A History of Kinematics from Zeno to Einstein: on the role of motion in the development of mathematics
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham
Springer
[2024]
|
| Schriftenreihe: | History of mechanism and machine science
Volume 46 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverzeichnis Seite 329-340. - Index |
| Beschreibung: | xv, 345 Seiten Illustrationen, Diagramme 24 cm |
| ISBN: | 9783031398711 |
Internformat
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| 100 | 1 | |a Koetsier, Teun |d 1946- |e Verfasser |0 (DE-588)139037896 |4 aut | |
| 245 | 1 | 0 | |a A History of Kinematics from Zeno to Einstein |b on the role of motion in the development of mathematics |c Teun Koetsier |
| 264 | 1 | |a Cham |b Springer |c [2024] | |
| 264 | 4 | |c ©2024 | |
| 300 | |a xv, 345 Seiten |b Illustrationen, Diagramme |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a History of mechanism and machine science |v Volume 46 | |
| 500 | |a Literaturverzeichnis Seite 329-340. - Index | ||
| 648 | 7 | |a Geschichte 490 v. Chr.-2000 |2 gnd |9 rswk-swf | |
| 650 | 0 | 7 | |a Kinematik |0 (DE-588)4030664-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematik |0 (DE-588)4037944-9 |2 gnd |9 rswk-swf |
| 653 | 0 | |a Kinematics / History | |
| 653 | 0 | |a Mathematical physics / History | |
| 653 | 0 | |a Cinématique / Histoire | |
| 653 | 0 | |a Physique mathématique / Histoire | |
| 653 | 0 | |a Kinematics | |
| 653 | 0 | |a Mathematical physics | |
| 653 | 6 | |a History | |
| 688 | 7 | |a Mathematik der Antike |0 (DE-2581)TH000007621 |2 gbd | |
| 688 | 7 | |a Bewegung |0 (DE-2581)TH000005884 |2 gbd | |
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Datensatz im Suchindex
| _version_ | 1835804153709854720 |
|---|---|
| adam_text | |
| adam_txt |
CONTENTS
1
2
3
PHILOSOPHERS,
MATHEMATICS
AND
MOTION
.
1
1.1
MOTION
DOES NOT EXIST
.
1
1.2
MATHEMATICS
AND
THE
IDEALIST TRADITION IN GREEK
PHILOSOPHY
.
5
1.3 MATHEMATICS
AND
MOTION
.
7
1.4
ARISTOTLE REFUTES ZENO
.
11
1.5
ZENO'S TRICK: MOTION IS INTERPRETED
AS A
SUPER-TASK
.
13
1.6
THE NEO-PLATONIST ONTOLOGICAL HIERARCHY
.
15
1.7
THE POSTULATES I THROUGH 3 IN NEO-PLATONISM:
PROCLUS
SOLUTION
.
17
1.8
ZEUTHEN'S THESIS
.
19
MOTION
BEYOND THE ELEMENTS
.
21
2.1 THE
EUCLIDEAN CONSTRUCTION
GAME
.
21
2.2 THE
INCOMPLETENESS
OF THE
EUCLIDEAN CONSTRUCTION GAME
.
24
2.3
ARCHYTAS
OF
TARENTE
.
26
2.4 A SOLUTION FROM PLATO'S ACADEMY
.
28
2.5 MENAECHMUS
AND
CONIC SECTIONS
.
31
2.6 A REMARKABLE APPLICATION
AND
HERON'S
SOLUTION
.
34
2.7
THE DOUBLING
OF
THE
CUBE: ERATOSTHENES'
INSTRUMENT
.
37
2.8 THE NEUSIS-CONSTRUCTION
AND
THE
CONCHOIDS
.
39
2.9
DIODES' CISSOID
.
42
GENERAL
CONSIDERATIONS
AND
KINEMATICAL
ASPECTS
OF
MOTION
.
45
3.1
PAPPUS' CLASSIFICATION
.
45
3.2
COMPOSITION
OF
DIFFERENT UNIFORM
MOTIONS: THE
QUADRATRIX
.
46
3.3
TIME-DEPENDENT KINEMATICAL ASPECTS
OF
MOTION
.
49
3.4
COMPOSITION
OF
UNIFORM MOTIONS
AND
PARADOXES
OF
MOTION IN MECHANICAL PROBLEMS
.
51
XII CONTENTS
3.5 A REMARK
ON
METHODOLOGY
AND A
THEOREM BY ARCHIMEDES
ON
UNIFORM
MOTION
.
53
3.6 ARCHIMEDES: MOTION IN
GEOMETRY
.
57
4
KINEMATICAL MODELS IN ASTRONOMY
.
63
4.1 PLATO
AND
ASTRONOMY
.
63
4.2 THE MODEL IN PLATO'S TIMAEUS
.
66
4.3 EUDOXUS' MODELS
.
69
4.4 APOLLONIUS' EPICYCLE MODEL
.
72
4.5
HIPPARCHUS' THEORY
OF
THE
MOTION
OF THE
SUN
(ABOUT 150 BCE)
.
76
4.6
PTOLEMY' CONTRIBUTIONS
.
80
4.7 PTOLEMY'S
CONTRIBUTIONS CONTINUED
.
82
4.8 ASTRONOMY IN
THE
ISLAMIC WORLD: THE TUSI-COUPLE
.
84
5 THE BIRTH
OF
INSTANTANEOUS
VELOCITY
.
87
5.1 INTRODUCTION
.
87
5.2 VELOCITY DISTRIBUTIONS IN
SPACE
AND
TIME
.
88
5.3 THE AVERAGE VELOCITY
OF A
ROTATING RADIUS
.
89
5.4 THE AVERAGE VELOCITY
OF A
ROTATING DISC
.
91
5.5 BRADWARDINE: TOWARDS
INSTANTANEOUS VELOCITY
.
92
5.6 DUMBLETON
AND
THE
MERTON
THEOREM
.
94
5.7
GIOVANNI CASALI
AND
NICOLE ORESME
.
95
5.8
ACCELERATION: EULER
AND
NEWTON'S SECOND
LAW
.
96
6 THE PARALLELOGRAM
OF
INSTANTANEOUS VELOCITIES
.
101
6.1
INTRODUCTION
.
101
6.2
GILLES PERSONNE DE ROBERVAL: THE TANGENT
AS
THE
LINE
OF
INSTANTANEOUS ADVANCE
.
102
6.3 ISAAC
NEWTON
ON
TANGENTS
.
104
6.4 D'ALEMBERT
ON
THE
PARALLELOGRAM OF INSTANTANEOUS
VELOCITIES
.
108
6.5 A
PHILOSOPHICAL ASIDE
AND
KANT
ON
THE
PARALLELOGRAM
OF
VELOCITIES
.
109
7 NAPIER, FERMAT, DESCARTES
.
113
7.1 INTRODUCTION
.
113
7.2 JOHN NAPIER'S KINEMATICAL
DEFINITION
OF
THE
LOGARITHM
AND
TORRICELLI'S `LOGARITHMICA
.
.
114
7.3 PIERRE DE FERMAT
AND
MOTION
IN HIS INTRODUCTION
TO
PLANE
AND
SOLID LOCI
.
118
7.4 RENE DESCARTES
.
121
7.5 DESCARTES' AMBITIONS
AND
HIS NEW COMPASSES
.
122
7.6 ALGEBRA COMES IN
.
126
7.7 PAPPUS' PROBLEM
.
127
7.8 AN EXAMPLE: THE TURNING
RULER
AND
MOVING CURVE
PROCEDURE
.
.
129
CONTENTS
XIII
7.9
DESCARTES' SOLUTION
OF
PAPPUS' 5-LINE PROBLEM
.
130
7.10
THE USE
OF
STRINGS
.
132
7.11
THE FINAL RESULTS
.
133
8
DE
WITT,
VAN
SCHOOTEN, NEWTON
AND
HUYGENS
.
135
8.1
FRANS
VAN
SCHOOTEN JUNIOR
.
135
8.2
JAN
DE WITT
.
136
8.3
FRANS
VAN
SCHOOTEN JUNIOR:
MECHANISMS
TO DRAW
A
PARABOLA
.
137
8.4
FRANS
VAN
SCHOOTEN JUNIOR: MECHANISMS
TO
DRAW
AN
ELLIPSE
.
139
8.5
FRANS
VAN
SCHOOTEN JUNIOR: MECHANISMS
TO
DRAW
A
HYPERBOLA
.
141
8.6
ISAAC NEWTON, MOTION
AND
THE
FUNDAMENTAL THEOREM
OF
THE
CALCULUS
.
143
8.7
THE METHOD
OF
FLUXIONS
.
146
8.8
CIRCULAR
MOTION
IN
THE
WORK
OF
HUYGENS
AND
NEWTON
.
147
8.9
HUYGENS
AND
GEAR
TRAINS
.
151
8.9.1
LEIBNIZ
AND
TRANSCENDENTAL CURVES
.
152
9
10
11
TOWARDS
THEORETICAL KINEMATICS
.
155
9.1
THE INSTANTANEOUS CENTER
OF
ROTATION, DESCARTES
AND
JOHANN BERNOULLI
.
155
9.2
THE CYCLOID
.
157
9.3
THE INFLEXION CIRCLE
.
159
9.4
DE LA HIRE'S PROOF
.
160
9.5
ELLIPTIC MOTION
.
162
9.6
EPICYCLOIDAL
GEARING
.
163
9.7
THE EULER-SAVARY FORMULA
.
166
9.8
EULER
AND
THE
EULER-SAVARY
FORMULA
.
169
9.9 THE
INSTANTANEOUS
AXIS
OF
ROTATION
IN
SPHERICAL
KINEMATICS
.
171
9.10
GIULIO MOZZI
AND
THE
INSTANTANEOUS
SCREW AXIS
.
173
THEORETICAL
KINEMATICS
AS A
SUBJECT
IN ITS OWN RIGHT
.
175
10.1 INTRODUCTION
.
175
10.2
AUGUSTIN LOUIS CAUCHY'S
1827 PAPER
.
176
10.3
MICHEL CHARLES
.
179
10.4
BOBILLIER'S THEOREM
.
183
10.5
JACQUES ANTOINE
CHARLES BRESSE
.
186
10.6
THE BALL POINTS
.
189
TOWARDS
A
NEW THEORY
OF
MACHINES
.
191
11.1
INTRODUCTION
.
191
11.2
LAZARE CARNOT
.
193
11.3
COLLISIONS
OF
HARD
BODIES
AND
GEOMETRICAL
MOVEMENTS
.
194
11.4
THE FIRST FUNDAMENTAL
EQUATION
.
195
XIV
CONTENTS
11.5 THE SECOND FUNDAMENTAL EQUATION
.
197
11.6 GASPARD MONGE
.
198
11.7 THE THEORY
OF
MACHINES IN FRANCE IN
THE
FIRST HALF
OF
THE
NINETEENTH CENTURY
.
201
11.8 CORIOLIS' VIEW
OF
MACHINES
.
203
11.9 AN EXAMPLE
OF A
CALCULATION
.
204
11.10 THE CORIOLIS FORCE
.
205
11.11 RICCIOLI
AND
GRIMALDI NOTICED
THE
CORIOLIS-EFFECT IN 1651
.
209
12 THE NEW SCIENCE IS GIVEN
A
NAME: KINEMATICS
.
211
12.1 A NEW CLASSIFICATION
OF
THE
SCIENCES
.
211
12.2 ROBERT WILLIS' PRINCIPLES
OF
MECHANISM
.
216
12.3 HENRI RESAL'S TRAITE DE CINEMATIQUE PURE
.
220
12.4 KINEMATICS
AS
THE
ESSENCE
OF
THEORETICAL MECHANICS
.
223
13 DEVELOPMENTS IN KINEMATICS
OF
MECHANISMS
.
225
13.1 SCHEMER'S PANTOGRAPH
.
225
13.2 THE YEAR
1784
.
226
13.3 SWEET SIMPLICITY
.
230
13.4 EARLY THEORETICAL
INTEREST IN
WATTS
LINKAGES
.
231
13.5 PEAUCELLIER
.
234
13.6 LIPMAN LIPKIN
.
236
14 THE WORK
OF
ENGLISH MATHEMATICIANS
ON
LINKAGES
DURING
THE
PERIOD 1869-1878
.
239
14.1 CHEBYSHEV'S ROLE
.
239
14.2 ROBERTS' WORK IN KINEMATICS BEFORE SYLVESTER'S LECTURE
.
241
14.3 KEMPE'S FIRST PAPER
.
244
14.4 SYLVESTER'S ROLE
.
245
14.5 ROBERTS' THEOREM
.
247
14.6 SOME REMARKS ABOUT FURTHER WORK
.
249
14.7 CONCLUDING REMARKS
.
251
15 FRANZ REULEAUX, KINEMATICS
AS
THE ESSENCE
OF
MECHANICAL
ENGINEERING
.
253
15.1 INTRODUCTION
.
253
15.2 FRANZ REULEAUX
.
254
15.3 THE CENTRAL IDEA: THE KINEMATICAL
CHAIN
.
254
15.4 INCOMPLETE PAIRS
AND
CHAINS
.
256
15.5
HIGHER KINEMATICAL PAIRS
.
257
15.6
EQUIVALENT MECHANISMS
.
258
15.7 EQUIVALENT ROTARY ENGINES
.
260
15.8 ANALYSIS VERSUS SYNTHESIS
.
260
CONTENTS
XV
16 LUDWIG BURMESTER, KINEMATICS
AS
PART
OF
GEOMETRY
.
265
16.1 INTRODUCTION
.
265
16.2 BURMESTER'S WORK
.
266
16.3 THE LEHRBUCH DER KINEMATIK: ITS CONTENTS
.
266
16.4 AN EXAMPLE: STEPHENSON'S MOTION
.
268
16.5 MARTIN GRUEBLER
.
271
16.6 A NOTE
ON
CHEBYSHEV
.
273
16.7 GRUEBLER
ON
CLASSIFYING KINEMATICAL
CHAINS
.
274
16.8 THE BURMESTER THEORY
AND
THE
BURMESTER POINTS
.
275
16.9 ON
THE
RECEPTION
OF
BURMESTER'S
WORK
.
279
16.10 REULEAUX' CRITICISM
OF
BURMESTER
.
281
16.11 SOME NINETEENTH
CENTURY DEVELOPMENTS ELSEWHERE
.
284
17 ALBERT EINSTEIN, THE
KINEMATICS
OF
SPECIAL RELATIVITY
.
287
17.1 INTRODUCTION
.
287
17.2 THE PRINCIPLE
OF
RELATIVITY
.
289
17.3 THE
PRINCIPLE
OF
THE
CONSTANCY
OF
LIGHT
AND THE
PARADOX
.
290
17.4 THE
WILLINGNESS
TO
GIVE UP
THE
AXIOM
OF
THE
ABSOLUTENESS
OF
TIME
.
291
17.5
CHECKING
THE
INSPIRATION
.
294
17.6 THE TECHNICAL DEVELOPMENT IN
THE
1905
PAPER
.
295
17.7 DERIVATION
OF
THE
DIFFERENTIAL EQUATION
FOR
T= R(X', Y, Z,
T)
.
297
17.8 THE DETERMINATION
OF
I; (X',
Y, Z,
T),
RL(X',
Y, Z, T) AND
Y(X',
Y, Z,
T)
.
299
17.9 TOWARDS
THE
FORMULAE
OF
THE
LORENTZ TRANSFORMATION
.
300
17.10 THE TWIN PARADOX
.
301
18 MINKOWSKI: THE UNIVERSE
IS
A
4-DIMENSIONAL MANIFOLD
.
303
18.1 EMPIRICISTS
AND
RATIONALISTS
.
303
18.2 DEVELOPMENTS
IN GEOMETRY
.
305
18.3 HILBERT'S INFLUENCE
AND
MINKOWSKI'S RATIONALISM
.
306
18.4 MINKOWSKI
AND
RELATIVITY
.
308
18.5 A 4-DIMENSIONAL
INTERPRETATION
OF
NEWTONIAN MECHANICS
.
309
18.6 SPECIAL RELATIVITY
DEDUCED
A
PRIORI
.
312
18.7 THE
TWIN PARADOX
.
316
19
KINEMATICS
IN
THE
20TH CENTURY
.
319
19.1
THE TWENTIETH CENTURY
.
319
19.2 INSTITUTIONALIZATION
.
322
19.3 TWENTIETH CENTURY MATHEMATICIANS
WORKING
IN KINEMATICS
.
323
.
BIBLIOGRAPHY
329
INDEX
.
341 |
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| any_adam_object_boolean | 1 |
| author | Koetsier, Teun 1946- |
| author_GND | (DE-588)139037896 |
| author_facet | Koetsier, Teun 1946- |
| author_role | aut |
| author_sort | Koetsier, Teun 1946- |
| author_variant | t k tk |
| building | Verbundindex |
| bvnumber | BV049390240 |
| ctrlnum | (OCoLC)1418691979 (DE-599)BVBBV049390240 |
| era | Geschichte 490 v. Chr.-2000 gnd |
| era_facet | Geschichte 490 v. Chr.-2000 |
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| id | DE-604.BV049390240 |
| illustrated | Illustrated |
| index_date | 2024-07-03T23:01:07Z |
| indexdate | 2025-06-24T10:01:11Z |
| institution | BVB |
| isbn | 9783031398711 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-034717684 |
| oclc_num | 1418691979 |
| open_access_boolean | |
| owner | DE-210 DE-11 |
| owner_facet | DE-210 DE-11 |
| physical | xv, 345 Seiten Illustrationen, Diagramme 24 cm |
| psigel | gbd_4_2402 |
| publishDate | 2024 |
| publishDateSearch | 2024 |
| publishDateSort | 2024 |
| publisher | Springer |
| record_format | marc |
| series | History of mechanism and machine science |
| series2 | History of mechanism and machine science |
| spelling | Koetsier, Teun 1946- Verfasser (DE-588)139037896 aut A History of Kinematics from Zeno to Einstein on the role of motion in the development of mathematics Teun Koetsier Cham Springer [2024] ©2024 xv, 345 Seiten Illustrationen, Diagramme 24 cm txt rdacontent n rdamedia nc rdacarrier History of mechanism and machine science Volume 46 Literaturverzeichnis Seite 329-340. - Index Geschichte 490 v. Chr.-2000 gnd rswk-swf Kinematik (DE-588)4030664-1 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Kinematics / History Mathematical physics / History Cinématique / Histoire Physique mathématique / Histoire Kinematics Mathematical physics History Mathematik der Antike (DE-2581)TH000007621 gbd Bewegung (DE-2581)TH000005884 gbd Kinematik (DE-588)4030664-1 s Mathematik (DE-588)4037944-9 s Geschichte 490 v. Chr.-2000 z DE-604 Erscheint auch als Online-Ausgabe 978-3-031-39872-8 History of mechanism and machine science Volume 46 (DE-604)BV022469341 46 Digitalisierung Deutsches Museum https://bvbr.bib-bvb.de:443/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034717684&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Koetsier, Teun 1946- A History of Kinematics from Zeno to Einstein on the role of motion in the development of mathematics History of mechanism and machine science Kinematik (DE-588)4030664-1 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4030664-1 (DE-588)4037944-9 |
| title | A History of Kinematics from Zeno to Einstein on the role of motion in the development of mathematics |
| title_auth | A History of Kinematics from Zeno to Einstein on the role of motion in the development of mathematics |
| title_exact_search | A History of Kinematics from Zeno to Einstein on the role of motion in the development of mathematics |
| title_exact_search_txtP | A History of Kinematics from Zeno to Einstein on the role of motion in the development of mathematics |
| title_full | A History of Kinematics from Zeno to Einstein on the role of motion in the development of mathematics Teun Koetsier |
| title_fullStr | A History of Kinematics from Zeno to Einstein on the role of motion in the development of mathematics Teun Koetsier |
| title_full_unstemmed | A History of Kinematics from Zeno to Einstein on the role of motion in the development of mathematics Teun Koetsier |
| title_short | A History of Kinematics from Zeno to Einstein |
| title_sort | a history of kinematics from zeno to einstein on the role of motion in the development of mathematics |
| title_sub | on the role of motion in the development of mathematics |
| topic | Kinematik (DE-588)4030664-1 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Kinematik Mathematik |
| url | https://bvbr.bib-bvb.de:443/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034717684&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV022469341 |
| work_keys_str_mv | AT koetsierteun ahistoryofkinematicsfromzenotoeinsteinontheroleofmotioninthedevelopmentofmathematics |