear that this is so. To these the earlier chapters are auxiliary. But Chapters ii and iv have been introduced as much for their own interest as for their illustrative value; the results obtained in these two chapters are not required in the subsequent pages. It is hoped that the Table of Contents, and the Index, may make it easy to use the volume. It will of course be understood that the volume is throughout intended to be introductory and illustrative; hardly anywhere is it complete.
Roberts, generalisation of a theorem for circles8 Rosenhain, equation of Kummer’s surface216 Salmon, radius of Hart circle on a sphere80 Schoute, on a six-dimensional polytope105 Segre, degenerate forms190 Segre, general investigation of Cyclides172 Segre, loci of third order in fourfold space116 Segre, representation of conics in fivefold space, on Veronese’s surface54 Segre, tetrahedral and linear complex, from planes in fourfold space36 Segre, theorem for a Cyclide180 Segre, theorem of five planes meeting six lines143 Segre’s cubic locus in fourfold space, from fivefold space160 Segre’s cubic locus in fourfold space, obtained from quadric surfaces through five points152 Segre’s cubic locus in fourfold space, regarded as a dual151 Segre’s cubic locus in fourfold space, theorem for lines upon155 Segre’s figure, by transformation from fivefold space208 Segre’s figure, incidences proved algebraically115 Segre’s figure, locus for which two planes coincide123 Segre’s figure, number notation for lines and solids114 Segre’s figure, of fifteen points and lines in fourfold space113203 Segre’s figure, planes found algebraically124 Segre’s figure, planes of a system meeting an arbitrary line136 Segre’s figure, reciprocating quadric for148 Segre’s figure, singular solids115124129 Segre’s figure, six systems of planes, two of any system through a point123 Segre’s quartic locus in fourfold space, and Weddle surface159 Segre’s quartic locus in fourfold space, contains a symmetrical figure of sixteen points and planes130134 Segre’s quartic locus in fourfold space, intersection with tangent solid138 Segre’s quartic locus in fourfold space, irrational equation of125 Segre’s quartic locus in fourfold space, is rational126 Segre’s quartic locus in fourfold space, particular form of equation142 Segre’s quartic locus in fourfold space, representing an involution of threefold space210 Segre’s quartic locus in fourfold space, six conics through a point met by lines in related ranges127 Segre’s quartic locus in fourfold space, tangent solid128 Segre’s quartic locus in fourfold space, tangential equation148 Segre’s quartic locus in fourfold space, thirty-two related ranges in131 Severi, surface with no chords through arbitrary point55 Similitude, centres of similitude for two circles66 Similitude, circle of, obtained by projection15 Sphere, angle of intersection of two spheres39
Sphere, centre of, by projection39 Sphere, determined by section of quadric in fourfold space36 Sphere, enveloping a Cyclide175 Sphere, represented by a point of fourfold space39 Sphere, touching four given spheres, or planes5758 Steiner, a theorem for two triads of points21 Steiner, by projection from fourfold space, or from fivefold space191 Steiner, circles cutting three given circles at given angles67 Steiner, solution of Malfatti’s problem68 Steiner’s quartic surface54 Stephanos, figure of fifteen circles, in anticipation of Segre116203 Study, mutual relations of four circles and four tangent circles86 Taylor’s theorem, for poles of a line in regard to six conics5 Tetrads, fifteen associated with six conjugate linear complexes206 Tetrads, Moebius, mutually inscribed, theorem for four141 Tetrads, property of tetrad in regard to a line, considered in fivefold space239 Tetrahedral complex in fivefold space239 Tetrahedral complex, determined from planes in fourfold space32 Tetrahedroid, or Wave surface217 Tore, or Anchor Ring, and Dupin’s Cyclide193199 Transversals of two lines, and points of a quadric surface31 Triangularly circumscribed conic35 Vaidyanathaswamy, property of a cubic curve147 Veronese’s surface in fivefold space, conics thereon5254 Veronese’s surface in fivefold space, projecting to Steiner’s quartic surface191 Veronese’s surface in fivefold space, theorem of reciprocity of a general figure149 Wakeford, on the theorem of a double-six of lines6 Wakeford, six conics triangularly circumscribed to another32 Wakeford, theorem for six lines with a common transversal60 Wallace’s theorem, additions to21 Wallace’s theorem, and Moebius’s figure of two tetrads18 Wallace’s theorem, generalised1058 Wave surface, or tetrahedroid217 Weber’s theorem, construction of six conjugate linear complexes from six points139 Weddle’s surface, and Kummer’s surface, from four quadrics in threefold space160 Weddle’s surface, correspondence of conjugate directions233 Weddle’s surface, equation of158 Weddle’s surface, from Segre’s quartic locus159 Weddle’s surface, origin of156 White, equation of a conic triangularly circumscribed to six conics5 White, proof of Clifford’s chain of theorems for circles64
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