Apollonius of Perga's Conica: text, context, subtext:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Leiden ; Köln [u.a.]
Brill
2001
|
| Schriftenreihe: | [Mnemosyne / Supplementum]
222 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 499 S. graph. Darst. |
| ISBN: | 9004119779 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804128579471015936 |
|---|---|
| adam_text | APOLLONIUS OF PERGAS CONICA
TEXT, CONTEXT, SUBTEXT
BY
MICHAEL N FRIED
SABETAI UNGURU
BRILL
LEIDEN • BOSTON • KOLN
CONTENTS
Preface and Acknowledgements xi
Introduction 1
Apollonius s Conica and its History 2
The Plan of the Present Work 12
I Geometrical Algebra 17
A Its Formulation 17
B 1 Its Origins 20
2 Strength and Weakness of Geometrical
Algebra 35
C The Influence of Geometrical Algebra in the
Interpretation of the Conica 38
Figures 52
II The Elements of Conic Sections in the Framework
of Books I-III 56
Introduction 56
Apollonius s Introduction and the General Nature
of Elements 57
The Initial Definitions 61
The Definitions of the Conic Sections and the
Symptomata 74
A Second Look at the Algebraic Interpretation of
the Elements of Conies 90
Symptomata and Equations 92
The Locus Problem 97
Intentiones Primae and Intentiones Secundae 101
The Place of Diameters 103
Conclusion 107
Figures 109
III Book IV of the Elements of Conic Sections:
How Conic Sections Meet in the Plane 117
Introduction 117
Vlll CONTENTS
The Investigation of Opposite Sections 119
How Conic Sections Meet in a Plane 128
Digression: Descartes Treatment of Cutting and
Touching in La Geometrie 133
The Possibility of Different Conic Sections in
One Plane 135
Conclusion 138
Figures 140
IV Maximum and Minimum Lines: Book V of the
Conica 146
Introduction 146
The Conventional View: Normals as Maxima
and Minima 148
The Importance of Normals 155
The Evolute 167
Maximum and Minimum Lines as Longest and
Shortest Lines 177
Neusis-like Constructions 187
Conclusion 203
Figures 205
V Equality and Similarity: Book VI of the Conica 221
Introduction 221
Equality 224
Similarity 242
Equality and Similarity 252
The Constructions 260
Conclusion 270
Figures 275
VI Diorismic Theorems and the Use of Analogy:
Book VII of the Conica 283
Introduction 283
Diorismoi and Diorismic Theorems 284
A Glance at Halley s Book VIII 293
The Diorismic Theorems of Book VII 298
Images of Diameters and Latera Recta 306
Conclusion 320
Figures 324
CONTENTS IX
VII Once Again, the use of Analog) in Apollonius:
Conies and Circles 332
Introduction 332
The Tangent and the Asymptote: An Internal
Analogy in the Conica 335
Circles and Conic Sections 344
Conclusion 355
Figures 357
VIII The Conica as an Integral Whole: Elementary
and Non-Elementary Books 364
Introduction 364
Was the Conica Written as One book? 365
Elementary and Advanced Books: The Basic
Division in the Conica 370
Conclusion 386
Figures 389
IX Some Circumscribed Reflections on the
Historiography of Hellenistic Mathematics 390
Appendix: English Translation of Book IV 413
Translator s Preface 413
Lettering Scheme for Diagrams in Book IV 415
Apollonius s Conica: Book IV 416
Diagrams 454
Bibliography 487
Index 495
|
| any_adam_object | 1 |
| author | Fried, Michael N. Unguru, Šabbetay 1931-2024 Apollonius Pergaeus v262-v190 |
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| author_facet | Fried, Michael N. Unguru, Šabbetay 1931-2024 Apollonius Pergaeus v262-v190 |
| author_role | aut aut aut |
| author_sort | Fried, Michael N. |
| author_variant | m n f mn mnf š u šu a |
| building | Verbundindex |
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| classification_rvk | FH 44853 |
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| dewey-raw | 516 |
| dewey-search | 516 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Philologie / Byzantinistik / Neulatein |
| era | Geschichte gnd |
| era_facet | Geschichte |
| format | Book |
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| spelling | Fried, Michael N. Verfasser aut Apollonius of Perga's Conica: text, context, subtext by Michael N. Fried ; Sabetai Unguru Leiden ; Köln [u.a.] Brill 2001 XII, 499 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier [Mnemosyne / Supplementum] 222 Apollonius från Perga / Conica Apollonius <of Perga> Kōnika Apollonius Pergaeus v262-v190 Conica (DE-588)4319941-0 gnd rswk-swf Geschichte gnd rswk-swf Conic sections Early works to 1800 Mathematics, Greek Kegelschnitt (DE-588)4125170-2 gnd rswk-swf Griechenland Altertum (DE-588)4093976-5 gnd rswk-swf Apollonius Pergaeus geom. TLG 0550 (DE-2581)TH000000216 gbd Mathematik der Antike (DE-2581)TH000007621 gbd Apollonius Pergaeus v262-v190 Conica (DE-588)4319941-0 u DE-604 Griechenland Altertum (DE-588)4093976-5 g Kegelschnitt (DE-588)4125170-2 s Geschichte z Unguru, Šabbetay 1931-2024 Verfasser (DE-588)120363879 aut Apollonius Pergaeus v262-v190 (DE-588)11864548X aut Conica Supplementum] [Mnemosyne 222 (DE-604)BV000000966 222 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009405667&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fried, Michael N. Unguru, Šabbetay 1931-2024 Apollonius Pergaeus v262-v190 Apollonius of Perga's Conica: text, context, subtext Apollonius från Perga / Conica Apollonius <of Perga> Kōnika Apollonius Pergaeus v262-v190 Conica (DE-588)4319941-0 gnd Conic sections Early works to 1800 Mathematics, Greek Kegelschnitt (DE-588)4125170-2 gnd |
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| title | Apollonius of Perga's Conica: text, context, subtext |
| title_alt | Conica |
| title_auth | Apollonius of Perga's Conica: text, context, subtext |
| title_exact_search | Apollonius of Perga's Conica: text, context, subtext |
| title_full | Apollonius of Perga's Conica: text, context, subtext by Michael N. Fried ; Sabetai Unguru |
| title_fullStr | Apollonius of Perga's Conica: text, context, subtext by Michael N. Fried ; Sabetai Unguru |
| title_full_unstemmed | Apollonius of Perga's Conica: text, context, subtext by Michael N. Fried ; Sabetai Unguru |
| title_short | Apollonius of Perga's Conica: text, context, subtext |
| title_sort | apollonius of perga s conica text context subtext |
| topic | Apollonius från Perga / Conica Apollonius <of Perga> Kōnika Apollonius Pergaeus v262-v190 Conica (DE-588)4319941-0 gnd Conic sections Early works to 1800 Mathematics, Greek Kegelschnitt (DE-588)4125170-2 gnd |
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