Holdings: The history of the theory of errors

The history of the theory of errors:

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Bibliographic Details
Main Author:	Šejnin, Oskar B. 1925- (Author)
Format:	Book
Language:	German
Published:	Egelsbach ; Frankfurt [Main] ; St. Peter Port Hänsel-Hohenhausen 1996
Series:	Deutsche Hochschulschriften 1118
Subjects:	Error analysis (Mathematics) - History Geschichte Error analysis (Mathematics) > History Fehlerrechnung Irrtum Mathematik
Online Access:	Inhaltsverzeichnis
Item Description:	Literaturverz. S. 153 - 176
Physical Description:	180 S.
ISBN:	3826711181

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MARC


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Record in the Search Index

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adam_text	OSCAR SHEYNIN THE HISTORY OF THE THEORY OF ERRORS .HANSEL^HOHENHAUSEN EGELSBACH \| FRANKFURT \| ST. PETER PORT CONTENTS 0. INTRODUCTION ............................................ 8 0.1. THE GOALS OF THE THEORY OF ERRORS 8 0.2. INTERRELATION WITH STATISTICS 9 0.3. ASTRONOMY AND GEODESY 10 0.4. WHY AND WHEN DID THE THEORY OF ERRORS EMERGE? ...... 11 0.5. THE SCOPE OF THIS BOOK 13 0.6. SOME TERMINOLOGY AND NOTATION 13 1. THE EARLY HISTORY 17 1.1. BOUNDS AND ESTIMATORS 17 1.2. REGULAR OBSERVATIONS 18 1.3. OPTIMAL CIRCUMSTANCES OF OBSERVATION ............... 18 1.4. PTOLEMY 19 1.3. SOME EXPLANATION 21 1.6. AL=BIRUNI 21 1.7. GALILEO 23 1.8. TYCHO BRAHE 24 1.9. KEPLER 25 NOTES 28 MAIN LITERATURE . 29 2. THE EIGHTEENTH CENTURY 31 2.1. THE ARITHMETIC MEAN ................................ 31 2.2. MAYER 31 2.3. LAMBERT 32 2.4. BOSCOVICH 36 2.5. SIMPSON 39 2.6. LAGRANGE . 42 2.7. DANIEL BERNOULLI I 42 2.8. EULER ; 45 NOTES 47 MAIN LITERATURE 50 3. LAPLACE 51 3.1. INTRODUCTION 51 3.2. EARLY MEMOIRS 52 3.3. LATER WORK (1810 * 1811) 56 3.4. THE THEORIE ANALYTIQUE DES PROBABILITES 58 3.5. SUPPLEMENT 1 (1616) 61 3.6. SUPPLEMENT 2 (1818) 62 3.7. SUPPLEMENT 3 (CA. 1819) 67 3.8. A FAULTY DISCUSSION OF DEPENDENT OBSERVATIONS ...... 69 NOTES 70 MAIN LITERATURE 73 4. THE NINETEENTH CENTURY BEFORE 1809 75 4.1. SOLVING REDUNDANT SYSTEMS OF EQUATIONS ............. 75 4.2. A VENERABLE PROBLEM IN LAND SURVEYING 76 4.3. HUBER 76 4.4. LEGENDRE 77 4.5. ADRAIN 78 4.6. GAUSS 82 NOTES 84 MAIN LITERATURE 84 5. GAUSS 85 5.1. THEORIA MOTUS ,,,.,,, 85 5.2. DETERMINING THE PRECISION OF OBSERVATIONS .......... 88 5.3 THEORIA COMBINATIONIS 90 5.4. PRACTICAL CONSIDERATIONS. THE ERROR THEORY SURVEYED 97 NOTES 101 MAIN LITERATURE 103 6. FROM GAUSS TO HELMERT AND BEYOND 105 6.1. SOME NEW WORK 105 6.2. PHYSICS, CHEMISTRY, METEOROLOGY ................... 108 6.3. THE NORMAL LAW 111 6.4. THE NORMAL LAW MODIFIED 114 6.5. THE THEORY OF ERRORS AND STATISTICS ............... 118 NOTES 121 MAIN LITERATURE 125 7. HELMERT 127 7.1. REJECTION OF OUTLYING OBSERVATIONS 127 7.2. REVEALING SYSTEMATIC ERRORS ....................... 127 7.3. REVEALING SYSTEMATIC ERRORS: THE ABBE CRITERION ... 129 7.4. THE SUMS OF NATURAL POWERS OF ERRORS 130 7.5. THE CHISQUARED DISTRIBUTION 131 7.6. THE PETERS FORMULA 132 7.7. THE GAUSS FORMULA 134 7.8. ANTICIPATING THE STUDENT * FISHER THEOREM 135 7.9. THE PRECISION OF THE MEAN SQUARE ERROR 135 7.10. IS UNBIASEDNESS NECESSARY? 136 NOTES 137 MAIN LITERATURE .......................................... 138 8. STABLE LAWS (LEVY) 139 8.1. RANDOM ERRORS 139 8.2. THE PRECISION OF OBSERVATIONS ....................... 139 8.3. THE MEAN SQUARE ERROR ............................... 140 8.4. A NEW CONCEPT OF PRECISION 141 8.5. STABLE LAWS. 141 NOTES 143 MAIN LITERATURE 143 9. THE DETERMINATE THEORY OF ERRORS ......................... 145 9.1. EXPERIMENTAL DESIGN AND PRELIMINARY DATA ANALYSIS ... 145 9.2. THE EIGHTEENTH CENTURY 14.5 9.3. LAPLACE 14.7 9.4. GAUSS AND BESSEL 148 9.5. HELMERT 151 NOTES 152 BIBLIOGRAPHY 153 / IKDERS. * JSTAAT5- U.T.J. RV.-\| V GOTTINGEN
any_adam_object	1
author	Šejnin, Oskar B. 1925-
author_GND	(DE-588)128703350
author_facet	Šejnin, Oskar B. 1925-
author_role	aut
author_sort	Šejnin, Oskar B. 1925-
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discipline	Mathematik
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spelling	Šejnin, Oskar B. 1925- Verfasser (DE-588)128703350 aut The history of the theory of errors Oscar Sheynin Egelsbach ; Frankfurt [Main] ; St. Peter Port Hänsel-Hohenhausen 1996 180 S. txt rdacontent n rdamedia nc rdacarrier Deutsche Hochschulschriften 1118 Literaturverz. S. 153 - 176 Error analysis (Mathematics) - History Geschichte Error analysis (Mathematics) -- History Fehlerrechnung (DE-588)4153837-7 gnd rswk-swf Irrtum (DE-588)4140092-6 gnd rswk-swf Geschichte (DE-588)4020517-4 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Fehlerrechnung (DE-588)4153837-7 s Geschichte (DE-588)4020517-4 s DE-604 Mathematik (DE-588)4037944-9 s Irrtum (DE-588)4140092-6 s Deutsche Hochschulschriften 1118 (DE-604)BV004679961 1118 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007309184&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Šejnin, Oskar B. 1925- The history of the theory of errors Deutsche Hochschulschriften Error analysis (Mathematics) - History Geschichte Error analysis (Mathematics) -- History Fehlerrechnung (DE-588)4153837-7 gnd Irrtum (DE-588)4140092-6 gnd Geschichte (DE-588)4020517-4 gnd Mathematik (DE-588)4037944-9 gnd
subject_GND	(DE-588)4153837-7 (DE-588)4140092-6 (DE-588)4020517-4 (DE-588)4037944-9
title	The history of the theory of errors
title_auth	The history of the theory of errors
title_exact_search	The history of the theory of errors
title_full	The history of the theory of errors Oscar Sheynin
title_fullStr	The history of the theory of errors Oscar Sheynin
title_full_unstemmed	The history of the theory of errors Oscar Sheynin
title_short	The history of the theory of errors
title_sort	the history of the theory of errors
topic	Error analysis (Mathematics) - History Geschichte Error analysis (Mathematics) -- History Fehlerrechnung (DE-588)4153837-7 gnd Irrtum (DE-588)4140092-6 gnd Geschichte (DE-588)4020517-4 gnd Mathematik (DE-588)4037944-9 gnd
topic_facet	Error analysis (Mathematics) - History Geschichte Error analysis (Mathematics) -- History Fehlerrechnung Irrtum Mathematik
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007309184&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV004679961
work_keys_str_mv	AT sejninoskarb thehistoryofthetheoryoferrors

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