Modern pure solid geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Bronx, NY
Chelsea Publ. Co.
1964
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 353 S. |
Internformat
MARC
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| 245 | 1 | 0 | |a Modern pure solid geometry |c by Nathan Altshiller-Court |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Bronx, NY |b Chelsea Publ. Co. |c 1964 | |
| 300 | |a XIV, 353 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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Datensatz im Suchindex
| _version_ | 1804135901775790080 |
|---|---|
| adam_text | TABLE OF CONTENTS
PAOB
CHAPTER I. PRELIMINARY 1
1. Introductory Propositions and Problems 1
2. The Hyperbolic Group of Lines 9
3. Harmonic Forms 12
4. Homothetic Figures 16
5. Perspective Tetrahedrons 21
CHAPTER II. THE TRIHEDRAL ANGLE 29
1. The Orthocentric Line 29
2. The Supplementary Trihedral Angle 32
3. Isoclinal Lines and Planes 34
4. Axes 40
5. Centroidal Lines 43
CHAPTER III. THE SKEW QUADRILATERAL 47
CHAPTER IV. THE TETRAHEDRON 54
1. The Centroid 54
a. Bimedians and Bialtitudes 54
b. Medians 57
c. The Circumscribed Parallelepiped 66
2. Altitudes 69
a. Special Cases 69
b. The General Case 74
c. The Monge Point 76
3. The Bisecting Planes of the Dihedral Angles 80
4. The Spheres Touching the Four Faces of a Tetra¬
hedron 81
a. The Inscribed Sphere 81
b. The Existence and Distribution of the Escribed
Spheres 83
c. Relative Position of the Centers to Each Other.... 87
d. The Points of Contact with the Faces 89
e. Relations Between the Radii 91
5. Volume of Tetrahedron 95
6. Special Tetrahedrons 100
a. The Trirectangular Tetrahedron 100
b. The Isosceles Tetrahedron 103
c. A Special Tetrahedron 113
d. A Doubly Special Tetrahedron 115
7. Miscellaneous Propositions 116
xiii
xiv TABLE OF CONTENTS
PAGE
CHAPTER V. TRANSVERSALS 127
1. The Skew Quadrilateral 127
2. The Tetrahedron 131
CHAPTER VI. THE OBLIQUE CONE WITH A CIRCU¬
LAR BASE 145
CHAPTER VII. SPHERES 157
1. Preliminaries 157
2. Inverse Points 161
3. Orthogonal Spheres 162
4. Poles and Polar Planes with Respect to a Sphere 166
5. The Imaginary Sphere 175
6. Centers, Axes, and Planes of Similitude 177
7. The Power of a Point with Respect to a Sphere 187
8. The Radical Plane of Two Spheres 193
9. Coaxal Pencils of Spheres 204
10. Coaxal Nets of Spheres 219
11. Four Spheres 229
CHAPTER VIII. INVERSION 247
CHAPTER IX. RECENT GEOMETRY OF THE TETRA¬
HEDRON 266
A. The General Tetrahedron 266
1. Harmonic Points and Planes 266
a. Tetrahedral Poles and Polar Planes 266
b. Desmic Systems of Tetrahedrons 271
2. Isogonal Points 278
3. Antiparallel Sections 285
4. Spheres Related to the Tetrahedron 288
a. Analogues of the Nine Point Circle 288
b. The Apollonian Spheres of the Tetrahedron 290
B. Special Tetrahedrons 294
1. The Circumscriptible Tetrahedron 294
2. The Orthocentric Tetrahedron 299
3. The Isodynamic Tetrahedron 314
a. The Lemoine Point and the Lemoine Plane 314
b. The Lemoine Tetrahedron 320
c. The Neuberg Spheres 324
4. The Isogonic Tetrahedron 328
BIBLIOGRAPHICAL NOTES 337
INDEX 347
|
| adam_txt |
TABLE OF CONTENTS
PAOB
CHAPTER I. PRELIMINARY 1
1. Introductory Propositions and Problems 1
2. The Hyperbolic Group of Lines 9
3. Harmonic Forms 12
4. Homothetic Figures 16
5. Perspective Tetrahedrons 21
CHAPTER II. THE TRIHEDRAL ANGLE 29
1. The Orthocentric Line 29
2. The Supplementary Trihedral Angle 32
3. Isoclinal Lines and Planes 34
4. Axes 40
5. Centroidal Lines 43
CHAPTER III. THE SKEW QUADRILATERAL 47
CHAPTER IV. THE TETRAHEDRON 54
1. The Centroid 54
a. Bimedians and Bialtitudes 54
b. Medians 57
c. The Circumscribed Parallelepiped 66
2. Altitudes 69
a. Special Cases 69
b. The General Case 74
c. The Monge Point 76
3. The Bisecting Planes of the Dihedral Angles 80
4. The Spheres Touching the Four Faces of a Tetra¬
hedron 81
a. The Inscribed Sphere 81
b. The Existence and Distribution of the Escribed
Spheres 83
c. Relative Position of the Centers to Each Other. 87
d. The Points of Contact with the Faces 89
e. Relations Between the Radii 91
5. Volume of Tetrahedron 95
6. Special Tetrahedrons 100
a. The Trirectangular Tetrahedron 100
b. The Isosceles Tetrahedron 103
c. A Special Tetrahedron 113
d. A Doubly Special Tetrahedron 115
7. Miscellaneous Propositions 116
xiii
xiv TABLE OF CONTENTS
PAGE
CHAPTER V. TRANSVERSALS 127
1. The Skew Quadrilateral 127
2. The Tetrahedron 131
CHAPTER VI. THE OBLIQUE CONE WITH A CIRCU¬
LAR BASE 145
CHAPTER VII. SPHERES 157
1. Preliminaries 157
2. Inverse Points 161
3. Orthogonal Spheres 162
4. Poles and Polar Planes with Respect to a Sphere 166
5. The Imaginary Sphere 175
6. Centers, Axes, and Planes of Similitude 177
7. The Power of a Point with Respect to a Sphere 187
8. The Radical Plane of Two Spheres 193
9. Coaxal Pencils of Spheres 204
10. Coaxal Nets of Spheres 219
11. Four Spheres 229
CHAPTER VIII. INVERSION 247
CHAPTER IX. RECENT GEOMETRY OF THE TETRA¬
HEDRON 266
A. The General Tetrahedron 266
1. Harmonic Points and Planes 266
a. Tetrahedral Poles and Polar Planes 266
b. Desmic Systems of Tetrahedrons 271
2. Isogonal Points 278
3. Antiparallel Sections 285
4. Spheres Related to the Tetrahedron 288
a. Analogues of the Nine Point Circle 288
b. The Apollonian Spheres of the Tetrahedron 290
B. Special Tetrahedrons 294
1. The Circumscriptible Tetrahedron 294
2. The Orthocentric Tetrahedron 299
3. The Isodynamic Tetrahedron 314
a. The Lemoine Point and the Lemoine Plane 314
b. The Lemoine Tetrahedron 320
c. The Neuberg Spheres 324
4. The Isogonic Tetrahedron 328
BIBLIOGRAPHICAL NOTES 337
INDEX 347 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 2. ed. |
| format | Book |
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| index_date | 2024-07-02T16:06:57Z |
| indexdate | 2024-07-09T20:47:52Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015156308 |
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| physical | XIV, 353 S. |
| publishDate | 1964 |
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| publisher | Chelsea Publ. Co. |
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| spelling | Court, Nathan Altshiller 1881-1968 Verfasser (DE-588)172026636 aut Modern pure solid geometry by Nathan Altshiller-Court 2. ed. Bronx, NY Chelsea Publ. Co. 1964 XIV, 353 S. txt rdacontent n rdamedia nc rdacarrier Geometry, Solid Stereometrie (DE-588)4057321-7 gnd rswk-swf Geometrie (DE-588)4020236-7 gnd rswk-swf Stereometrie (DE-588)4057321-7 s DE-604 Geometrie (DE-588)4020236-7 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015156308&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Court, Nathan Altshiller 1881-1968 Modern pure solid geometry Geometry, Solid Stereometrie (DE-588)4057321-7 gnd Geometrie (DE-588)4020236-7 gnd |
| subject_GND | (DE-588)4057321-7 (DE-588)4020236-7 |
| title | Modern pure solid geometry |
| title_auth | Modern pure solid geometry |
| title_exact_search | Modern pure solid geometry |
| title_exact_search_txtP | Modern pure solid geometry |
| title_full | Modern pure solid geometry by Nathan Altshiller-Court |
| title_fullStr | Modern pure solid geometry by Nathan Altshiller-Court |
| title_full_unstemmed | Modern pure solid geometry by Nathan Altshiller-Court |
| title_short | Modern pure solid geometry |
| title_sort | modern pure solid geometry |
| topic | Geometry, Solid Stereometrie (DE-588)4057321-7 gnd Geometrie (DE-588)4020236-7 gnd |
| topic_facet | Geometry, Solid Stereometrie Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015156308&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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