Inversive geometry:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
Chelsea
1954
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 273 S. Ill. |
Internformat
MARC
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| 300 | |a IX, 273 S. |b Ill. | ||
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Datensatz im Suchindex
| _version_ | 1804118059368054784 |
|---|---|
| adam_text | CONTENTS
Preface Page v
Part I
Chapter I. OPERATIONS OF ELEMENTARY GEOMETRY Page 1
§§ 1. Instruments 2. Rotations 3. Translations and
Reversions 4. The Product of Reversions 5.
Stretches 6. Parallel Co ordinates.
Chapter II. ALGEBRA Page 12
§§ 7. Algebra 8. Multiplication 9. Trigonometry 10.
Functions 11. The Derivative 12. The Logarithm
13. The Exponential.
Chapter III. THE EUCLIDEAN GROUP Page 24
§§ 14. Homologies 15. Antilogies 16. The Product of
Stretches 17. The Product of Rotations 18. The
Product of Homologies 19. Twists.
Chapter IV. INVERSIONS Page 38
§§ 20. Cross ratios 21. Inversions 22. Inversors 23.
Properties of an Inversion 24. Normal Circles
25. The Lune and the Ring 26. The Canonical
Form.
Chapter V. QUADRATICS Page 52
§§ 27. The Bilinear Invariant 28. The Jacobian 29.
The Vector 30. Theory of the Four point 31. The
Ordered Six point 32. The Complete System.
Chapter VI. THE INVERSIVE GROUP OF THE PLANE Page 63
§§ 33. Fixed Points 34. Invariants of a Homography
35. Composition of Homographies 36. Invariants
of an Antigraphy 37. The Canonical Form 38. The
Determinant of Powers.
Chapter VII. FINITE INVERSIVE GROUPS Page 75
§§ 39. The Inversive Group of the Three point 40. The
Cycle of Six Points 41. Intrinsic Co ordinates
42. Geometric Solution of the Cubic Equation
43. The Groups of the Rectangle and Rhombus
44. Doubly special Four points 45. The Regular
Polyhedra.
vii
viii INVERSIVE GEOMETRY
Chapter VIII. PARABOLIC, HYPERBOLIC, AND ELLIPTIC
GEOMETRIES Page 87
§§ 46. Analytic Expressions for the Three Subgroups
47. Infinity 48. Distance 49. Curvature 50.
Motions 51. The Vector of Two Homographies.
Chapter IX. THE CELESTIAL SPHERE Page 97
§§ 52. Geometry within a Sphere 53. The Directed
Cylinder 54. The Determinant of Powers 55.
The Radius of the Cylinder 56. The Rect¬
angular Hexagon 57. The Configuration of
Ten Lines 58. Geometry of the Three line
59. Rectangular Axes 60. The Euclidean Case
61. Six Perpendicular Lines 62. The Vector
of Two Directed Cylinders 63. The Relation
D5 64. The Caustic of a Correspondence.
Chapter X. FLOW Page 117
§§ 65. Analytic Flow 66. Standard Case of Radial
Flow 67. Two Equal Sinks 68. Three Equal
Sinks 69. The Rational Fraction 70. The
Doublet 71. Two Opposed Doublets 72. Flow
with Doublets, Sinks, and Sources 73. Vortices.
Chapter XI. DIFFERENTIAL GEOMETRY Page 130
§§74. The Translational Derivative 75. The Homo¬
logous Derivative 76. The Homographic De¬
rivative 77. Homographic Invariants of a
Curve 78. Special Cases 79. Schwarz s In¬
tegral 80. Conformal Mapping.
Part II
Chapter XII. THE LINE AND THE CIRCLE Page 151
§§ 81. Map equations of a Line 82. Self conjugate
Equations of a Line 83. The Base circle 84.
Envelopes 85. Map equations of a Circle 86.
Self conjugate Equation of a Circle 87. The
n line 88. Stretches.
Chapter XIII. REGULAR POLYGONS Page 166
§§ 89. The Regular Pentagon 90. The Regular
Heptagon 91. The Regular 11 gon 92. Knots.
Chapter XIV. MOTIONS Page 177
§§ 93. The Equation of a Motion 94. The Point of
No Velocity 95. The Points of No Acceleration
96. The Curvature of a Path 97. Envelopes
98. The da Vinci Motion 99. Three bar
Motion.
CONTENTS ix
Chapter XV. THE TRIANGLE Page 186
§§100. The Nine point Circle 101. The Orthocentre
102. TheCentroid 103. Euler s Relation 104.
Feuerbach s Theorem 105. Interpolation
106. Taylor s Circle 107. The Incentres
108. The Circle of Images 109. Focal Pairing
110. The Pedal Circles 111. The Invariant I,.
Chapter XVI. INVARIANTS UNDER HOMOLOGIES Page 201
§§ 112. Constants under Translations 113. La
grange Resolvents 114. The Case of the
Triangle 115. The Four point 116. The
Hexagon 117. Barycentric Co ordinates 118.
Foci.
Chapter XVII. RATIONAL CURVES Page 219
§§ 119. The Curves 120. The Foci 121. The
Double Points 122. Cusps 123. The Curve R*
124. Sections of R» by a Circle 125. Sections
of an R by a C 2 126. Degeneration 127.
Mechanical Description of R .
Chapter XVIII. CONICS Page 228
§§ 128. The Parabola 129. Lines of the Curve
130. Theory of the Four line 131. Sections by
a Circle 132. Bifocal Conies 133. lines of the
Curve 134. Theory of the Five line 135.
Section by a Circle 136. The Images of a Point.
Chapter XIX. THE CARDIOID AND THE DELTOID Page 239
§§ 137. The Cardioid 138. Lines of the Cardioid
139. The Section by a Line 140. TwoCardioids
141. The Deltoid.
Chapter XX. CREMONA TRANSFORMATIONS Page 248
§§ 142. A Simple Illustration 143. Focal Pairing
144. Intrinsic Co ordinates 145 The Geiser
Transformation 146. The Bertini Transfor¬
mation
Chapter XXI. THE n LINE Page 259
§§ 147. Oyclogens 148. Osculants 149. Construc¬
tion of a Cyclogen 150. Clifford s Chain
151. The n fold Parabola 152. Foci.
Index Page 273
|
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| dewey-full | 516.9 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.9 |
| dewey-search | 516.9 |
| dewey-sort | 3516.9 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T16:04:16Z |
| institution | BVB |
| language | English |
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| owner_facet | DE-91G DE-BY-TUM DE-20 DE-83 DE-188 |
| physical | IX, 273 S. Ill. |
| publishDate | 1954 |
| publishDateSearch | 1954 |
| publishDateSort | 1954 |
| publisher | Chelsea |
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| spelling | Morley, Frank Verfasser aut Inversive geometry by Frank Morley ; F. V. Morley New York Chelsea 1954 IX, 273 S. Ill. txt rdacontent n rdamedia nc rdacarrier Geometry, Modern Inversion Mathematik (DE-588)4162235-2 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 s Inversion Mathematik (DE-588)4162235-2 s DE-604 Morley, Frank Vigor Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002364399&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Morley, Frank Morley, Frank Vigor Inversive geometry Geometry, Modern Inversion Mathematik (DE-588)4162235-2 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| subject_GND | (DE-588)4162235-2 (DE-588)4001161-6 |
| title | Inversive geometry |
| title_auth | Inversive geometry |
| title_exact_search | Inversive geometry |
| title_full | Inversive geometry by Frank Morley ; F. V. Morley |
| title_fullStr | Inversive geometry by Frank Morley ; F. V. Morley |
| title_full_unstemmed | Inversive geometry by Frank Morley ; F. V. Morley |
| title_short | Inversive geometry |
| title_sort | inversive geometry |
| topic | Geometry, Modern Inversion Mathematik (DE-588)4162235-2 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| topic_facet | Geometry, Modern Inversion Mathematik Algebraische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002364399&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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