Extension theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
2000
|
| Schriftenreihe: | History of mathematics
19 : Sources |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII, 411 S. graph. Darst. |
| ISBN: | 0821820311 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804128064075988992 |
|---|---|
| adam_text | Titel: Extension theory
Autor: Graßmann, Hermann
Jahr: 2000
Contents
Translator s Note ix
Foreword xiii
Part 1. The Elementary Conjunctions of Extensive Magnitudes 1
Chapter 1. Addition, Subtraction, Multiples and Fractions of Extensive
Magnitudes 3
1. Concepts and laws of calculation 3
2. Connection between the magnitudes derived from a system of units 8
3. Number as the quotient of extensive magnitudes and the replacement of
the equations between extensive magnitudes by numerical equations 14
Chapter 2. The Product Structure in General 19
1. Product of two magnitudes 19
2. Product of several magnitudes 22
3. The various types of product structure 24
Chapter 3. Combinatorial Product 29
1. General laws of combinatorial multiplication 29
2. The combinatorial product as magnitude 36
3. Outer multiplication of magnitudes of higher order 45
4. Supplement of magnitudes with respect to a principal domain 49
5. Product with respect to a principal domain 52
6. Interchange of factors and removal of parentheses in a pure and in a
mixed product 69
7. Shadow and replacement 80
8. Elimination of the unknowns from algebraic equations by combinatorial
multiplication 85
Chapter 4. Inner Product 93
1. Fundamental laws of inner multiplication 93
2. Concept of the normal and its correlates 98
3. Laws of the inner product associated with the concept of the normal 103
4. Special theorems on the inner multiplication of two magnitudes of first
order 115
5. Introduction of the angle 117
CONTENTS
vin
Chapter 5. Applications to Geometry 123
1. Addition, subtraction, multiples and fractions
of points and displacements 123
2. Spatial domains
3. Combinatorial multiplication of points I33
4. Addition of lines and surfaces 151
5. Planimetric and stereometric multiplication 157
6. Special laws for a planimetric {and stereometric} product set to zero.
Plane {algebraic} curves. {Algebraic surfaces} 162
7. Inner multiplication in geometry 176
Part 2. The Theory of Functions 191
Chapter 1. Functions in General 193
1. Concept of a function, and reduction of several functions of several
variables to a single function of a single variable 193
2. Complete functions and their representation by open products 196
3. Algebraic multiplication 201
4. Complete functions of first degree. Quotient 207
5. Functions as extensive magnitudes 226
6. Relations considered from the standpoint of functional conjunctions 231
7. Normal units of functions, continuity of the latter 239
Chapter 2. Differential Calculus 249
1. Differential of first order * 249
2. Differential quotient of first order 252
3. Differentials of higher order 258
Chapter 3. Infinite Series 263
1. Infinite series in general 263
2. Series as functions of a numerical magnitude 265
3. Development of functions of several numerical magnitudes or a single
extensive magnitude in series 273
Chapter 4. Integral Calculus 279
1. Integration of differential expressions 279
2. Integration of differential equations when the independent variable is
a numerical magnitude 288
3. Integration of differential equations when the independent variable is
an extensive magnitude 294
Index of Technical Terms 327
Editorial Notes 33I
Grassmann s investigations into Pfaff s problem 378
Supplementary Notes 39I
Subject Index 399
|
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| author_facet | Graßmann, Hermann |
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| author_sort | Graßmann, Hermann |
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| bvnumber | BV013296552 |
| ctrlnum | (OCoLC)246994986 (DE-599)BVBBV013296552 |
| dewey-full | 512.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.5 |
| dewey-search | 512.5 |
| dewey-sort | 3512.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV013296552 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:43:18Z |
| institution | BVB |
| isbn | 0821820311 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009064442 |
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| physical | XVIII, 411 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | History of mathematics |
| series2 | History of mathematics |
| spelling | Graßmann, Hermann Verfasser aut Die Ausdehnungslehre Extension theory Hermann Grassmann Providence, RI American Math. Soc. 2000 XVIII, 411 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier History of mathematics 19 : Sources Ausdehnungslehre (DE-588)4688695-3 gnd rswk-swf Ausdehnungslehre (DE-588)4688695-3 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-3887-6 History of mathematics 19 : Sources (DE-604)BV001327576 19 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009064442&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Graßmann, Hermann Extension theory History of mathematics Ausdehnungslehre (DE-588)4688695-3 gnd |
| subject_GND | (DE-588)4688695-3 |
| title | Extension theory |
| title_alt | Die Ausdehnungslehre |
| title_auth | Extension theory |
| title_exact_search | Extension theory |
| title_full | Extension theory Hermann Grassmann |
| title_fullStr | Extension theory Hermann Grassmann |
| title_full_unstemmed | Extension theory Hermann Grassmann |
| title_short | Extension theory |
| title_sort | extension theory |
| topic | Ausdehnungslehre (DE-588)4688695-3 gnd |
| topic_facet | Ausdehnungslehre |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009064442&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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