The mathematics of the heavens and the earth: the early history of trigonometry
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Princeton, N.J. [u.a.]
Princeton Univ. Press
2009
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XVII, 329 S. Ill., graph. Darst. 24 cm |
| ISBN: | 9780691129730 |
Internformat
MARC
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| 245 | 1 | 0 | |a The mathematics of the heavens and the earth |b the early history of trigonometry |c Glen van Brummelen |
| 264 | 1 | |a Princeton, N.J. [u.a.] |b Princeton Univ. Press |c 2009 | |
| 300 | |a XVII, 329 S. |b Ill., graph. Darst. |c 24 cm | ||
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| 500 | |a Includes bibliographical references and index | ||
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| 650 | 4 | |a Geschichte | |
| 650 | 4 | |a Trigonometry |x History | |
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Datensatz im Suchindex
| _version_ | 1804138572991692800 |
|---|---|
| adam_text | CONTENTS PREFACE XI THE ANCIENT HEAVENS 1 1 PRECURSORS 9 WHAT IS
TRIGONOMETRY? 9 THE SEQED IN ANCIENT EGYPT 10 * TEXT 1.1 FINDING THE
SLOPE OF A PYRAMID 11 BABYLONIAN ASTRONOMY, ARC MEASUREMENT, AND THE
360 CIRCLE 12 THE GEOMETRIC HEAVENS: SPHERICS IN ANCIENT GREECE 18 A
TRIGONOMETRY OF SMALL ANGLES? ARISTARCHUS AND ARCHIMEDES ON ASTRONOMICAL
DIMENSIONS 20 * TEXT 1.2 ARISTARCHUS, THE RATIO OF THE DISTANCES OF THE
SUN AND MOON 24 2 ALEXANDRIAN GREECE 33 CONVERGENCE 33 HIPPARCHUS 34 A
MODEL FOR THE MOTION OF THE SUN 37 * TEXT 2.1 DERIVING THE ECCENTRICITY
OF THE SUN S ORBIT 39 HIPPARCHUS S CHORD TABLE 41 THE EMERGENCE OF
SPHERICAL TRIGONOMETRY 46 THEODOSIUS OF BITHYNIA 49 MENELAUS OF
ALEXANDRIA 53 THE FOUNDATIONS OF SPHERICAL TRIGONOMETRY: BOOK III OF
MENELAUS S SPHERICS 56 * TEXT 2.2 MENELAUS, DEMONSTRATING MENELAUS S
THEOREM 57 SPHERICAL TRIGONOMETRY BEFORE MENELAUS? 63 CLAUDIUS PTOLEMY
68 PTOLEMY S CHORD TABLE 70 PTOLEMY S THEOREM AND THE CHORD
SUBTRACTION/ADDITION FORMULAS 74 THE CHORD OF 1 76 THE INTERPOLATION
TABLE 77 VIII CONTENTS CHORDS IN GEOGRAPHY: GNOMON SHADOW LENGTH TABLES
77 * TEXT 2.3 PTOLEMY, FINDING GNOMON SHADOW LENGTHS 78 SPHERICAL
ASTRONOMY IN THE ALMAGEST 80 PTOLEMY ON THE MOTION OF THE SUN 82 R TEXT
2.4 PTOLEMY, DETERMINING THE SOLAR EQUATION 84 THE MOTIONS OF THE
PLANETS 86 TABULATING ASTRONOMICAL FUNCTIONS AND THE SCIENCE OF
LOGISTICS 88 TRIGONOMETRY IN PTOLEMY S OTHER WORKS 90 * TEXT 2.5
PTOLEMY, CONSTRUCTING LATITUDE ARCS ON A MAP 91 AFTER PTOLEMY 93 3 INDIA
94 TRANSMISSION FROM BABYLON AND GREECE 94 THE FIRST SINE TABLES 95
ARYABHATA S DIFFERENCE METHOD OF CALCULATING SINES 99 A TEXT 3.1
ARYABHATA, COMPUTING SINES 100 BHASKARA I S RATIONAL APPROXIMATION TO
THE SINE 102 IMPROVING SINE TABLES 105 OTHER TRIGONOMETRIC IDENTITIES
107 * TEXT 3.2 VARAHAMIHIRA, A HALF-ANGLE FORMULA 108 * TEXT 3.3
BRAHMAGUPTA, THE LAW OF SINES IN PLANETARY THEORY? 109 BRAHMAGUPTA S
SECOND-ORDER INTERPOLATION SCHEME FOR APPROXIMATING SINES 111 * TEXT 3.4
BRAHMAGUPTA, INTERPOLATING SINES 111 TAYLOR SERIES FOR TRIGONOMETRIC
FUNCTIONS IN MADHAVA S KERALA SCHOOL 113 APPLYING SINES AND COSINES TO
PLANETARY EQUATIONS 121 SPHERICAL ASTRONOMY 124 * TEXT 3.5 VARAHAMIHIRA,
FINDING THE RIGHT ASCENSION OF A POINT ON THE ECLIPTIC 125 USING
ITERATIVE SCHEMES TO SOLVE ASTRONOMICAL PROBLEMS 129 * TEXT 3.6
PARAME9VARA, USING FIXED-POINT ITERAT ION TO COMPUTE SINES 131
CONCLUSION 133 CONTENTS IX 4 ISLAM 135 FOREIGN JUNKETS: THE ARRIVAL OF
ASTRONOMY FROM INDIA 135 BASIC PLANE TRIGONOMETRY 137 BUILDING A BETTER
SINE TABLE 140 *TEXT 4.1 AL-SAMAW AL IBNYAHYA AL-MAGHRIBI, WHY THE
CIRCLE SHOULD HAVE 480 DEGREES 146 INTRODUCING THE TANGENT AND OTHER
TRIGONOMETRIC FUNCTIONS 149 * TEXT 4.2 ABN 1-RAYHAN AL-BIRUNI, FINDING
THE CARDINAL POINTS OF THE COMPASS 152 STREAMLINING ASTRONOMICAL
CALCULATION 156 * TEXT 4.3 KUSHYAR IBN LABBAN, FINDING THE SOLAR
EQUATION 156 NUMERICAL TECHNIQUES: APPROXIMATION, ITERATION,
INTERPOLATION 158 * TEXT 4.4 IBN YNNUS, INTERPOLATING SINE VALUES 164
EARLY SPHERICAL ASTRONOMY: GRAPHICAL METHODS AND ANALEMMAS 166 * TEXT
4.5 AL-KHWARIZMI, DETERMINING THE ORTIVE AMPLITUDE GEOMETRICALLY 168
MENELAUS IN ISLAM 173 * TEXT 4.6 AL-KIIHI, FINDING RISING TIMES USING
THE TRANSVERSAL THEOREM 175 MENELAUS S REPLACEMENTS 179 SYSTEMATIZING
SPHERICAL TRIGONOMETRY: IBN MUCADH S DETERMINATION OF THE MAGNITUDES AND
NAIR AL-DIN AL-TUSI S TRANSVERSAL FIGURE 186 APPLICATIONS TO RELIGIOUS
PRACTICE: THE QIBLA AND OTHER RITUAL NEEDS 192 * TEXT 4.7 AL-BATTANI, A
SIMPLE APPROXIMATION TO THE QIBLA 195 ASTRONOMICAL TIMEKEEPING:
APPROXIMATING THE TIME OF DAY USING THE HEIGHT OF THE SUN 201 NEW
FUNCTIONS FROM OLD: AUXILIARY TABLES 205 * TEXT 4.8 AL-KHALILI, USING
AUXILIARY TABLES TO FIND THE HOUR-ANGLE 207 TRIGONOMETRIC AND
ASTRONOMICAL INSTRUMENTS 209 * TEXT 4.9 AL-SIJZI (? ), ON AN APPLICATION
OF THE SINE QUADRANT 213 TRIGONOMETRY IN GEOGRAPHY 215 TRIGONOMETRY IN
AL-ANDALUS 217 X CONTENTS 5 THE WEST TO 1550 223 TRANSMISSION FROM THE
ARAB WORLD 223 AN EXAMPLE OF TRANSMISSION: PRACTICAL GEOMETRY 224 R TEXT
5.1 HUGH OF ST. VICTOR, USING AN ASTROLABE TO FIND THE HEIGHT OF AN
OBJECT 225 * TEXT 5.2 FINDING THE TIME OF DAY FROM THE ALTITUDE OF THE
SUN 227 CONSOLIDATION AND THE BEGINNINGS OF INNOVATION: THE TRIGONOMETRY
OF LEVI BEN GERSON, RICHARD OF WALLINGFORD, AND JOHN OF MURS 230 * TEXT
5.3 LEVI BEN GERSON, THE BEST STEP SIZE FOR A SINE TABLE 233 * TEXT 5.4
RICHARD OF WALLINGFORD, FINDING SIN(1 ) WITH ARBITRARY ACCURACY 237
INTERLUDE: THE MARTELOIO IN NAVIGATION 242 R TEXT 5.5 MICHAEL OF RHODES,
A NAVIGATIONAL PROBLEM FROM HIS MANUAL 244 FROM PTOLEMY TO TRIANGLES:
JOHN OF GMUNDEN, PEURBACH, REGIOMONTANUS 247 * TEXT 5.6 REGIOMONTANUS,
FINDING THE SIDE OF A RECTANGLE FROM ITS AREA AND ANOTHER SIDE 254 *
TEXT 5.7 REGIOMONTANUS, THE ANGLE-ANGLE-ANGLE CASE OF SOLVING RIGHT
TRIANGLES 255 SUCCESSORS TO REGIOMONTANUS: WERNER AND COPERNICUS 264 *
TEXT 5.8 COPERNICUS, THE ANGLE-ANGLE-ANGLE CASE OF SOLVING TRIANGLES 267
* TEXT 5.9 COPERNICUS, DETERMINING THE SOLAR ECCENTRICITY 270 BREAKING
THE CIRCLE: RHETICUS, OTHO, PITISCUS AND THE OPUS PALATINUM 273
CONCLUDING REMARKS 284 BIBLIOGRAPHY 287 INDEX 323
|
| any_adam_object | 1 |
| author | Van Brummelen, Glen |
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| callnumber-first | Q - Science |
| callnumber-label | QA24 |
| callnumber-raw | QA24 |
| callnumber-search | QA24 |
| callnumber-sort | QA 224 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SG 500 SG 590 |
| ctrlnum | (OCoLC)236082858 (DE-599)BVBBV035280797 |
| dewey-full | 516.2409 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.2409 |
| dewey-search | 516.2409 |
| dewey-sort | 3516.2409 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| era | Geschichte Anfänge-1600 gnd |
| era_facet | Geschichte Anfänge-1600 |
| format | Book |
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| indexdate | 2024-07-09T21:30:20Z |
| institution | BVB |
| isbn | 9780691129730 |
| language | English |
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| physical | XVII, 329 S. Ill., graph. Darst. 24 cm |
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| publisher | Princeton Univ. Press |
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| spelling | Van Brummelen, Glen Verfasser aut The mathematics of the heavens and the earth the early history of trigonometry Glen van Brummelen Princeton, N.J. [u.a.] Princeton Univ. Press 2009 XVII, 329 S. Ill., graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Geschichte Anfänge-1600 gnd rswk-swf Geschichte Trigonometry History Trigonometrie (DE-588)4060888-8 gnd rswk-swf Trigonometrie (DE-588)4060888-8 s Geschichte Anfänge-1600 z b DE-604 Digitalisierung Deutsches Museum application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017086011&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Van Brummelen, Glen The mathematics of the heavens and the earth the early history of trigonometry Geschichte Trigonometry History Trigonometrie (DE-588)4060888-8 gnd |
| subject_GND | (DE-588)4060888-8 |
| title | The mathematics of the heavens and the earth the early history of trigonometry |
| title_auth | The mathematics of the heavens and the earth the early history of trigonometry |
| title_exact_search | The mathematics of the heavens and the earth the early history of trigonometry |
| title_full | The mathematics of the heavens and the earth the early history of trigonometry Glen van Brummelen |
| title_fullStr | The mathematics of the heavens and the earth the early history of trigonometry Glen van Brummelen |
| title_full_unstemmed | The mathematics of the heavens and the earth the early history of trigonometry Glen van Brummelen |
| title_short | The mathematics of the heavens and the earth |
| title_sort | the mathematics of the heavens and the earth the early history of trigonometry |
| title_sub | the early history of trigonometry |
| topic | Geschichte Trigonometry History Trigonometrie (DE-588)4060888-8 gnd |
| topic_facet | Geschichte Trigonometry History Trigonometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017086011&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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