The mathematics of measurement: a critical history
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London
Athlone Press
1998
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 330 S. graph. Darst. |
| ISBN: | 0387915818 |
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Datensatz im Suchindex
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|---|---|
| adam_text | THE MATHEMATICS OF MEASUREMENT A CRITICAL HISTORY JOHN J. ROCHE THE
ATHLONE PRESS LONDON SPRINGER CONTENTS PREFACE AND INTRODUCTION 1
CHAPTER 1 THE EMERGENCE OF THE PRACTICAL CONCEPTION OF NUMBER 9 THE USES
OF NUMBER IN PHYSICS 9 PHYSICAL NUMBERS 9 NUMBER WORDS AND RECITATION
COUNTING 11 WRITTEN NUMERALS 13 NUMERALS MIMICKING NUMBERS 13 THE EARLY
WORKING CONCEPT OF NUMBER 14 HISTORICAL BEGINNINGS OF THEORIES OF NUMBER
14 ABSTRACT NUMBERS 16 INFORMAL BEGINNINGS OF CONVENTIONAL AND FORMAL
NUMBERS 17 THE INTERPRETATION OF IRRATIONALS, NEGATIVES AND IMAGINARY
NUMBERS 18 CHAPTER 2 EARLY SCIENTIFIC METROLOGY AND QUANTITATIVE LAWS 22
NUMBER AND MEASUREMENT IN SCIENCE AND IN THE ARTS 22 EARLY WEIGHTS AND
MEASURES 23 ANCIENT UNITS OF LENGTH AND MASS 23 LIMITATIONS OF THE
TECHNOLOGY OF MEASUREMENT 26 ANGLE AND TIME MEASUREMENTS IN ASTRONOMY 27
QUANTIFICATION WITHOUT METROLOGY 30 QUANTITATIVE LAWS IN ANTIQUITY AND
IN THE MIDDLE AGES 31 CHAPTER 3 EARLY APPLICATIONS OF GEOMETRY AND
PROPORTION 32 THE USES OF MATHEMATICS 32 EXACT, DESCRIPTIVE AND APPLIED
SCIENCE AMONG THE GREEKS 32 THE CHARACTER OF GREEK THEORETICAL GEOMETRY
34 EUCLIDEAN GEOMETRY 35 ABSTRACT POINTS, LINES AND SURFACES 36 APPLYING
IDEALIZED GEOMETRY TO NATURE 38 CONFIGURATIONS FOR PHYSICAL QUANTITIES
AND RELATIONS 39 PROPORTION **. 41 HOMOGENEOUS AND HETEROGENEOUS
PROPORTIONS 42 PHYSICAL LAWS AND COMPOUND RATIOS 44 NON-EUCLIDEAN
QUANTITIES 44 VIII CONTENTS PROPORTION IN MEDIEVAL EXACT SCIENCE 45
RATIO REDUCED TO A SINGLE NUMBER 46 FEATURES OF LAWS STATED AS
PROPORTIONS 47 APPLICATIONS OF EARLY TRIGONOMETRY 48 TRIGONOMETRY DURING
THE RENAISSANCE 50 CHAPTER 4 THE PROGRESS OF QUANTIFICATION 51 THE
CONCEPT OF PHYSICS 51 THE BASIC REFERENCE QUANTITIES OF MEASUREMENT 52
UNITS IN SCIENCE AND COMMERCE BEFORE THE METRIC REFORM 52 APPLICATIONS
OF MEASUREMENT AND MATHEMATICS FROM THE RENAISSANCE 56 SENSITIVITY TO
OBSERVATIONAL ERROR 57 MEASUREMENTS OF ANGLE AND LENGTH 57 IMPROVEMENTS
IN CLOCKWORK 58 BALANCES TO THE EIGHTEENTH CENTURY 59 PHILOSOPHICAL
INSTRUMENTS AND PHILOSOPHICAL MEASUREMENTS 59 THE DISCOVERY OF
QUANTITATIVE LAWS 61 GALILEAN ABSTRACTION 62 QUALITATIVE AND
QUANTITATIVE CONCEPTS IN MAGNETISM 62 THE QUANTIFICATION OF ELECTRIC
CHARGE, TENSION AND CURRENT 63 CHAPTER 5 ARITHMETICAL ALGEBRA AND
SYMBOLIC GEOMETRY 66 VERBAL ARITHMETICAL ALGEBRA 66 VERBAL GEOMETRICAL
ALGEBRA 68 APPLICATIONS OF ARITHMETICAL ALGEBRA TO NATURAL PHILOSOPHY 70
SYMBOLIC ALGEBRA AND SYMBOLIC GEOMETRY FROM THE RENAISSANCE 70
ANALYTICAL TRIGONOMETRY 74 THE GROWING COMPETENCE OF NUMBER 75 THE
PROMOTION OF HETEROGENEOUS RATIOS 77 OPPOSITION TO ALGEBRA 78
JUSTIFICATIONS OF ALGEBRA 80 THE INFINITESIMAL CALCULUS 82 CHAPTER 6
ALGEBRA IN PHYSICS IN THE SEVENTEENTH CENTURY 86 ACCOMMODATING
MATHEMATICS TO PHYSICS 86 THE INFLUENCE OF GEOMETRY 87 COMPARATIVE
MEASUREMENT 89 POINTS OF ENTRY OF ALGEBRA INTO TECHNOLOGY AND PHYSICS 90
AN ISOLATED BEGINNING: THOMAS HARRIOT 94 THE CONCEPT OF THE MOMENT OF A
FORCE 96 THE ALGEBRAIC REPRESENTATION OF THE MOMENT OF A FORCE 98
VARIETIES OF FORCE 99 COMPONENTS OF A FORCE 100 THE QUANTIFICATION OF
VELOCITY 100 CONTENTS IX DYNAMICAL MOMENTUM 105 MECHANICAL WORK AND VIS
VIVA 108 SYMBOLIC ALGEBRA AND THE CALCULUS IN KINEMATICS 110 SYMBOLIC
ALGEBRA IN GEOMETRICAL OPTICS AND ASTRONOMY 112 THE LANGUAGE OF NEWTON S
PRINCIPIA 113 CHAPTER 7 MATHEMATICS IN EIGHTEENTH-CENTURY EXACT SCIENCE
117 NEWTON AND THE LATITUDE OF FORMS 117 QUANTITY OF MATTER 118 THE
CONCEPT OF INERTIA 122 NEWTON S LAWS OF MOTION AND HIS LAW OF GRAVITY
124 ABBREVIATED RATIO EQUATIONS, UNITS AND FUNCTIONAL EQUATIONS 126
VARIGNON S ANALYTICAL KINEMATICS AND DYNAMICS 127 ALGEBRA IN SCIENTIFIC
ENGINEERING 131 EULER TO LAGRANGE 132 CELESTIAL MECHANICS 136 ALGEBRA IN
MAGNETISM AND ELECTRICITY 138 THE BEGINNINGS OF THE ANALYTICAL THEORY OF
HEAT 142 CHAPTER 8 THE METRIC REFORM AND THE UNITS OF PHYSICS 145
BEGINNINGS OF THE METRIC REFORM 145 THE CENTIGRADE SCALE OF TEMPERATURE
147 THE IMPACT OF THE METRIC MOVEMENT 148 ABSOLUTE UNITS AND EQUATIONS
IN THE THEORY OF HEAT 149 BIOT S TRAITE DE PHYSIQUE 154 ABSOLUTE UNITS
IN MECHANICS 155 WORK, KINETIC ENERGY AND THERMODYNAMICS 159 ABSOLUTE
UNITS IN DYNAMICAL ASTRONOMY 160 CHAPTER 9 ABSOLUTE QUANTIFICATION IN
ELECTRICITY AND MAGNETISM 163 ANALYTICAL ELECTROSTATICS . 163 POISSON
AND MAGNETIC UNITS 164 GAUSS AND ABSOLUTE UNITS IN MAGNETISM 166 AMPERE
AND ANALYTICAL ELECTRODYNAMICS 168 BIOT, SAVART, LAPLACE AND ANALYTICAL
ELECTROMAGNETISM 170 WILHELM WEBER AND ABSOLUTE ELECTRIC CURRENT 171
ABSOLUTE UNITS FOR ELECTRICAL RESISTANCE AND FOR ELECTROMOTIVE FORCE 172
THE CONCEPT OF ENERGY IN ELECTRICITY 175 THE PROLIFERATION OF UNIT
SYSTEMS IN ELECTROMAGNETISM 177 THE BRITISH ASSOCIATION STANDARDS 179
THE PRACTICAL SYSTEM OF ELECTRICAL UNITS 183 THE GIORGI SYSTEM AND THE
SYSTEME INTERNATIONAL 184 X CONTENTS CHAPTER 10 DIMENSIONAL ANALYSIS AND
THE QUANTITY CALCULUS 188 THE NEW MATHEMATICS OF MEASUREMENT 188 ORIGINS
OF THE THEORY OF DIMENSIONS 188 THE DIMENSIONAL ANALYSIS OF FOURIER 191
GAUGE INVARIANCE, CONVERSION FACTORS AND DIMENSIONS 193 THE QUANTITY
CALCULUS 197 WEBER S BASE CALCULUS 200 A MERGING OF INTERPRETATIONS:
MAXWELL S DIMENSIONAL ANALYSIS 202 MULTIPLE AMBIGUITY 205 CHAPTER 11
DIMENSIONAL EXPLORATION 208 RAYLEIGH AND VASCHY 208 THE OPTIMUM NUMBER
OF BASE QUANTITIES 214 DIMENSIONLESS QUANTITIES 215 THE STATUS OF
DIMENSIONAL THEORY 217 CHAPTER 12 INTERPRETING THE ALGEBRA OF PHYSICS
219 PHYSICAL NUMBERS IN MODERN PHYSICS 219 FORMAL ALGEBRA AND FORMAL
ARITHMETIC IN MODERN PHYSICS 221 DEBATES OVER THE QUANTITY CALCULUS 224
A SYMBOLIC MIMICRY OF NATURE? 229 CONCLUSIONS 236 APPENDIX UNITS IN THE
SYSTEME INTERNATIONAL . 237 DEFINITIONS OF BASE UNITS IN THE SYSTEME
INTERNATIONAL D UNITES (SI) 237 A COHERENT SYSTEM OF MEASUREMENT 23.8
NOTES 240 BIBLIOGRAPHY 282 INDEX . 308
|
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| discipline | Physik Mathematik |
| edition | 1. publ. |
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| language | English |
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| spelling | Roche, John J. Verfasser aut The mathematics of measurement a critical history John J. Roche 1. publ. London Athlone Press 1998 X, 330 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathématiques - Histoire ram Meetmethoden gtt Mesure - Histoire ram Metrologie gtt Wiskunde gtt Geschichte Mathematik Mathematics History Measurement History Mathematik (DE-588)4037944-9 gnd rswk-swf Messung (DE-588)4038852-9 gnd rswk-swf Geschichte (DE-588)4020517-4 gnd rswk-swf Messung (DE-588)4038852-9 s Mathematik (DE-588)4037944-9 s Geschichte (DE-588)4020517-4 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008539341&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Roche, John J. The mathematics of measurement a critical history Mathématiques - Histoire ram Meetmethoden gtt Mesure - Histoire ram Metrologie gtt Wiskunde gtt Geschichte Mathematik Mathematics History Measurement History Mathematik (DE-588)4037944-9 gnd Messung (DE-588)4038852-9 gnd Geschichte (DE-588)4020517-4 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4038852-9 (DE-588)4020517-4 |
| title | The mathematics of measurement a critical history |
| title_auth | The mathematics of measurement a critical history |
| title_exact_search | The mathematics of measurement a critical history |
| title_full | The mathematics of measurement a critical history John J. Roche |
| title_fullStr | The mathematics of measurement a critical history John J. Roche |
| title_full_unstemmed | The mathematics of measurement a critical history John J. Roche |
| title_short | The mathematics of measurement |
| title_sort | the mathematics of measurement a critical history |
| title_sub | a critical history |
| topic | Mathématiques - Histoire ram Meetmethoden gtt Mesure - Histoire ram Metrologie gtt Wiskunde gtt Geschichte Mathematik Mathematics History Measurement History Mathematik (DE-588)4037944-9 gnd Messung (DE-588)4038852-9 gnd Geschichte (DE-588)4020517-4 gnd |
| topic_facet | Mathématiques - Histoire Meetmethoden Mesure - Histoire Metrologie Wiskunde Geschichte Mathematik Mathematics History Measurement History Messung |
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