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Euclid - the creation of mathematics:

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Bibliographische Detailangaben
Beteilige Person:	Artmann, Benno 1933-2010 (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	New York [u.a.] Springer 1999
Schlagwörter:	Euclide <ca 3e siècle av. J.-C> / Éléments Euclid Euclid > Elements Euclides > ca. v3. Jh. > Elementa Euclides > ca. v3. Jh. Geschichte Euclide, Éléments d' Griekse oudheid Mathématiques grecques Wiskunde Mathematik Mathematics, Greek Griechenland (Altertum)
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008558000&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Beschreibung:	Einheitssacht. des kommentierten Werkes: Elementa
Umfang:	XVI, 343 S. Ill., graph. Darst.
ISBN:	0387984232

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adam_text	Contents Preface v Notes to the Reader xv 1 General Historical Remarks 1 2 The Contents of the Elements 3 2.1 Book I: Foundations of Plane Geometry 3 2.2 Book II: The Geometry of Rectangles 4 2.3 Book III: The Geometry of the Circle 5 2.4 Book IV: Regular Polygons in Circles 5 2.5 Book V: The General Theory of Magnitudes in Proportion 5 2.6 Book VI: The Plane Geometry of Similar Figures . . . 6 2.7 Book VII: Basic Arithmetic 7 2.8 Book VIII: Numbers in Continued Proportion 7 2.9 Book IX: Numbers in Continued Proportion; the Theory of Even and Odd Numbers, Perfect Numbers 8 2.10 Book X: Incommensurable Line Segments 8 2.11 Book XI: Foundations of Solid Geometry 9 ix 2.12 Book XII: Areas and Volumes; Eudoxus s Method of Exhaustion 9 2.13 Book XIII: The Platonic Solids 10 3 The Origin of Mathematics 1: The Testimony of Eudemus 11 Time Table 16 4 Euclid Book I 17 4.1 The Overall Composition of Book I 17 4.2 Definitions and Axioms 18 4.3 Book I, Part A: Foundations 21 4.4 Book I, Part B: The Theory of Parallels 31 4.5 Book I, Part C: Parallelograms and Their Areas .... 36 4.6 Book I, Part D: The Theorem of Pythagoras 42 5 The Origin of Mathematics 2: Parallels and Axioms 47 6 The Origin of Mathematics 3: Pythagoras of Samos 51 7 Euclid Book II 61 8 The Origin of Mathematics 4: Squaring the Circle 73 9 Euclid Book III 79 9.1 The Overall Composition of Book III 79 9.2 The Definitions of Book III 80 9.3 Book III, Part A: Chords in Circles, Circles Intersecting or Touching Each Other 81 9.4 Book III, Part B: Tangents 82 9.5 Book III, Part C Angles in Segments of Circles ... 84 9.6 Book III, Part C2: Chords, Arcs, and Angles 86 9.7 Book III, Part C3: More About Angles in Circles ... 86 9.8 Book III, Part D: Intersecting Chords, Secants, and Tangents 88 10 The Origin of Mathematics 5: Problems and Theories 93 11 Euclid Book IV 97 11.1 The Contents of Book IV 97 11.2 The Regular Pentagon 99 11.3 Speculations About the Pentagon 102 12 The Origin of Mathematics 6: The Birth of Rigor 109 13 The Origin of Mathematics 7: Polygons After Euclid 113 13.1 What We Missed in Book IV 113 13.2 What Euclid Knew 114 13.3 What Archimedes Did 115 13.4 What Gauss Proved 116 13.5 How Gauss Did It 117 13.6 The Moral of the Story 119 13.7 What Plotinus Has to Say About All This 120 14 Euclid Book V 121 14.1 Proportions Outside of Mathematics 121 14.2 General Remarks About Book V 123 14.3 Proportions in a Modern Version 124 14.4 The Definitions of Book V 127 14.5 The Propositions of Book V 129 15 Euclid Book VI 135 15.1 The Overall Composition of Book VI 135 15.2 The Basis of Similarity Geometry 136 15.3 The Basic Theorems of Similarity Geometry .... 138 15.4 Book VI, Part C: Proportions and Areas (Products) 141 15.5 Book VI, Part D: Similar Rectilinear Figures 144 15.6 Book VI, Part E: The Application of Areas 146 16 The Origin of Mathematics 8: Be Wise, Generalize 151 16.1 Extending a Result 152 16.2 Weakened Hypotheses 152 16.3 Abstraction 153 16.4 The Case of Pythagoras s Theorem 153 16.5 The Generalization of Ptolemy 155 16.6 Marcel Proust on Abstraction 159 17 Euclid Book VII 161 17.1 The Historical Background 161 17.2 The Overall Composition of Book VII 163 17.3 Definitions 163 17.4 Book VII, Part A: The Euclidean Algorithm 165 17.5 Book VII, Parts B and C: Proportion for Numbers . . 167 17.6 Book VII, Part D: Proportions and Products 171 17.7 Book VII, Part E: The Greatest Common Divisor and Prime Divisors 176 17.8 Book VII, Part F: The Least Common Multiple ... 182 18 The Origin of Mathematics 9: Nicomachus and Diophantus 183 18.1 Nicomachus: Introduction to Arithmetic 183 18.2 Diophantus: The Arithmetica 188 19 Euclid Book VIII 193 19.1 The Overall Composition of Books VIII and IX ... 193 19.2 Book VIII, Part A: Numbers in Continued Proportion 194 19.3 Book VIII, Part B: The Geometry of Numbers . ... 196 20 The Origin of Mathematics 10: Tools and Theorems 203 21 Euclid Book IX 207 21.1 Book IX, Parts B, C, D, and E: More About Numbers in Continued Proportion 207 21.2 Book IX, Part F: The Number of Primes 209 21.3 Book IX, Part G: Odd and Even Numbers, and Perfect Numbers 210 22 The Origin of Mathematics 11: Math Is Beautiful 213 23 Euclid Book X 223 23.1 Commensurability and Its Relation to Other Notions 227 24 The Origin of Mathematics 12: Incommensurability and Irrationality 229 25 Euclid Book XI 255 25.1 The Overall Composition of Book XI 255 25.2 The Definitions of Book XI 256 25.3 Foundations of Solid Geometry 257 25.4 The Affinities of Books I and XI 258 25.5 The Duplication of the Cube 263 26 The Origin of Mathematics 13: The Role of Definitions 267 27 Euclid Book XII 271 27.1 The Overall Composition of Book XII 271 27.2 The Circle 271 27.3 The Pyramid 274 27.4 Cylinders, Cones, and Spheres 278 28 The Origin of Mathematics 14: The Taming of the Infinite 279 29 Euclid Book XIII 283 29.1 The Overall Composition of Book XIII 283 29.2 Division in Extreme and Mean Ratio and the Pentagon 284 29.3 About the Decagon 286 29.4 The Regular Solids 292 29.5 The Classification of the Regular Solids 296 30 The Origin of Mathematics 15: Symmetry Through the Ages 299 30.1 Nature 300 30.2 Art 300 30.3 Philosophy 305 30.4 Mathematics 308 31 The Origin of Mathematics 16: The Origin of the Elements 313 Notes 317 Bibliography 329 Index 341
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spellingShingle	Artmann, Benno 1933-2010 Euclid - the creation of mathematics Euclide <ca 3e siècle av. J.-C> / Éléments Euclid Euclid Elements Euclides ca. v3. Jh. Elementa (DE-588)4266253-9 gnd Euclides ca. v3. Jh. (DE-588)118638955 gnd Euclide, Éléments d' ram Griekse oudheid gtt Mathématiques grecques Mathématiques grecques ram Wiskunde gtt Mathematik Mathematics, Greek Mathematik (DE-588)4037944-9 gnd
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title	Euclid - the creation of mathematics
title_auth	Euclid - the creation of mathematics
title_exact_search	Euclid - the creation of mathematics
title_full	Euclid - the creation of mathematics Benno Artmann
title_fullStr	Euclid - the creation of mathematics Benno Artmann
title_full_unstemmed	Euclid - the creation of mathematics Benno Artmann
title_short	Euclid - the creation of mathematics
title_sort	euclid the creation of mathematics
topic	Euclide <ca 3e siècle av. J.-C> / Éléments Euclid Euclid Elements Euclides ca. v3. Jh. Elementa (DE-588)4266253-9 gnd Euclides ca. v3. Jh. (DE-588)118638955 gnd Euclide, Éléments d' ram Griekse oudheid gtt Mathématiques grecques Mathématiques grecques ram Wiskunde gtt Mathematik Mathematics, Greek Mathematik (DE-588)4037944-9 gnd
topic_facet	Euclide <ca 3e siècle av. J.-C> / Éléments Euclid Euclid Elements Euclides ca. v3. Jh. Elementa Euclides ca. v3. Jh. Euclide, Éléments d' Griekse oudheid Mathématiques grecques Wiskunde Mathematik Mathematics, Greek Griechenland (Altertum)
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