Aspects of the Astrolabe: 'architectonica ratio' in tenth- and eleventh-century Europe
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Stuttgart
Steiner
2008
|
| Series: | Sudhoffs Archiv
Beihefte ; 57 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Zugl.: Diss. |
| Physical Description: | 270 S. Ill., graph. Darst. 24 cm |
| ISBN: | 9783515091299 |
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| adam_text | CONTENTS
List of figures and tables
................................................................................... 12
Acknowledgements
........................................................................................... 14
1
Introduction
................................................................................................ 16
1.1
The astrolabe and medieval mathematical thought
............................. 16
1.2
The astrolabe and its aspects
............................................................... 17
1.3
The early history of the astrolabe
........................................................ 19
1.4
Latin scholars and the astrolabe
........................................................... 20
1.5
The two main theses of this study
....................................................... 21
1.6
Strategies of knowledge transfer: positive and negative definitions
... 22
1.7
Images of knowledge as premise and subj ect of research
................... 23
1.8
Plan of the work
.................................................................................. 24
2
Mathematical and practical aspects of the astrolabe
.................................. 27
2.1
Some considerations on mathematical thinking
.................................. 27
2.1.1
Mathematical thinking as a set of prototypes
......................... 27
2.1.2
Mathematics across cultures and time
.................................... 27
2.1.3
Mathematical thinking and mathematical
communication
....................................................................... 28
2.1.4
Geometrical imagination
........................................................ 29
2.1.5
Mathematics, the
minďs
eye... and hands
.............................. 30
2.1.6
Images of knowledge and mathematical truth: proof vs.
evidence
.................................................................................. 32
2.1.7
Geometrical imagination and tacit knowing
........................ 33
2.2
The mathematical aspects of the astrolabe
.......................................... 34
2.2.1
The shadow triangle
............................................................... 34
2.2.2
The homocentric-spheres-model
............................................ 35
2.2.2.1
The celestial and terrestrial spheres
........................................ 35
2.2.2.2
Geometrical imagination and natural philosophy in the
homocentric-spheres-model
................................................... 36
2.2.2.3
From the solid spheres to the astrolabe
.................................. 37
2.2.2.4
The poles and equator
............................................................. 37
2.2.2.5
The horizon and the altitude circles
.......................................
З8
2.2.2.6
The sun and the zodiac
........................................................... 39
2.2.2.7
Zodiac signs and constellations
.............................................. 40
2.2.2.8
Seasonal variations in the length of daylight and in the
night sky
................................................................................. 4]
2.2.2.9
The seven climates
................................................................. 41
2.2.3
The flat sphere
........................................................................ 43
Contents
2.2.3.1
Theses to be demonstrated by means of my description
of the flat sphere s structure
................................................... 43
2.2.3.2
The general method for flattening the sphere
......................... 44
2.2.3.3
How to draw the flat sphere: the equator and
the north pole
.......................................................................... 44
2.2.3.4
The tropics on the flat sphere
................................................. 45
2.2.3.5
Ninety-degrees-tilting as a key trick in drawing
the flat sphere
......................................................................... 45
2.2.3.6
The circle-into-circle property
................................................ 48
2.2.3.7
Consequences of the circle-into-circle property
..................... 48
2.2.3.8
The zodiac and the horizons
................................................... 49
2.2.3.9
Conclusions: the basic three-step-procedure for
projecting circles onto the flat sphere
..................................... 51
2.3
The practical aspects of the astrolabe
.................................................. 53
2.3.1
The planispheric astrolabe
...................................................... 53
2.3.2
The back of the planispheric astrolabe
................................... 54
2.3.2.1
The alidade as a sighting tool
................................................. 54
2.3.2.2
The shadow square
................................................................. 54
2.3.2.3
The scale of solar longitudes
.................................................. 56
2.3.3
The front of the planispheric astrolabe
................................... 57
2.3.3.1
The disc of the celestial sphere and the disc of the
local horizon
........................................................................... 57
2.3.3.2
The collection of horizon plates
............................................. 57
2.3.3.3
Possible uses of the front of the planispheric astrolabe
.......... 59
2.3.3.4
The hour lines and monastic timekeeping
.............................. 60
2.3.4
Could astrolabe artefacts actually perform the functions
they were built for?
................................................................. 62
Sources and results of previous research
.................................................... 63
3.1
Introduction: historical and cultural context
........................................ 63
3.1.1
The earliest evidence on the method of the flat sphere
and on the astrolabe
................................................................ 63
3.1.2
The astrolabe in the Arabic-Islamic, Byzantine and
Jewish cultures
....................................................................... 64
3.1.3
The network of high medieval astronomical and
mathematical studies
.............................................................. 66
3.1.4
al-Andalus, its school of astronomy of the tenth and
eleventh centuries
................................................................... 67
3.1.5
Prominent figures in the diffusion of astrolabe
knowledge in Latin Europe
.................................................... 69
3.1.6
The interplay of modes of communication in the Latin
Middle Ages
........................................................................... 70
3.1.7
The rise of literacy in eleventh-and twelfth-century
Europe
.................................................................................... 72
Contents 7
3.2 Material
and pictorial sources: catalogues, analyses and open
questions
.............................................................................................. 73
3.2.1
Arabic-Islamic and European astrolabe artefacts
.................. 73
3.2.2
The Frankfurt catalogue of medieval astronomical
instruments and previous cataloguing projects
...................... 74
3.2.3
Difficulties in dating European astrolabe artefacts
................ 75
3.2.4
European astrolabe artefacts and astrolabe drawings
used as evidence in this study
................................................. 75
3.2.5
The earliest European astrolabe
(#3042)................................ 76
3.2.6
Early
Andalusi
astrolabe artefacts with additional
non-
Arabic engravings as evidence of cultural
exchange
................................................................................. 77
3.2.7
Additional pictorial sources
.................................................... 79
3.3
Textual sources: research results and open questions
......................... 79
3.3.1
Extant astrolabe manuscripts
.................................................. 79
3.3.2
Astrolabe manuscripts as a source for this study
................... 80
3.3.3
Additional textual evidence
.................................................... 80
3.3.4
Preliminary remarks on earlier and later Latin texts
on the astrolabe
....................................................................... 81
3.3.5
The reconstruction of eleventh-century astrolabe texts
.......... 82
3.3.6
Problems in the philological reconstruction of the
earliest Latin astrolabe texts: the example of
J
..................... 83
3.3.6.1 Nicolaus
Bubnové
edition of
de utilitatibus
astrolabii (J)
.......................................................................... 83
3.3.6.2
André
Van
de
Vyveťs
analysis of the earliest Latin
astrolabe manuscripts
............................................................. 85
3.3.6.3
Millas
Vallicrosa s studies on ms. Ripoll
225 ....................... 85
3.3.6.4
Millas
Vallicrosa s edition of early astrolabe texts
................ 86
3.3.6.5
Werner
Bergmaruťs
thesis of the two-stages
composition of
J
..................................................................... 87
3.3.7
The sources of h: the problem of the lost original?
................ 88
3.3.8
The problem of relating the earliest Latin astrolabe
texts to Arabic sources
........................................................... 89
3.3.9
Paul
Kunitzsclťs
analysis of the relationship of the
text J to Arabic sources
......................................................... 90
3.3.10
Conclusions: the theory of written transmission of
astrolabe knowledge and its problems
.................................... 91
3.4
Medieval mathematical texts and readability: the example of the
Geometria
incerti
auctoris
(GIÀ)......................................................
92
3.4.1
Catherine Jacquemard s analysis of the GIA and its
relevance for the present study
............................................... 92
3.4.2
The GIA as product of progressive rewriting
........................ 93
3.4.3
Were the single stages of rewriting of the GIA III an
individual or a collective enterprise?
...................................... 94
Contents
3.4.4
The question of readability and its possible solutions:
the literary and the recipe style
............................................ 95
3.4.5
Conclusions: different criteria for evaluating
eleventh-century astrolabe texts
............................................. 97
Non-written and non-verbal modes of communication in the
diffusion of astrolabe knowledge
............................................................... 99
4.1
Memory, notes and geometrical patterns in high medieval
mathematical arts
................................................................................. 99
4.1.1
The main thesis of the present chapter: astrolabe
manuscripts as written traces of a primarily
non-written transmission
........................................................ 99
4.1.2
The medieval craft of memory
............................................... 100
4.1.3
The embodiment of mnemonic patterns in images and
artefacts
.................................................................................. 101
4.1.4
Memory and medieval learning
.............................................. 103
4.1.5
Modes of communication in the medieval
mathematical arts
.................................................................... 104
4.1.6
Thinking numbers as geometrical patterns
............................. 105
4.1.7
Conclusions: quadrivium, memory and manual crafts
........... 108
4.2
Memory and the astrolabe
................................................................... 109
4.2.1
Memory in astrolabe-related texts
.......................................... 109
4.2.2
Note-taking as a complement to memory
............................... 111
4.2.3
Fulbert
of
Chartres
mnemonic verses and the letters
of Radulf of
Liège
and Regimbold of Cologne
...................... 112
4.3
Drawings as a mode of transmission of astronomical
knowledge
............................................................................................ 113
4.3.1
Astronomy in number and/or in measure
............................... 113
4.3.2
Diagrams as an independent mode of communication
........... 114
4.3.3 Stereographic
projection in ninth-century astronomic
diagrams
................................................................................. 115
4.3.4
The astronomical diagrams of Abbo of Fleury and
Byrtferth of Ramsey, the astronomical devices of
Gerbert of Aurillac
................................................................. 117
4.4
Drawings and knowledge transmission: the construction
of tropics and zodiac
............................................................................ 118
4.4.1
The sources: texts hi, h2 and h3 and drawings dl and d2
.... 118
4.4.2
Relationship between the strictly verbal contents of
hi, h2 and h3
.......................................................................... 119
4.4.3
The construction of tropics and zodiac in the text h2
and in the drawing dl
.......................................................... 120
4.4.4
The construction of the tropics in h3: a product of
notetaking?
.............................................................................. 124
4.4.5
Comparison of the manuscript tradition of h2 and h3
........... 126
4.4.6
The construction of tropics and zodiac in hi
......................... 126
Contents 9
4.4.7
Conclusions:
transfer
of astrolabe knowledge by means
of memory, drawings and notes
............................................. 128
4.5
The relationship between Ptolemy s Planisphaerium
and early Latin astrolabe texts and drawings
....................................... 129
4.5.1
Greek, Latin and Arabic version of the Planisphaerium?
...... 129
4.5.2
Relevance of the Planisphaerium for this study
.................. 130
4.5.3
What Ptolemy did not say in the Planisphaerium
................ 131
4.5.4
The contents of the Planisphaerium
..................................... 131
4.5.5
The construction of tropics and zodiac in the
Planisphaerium
.................................................................... 132
4.5.6
The coincidence between dl and the drawing illustrating
chapter
1
of the Planisphaerium
.......................................... 134
4.6
The division of the astrolabe s zodiac in eleventh-century
Latin Europe
........................................................................................ 137
4.6.1
The measure of the zodiac
...................................................... 139
4.6.2
The division of the zodiac in the text dzl
.............................. 140
4.6.3
The division of the zodiac in the texts dz2, dz3 and dz4
....... 143
4.6.4
The division of the zodiac in the text Iubet rex
Ptolomeus (pt)
....................................................................... 144
4.6.5
The division of the zodiac in the text hi
................................ 146
4.6.6
The language of proportions in pt and hi
.............................. 147
4.6.7
The division of the zodiac in the treatises of Ascelin of
Augsburg (a) and Herman of Reichenau (h)
.......................... 148
4.6.8
The division of the zodiac in eleventh-century drawings
of astrolabe parts
................................................................... 149
4.6.9
Conclusions: the problem of dividing the astrolabe s
zodiac as a focus of natural philosophical discussion
in high medieval astrolabe studies
.......................................... 153
4.6.10
The zodiac circle on the astrolabe
#3042............................... 154
4.6.11
The division of the zodiac on the astrolabe
#3042................. 155
The philosophical aspects of the astrolabe
................................................. 158
5.1
Why did medieval Latin scholars study the astrolabe?
....................... 158
5.1.1
The astrolabe as a new mathematical and philosophical
instrument of the mathematical arts
....................................... 158
5.1.2
The main thesis of the present chapter: the astrolabe as
architectonica ratio
............................................................... 160
5.1.3
Was there actually an interplay between abstract and
material side in astrolabe studies?
.......................................... 162
5.1.4
Evidence on medieval sundials
.............................................. 164
5.1.5
Evidence on gnomons and sundials as devices for
astronomical observations
...................................................... 165
5.1.6
The analysis of ms. BnF
lat.
7412
as evidence on
the motivation of Latin astrolabe studies
............................... 166
5.2
The astrolabe as
architectonica ratio of the
machina
mundi ..........
166
10 Contents
5.2.1
The first chapter of the text J: the
machina
mundi
and its architectonica ratio
................................................... 166
5.2.2
The Prologue
Ad intimas
(pa) and its possible relation
to Vitravius
............................................................................ 168
5.2.3
The architectonica ratio of the astrolabe as a
forbidden art
........................................................................... 173
5.2.4
Chapters
J
2-7:
determining temporal hours with the
astrolabe
................................................................................. 174
5.2.5
Was the gesture of raising the astrolabe a recipe or a
symbolic act?
.......................................................................... 175
5.3
The astrolabe and the measure of time and space
............................... 176
5.3.1
The measure of time as a philosophical problem
................... 176
5.3.2
Chapter
J
8:
the astrolabe and the parts of the hours
............. 177
5.3.3
The assimilation of temporal and equinoctial hours
.............. 178
5.3.4
The order of the sky and its projection on earth:
the seven climates
................................................................... 180
5.3.5
The three-dimensional sphere and the measure of
time (J a)
............................................................................... 181
5.3.6
Abstract patterns and their embodiment in astronomical
devices and surveying methods
.............................................. 183
5.3.7
The sinker and the astrolabe (dpp)
......................................... 184
5.3.8
The traces of the Planisphaerium in ms. BnF
lat.
7412....... 187
5.4
Euclid s and Ptolemy s geometric constructions
................................. 188
5.4.1
The drawings in ms. BnF
lat.
7412
and the knowledge
they conveyed
......................................................................... 188
5.4.2
Drawings from Euclid s Elements (f.l4v)
.......................... 188
5.4.3
Drawing from the Planisphaerium (f.l4v)
........................... 189
5.4.4
Drawings of a sphere with sighting tubes and of
a polar sighting tube (f.l5r)
................................................... 192
5.4.5
The universal horary quadrant: text and drawing
(f.lórandf.
Ιδν-^Γ)
............................................................. 195
5.5
The equatorial sundial and the
géométrisation
of the flow of time
..... 197
5.5.1
The equatorial sundial (f. 19r)
................................................ 197
5.5.2
Material evidence for high medieval equatorial sundials
........ 200
5.5.3
Written evidence of high medieval equatorial sundials
.......... 201
5.6
The astrolabe drawings in ms. BnF
lat.
7412 (#4024)......................... 203
5.6.1
Overview on the astrolabe drawings
#4024........................... 203
5.6.2
The astrolabe drawings
#4024
and other early European
astrolabe artefacts
................................................................... 206
5.6.3
Abraham and his astrolabe in BnF
lat.
12117 f. 106r............. 210
6
Summary and outlook: the aspects of the astrolabe in
twelfth-century Europe
........................................................................... 214
6.1
The aspects of the astrolabe and their interplay
................................... 214
6.2
Twelfth-century astrolabe treatises and their fortunes
......................... 216
Contents 11
6.3
The astronomer with astrolabe in Oxf.
Bodl.
614.
f.35r
...................... 218
6.4
The astrolabe as a symbol
.................................................................... 219
6.5
Working knowledge in astrolabe lore
.................................................. 221
6.6
Working knowledge, forbidden knowledge and the written word
....... 222
6.7
The astrolabe as a model to be imitated and the development
of astronomical clocks
......................................................................... 223
7
Appendix A: Eleventh- and twelfth-century manuscripts containing
astrolabe texts and/or drawings
.................................................................. 226
8
Appendix B: Thirteenth-, fourteenth- and fifteenth-century
manuscripts containing eleventh- and twelfth-century
astrolabe texts
............................................................................................. 233
9
Appendix C: Abbreviations used in this work to indicate
eleventh-century astrolabe-related texts and drawings
.............................. 238
10
Appendix D: Most diffused twelfth-century astrolabe treatises
................. 240
11
Appendix E: Contents of the manuscript Paris, BnF
lat.
7412,
f.lr^vülthc.)....................................................................................... 242
12
Appendix
F:
Astrolabe artefacts and astrolabe drawings discussed
in this study
................................................................................................ 244
13
Bibliography
............................................................................................... 246
Name index
....................................................................................................... 267
Subject index
.....................................................................................................
Tgg
|
| adam_txt |
CONTENTS
List of figures and tables
. 12
Acknowledgements
. 14
1
Introduction
. 16
1.1
The astrolabe and medieval mathematical thought
. 16
1.2
The astrolabe and its aspects
. 17
1.3
The early history of the astrolabe
. 19
1.4
Latin scholars and the astrolabe
. 20
1.5
The two main theses of this study
. 21
1.6
Strategies of knowledge transfer: positive and negative definitions
. 22
1.7
Images of knowledge as premise and subj ect of research
. 23
1.8
Plan of the work
. 24
2
Mathematical and practical aspects of the astrolabe
. 27
2.1
Some considerations on mathematical thinking
. 27
2.1.1
Mathematical thinking as a set of prototypes
. 27
2.1.2
Mathematics across cultures and time
. 27
2.1.3
Mathematical thinking and mathematical
communication
. 28
2.1.4
Geometrical imagination
. 29
2.1.5
Mathematics, the
minďs
eye. and hands
. 30
2.1.6
Images of knowledge and mathematical truth: proof vs.
evidence
. 32
2.1.7
Geometrical imagination and "tacit knowing'
. 33
2.2
The mathematical aspects of the astrolabe
. 34
2.2.1
The shadow triangle
. 34
2.2.2
The homocentric-spheres-model
. 35
2.2.2.1
The celestial and terrestrial spheres
. 35
2.2.2.2
Geometrical imagination and natural philosophy in the
homocentric-spheres-model
. 36
2.2.2.3
From the solid spheres to the astrolabe
. 37
2.2.2.4
The poles and equator
. 37
2.2.2.5
The horizon and the altitude circles
.
З8
2.2.2.6
The sun and the zodiac
. 39
2.2.2.7
Zodiac signs and constellations
. 40
2.2.2.8
Seasonal variations in the length of daylight and in the
night sky
. 4]
2.2.2.9
The seven climates
. 41
2.2.3
The flat sphere
. 43
Contents
2.2.3.1
Theses to be demonstrated by means of my description
of the flat sphere's structure
. 43
2.2.3.2
The general method for flattening the sphere
. 44
2.2.3.3
How to draw the flat sphere: the equator and
the north pole
. 44
2.2.3.4
The tropics on the flat sphere
. 45
2.2.3.5
Ninety-degrees-tilting as a key trick in drawing
the flat sphere
. 45
2.2.3.6
The circle-into-circle property
. 48
2.2.3.7
Consequences of the circle-into-circle property
. 48
2.2.3.8
The zodiac and the horizons
. 49
2.2.3.9
Conclusions: the basic three-step-procedure for
projecting circles onto the flat sphere
. 51
2.3
The practical aspects of the astrolabe
. 53
2.3.1
The planispheric astrolabe
. 53
2.3.2
The back of the planispheric astrolabe
. 54
2.3.2.1
The alidade as a sighting tool
. 54
2.3.2.2
The shadow square
. 54
2.3.2.3
The scale of solar longitudes
. 56
2.3.3
The front of the planispheric astrolabe
. 57
2.3.3.1
The disc of the celestial sphere and the disc of the
local horizon
. 57
2.3.3.2
The collection of horizon plates
. 57
2.3.3.3
Possible uses of the front of the planispheric astrolabe
. 59
2.3.3.4
The hour lines and monastic timekeeping
. 60
2.3.4
Could astrolabe artefacts actually perform the functions
they were built for?
. 62
Sources and results of previous research
. 63
3.1
Introduction: historical and cultural context
. 63
3.1.1
The earliest evidence on the method of the flat sphere
and on the astrolabe
. 63
3.1.2
The astrolabe in the Arabic-Islamic, Byzantine and
Jewish cultures
. 64
3.1.3
The network of high medieval astronomical and
mathematical studies
. 66
3.1.4
al-Andalus, its school of astronomy of the tenth and
eleventh centuries
. 67
3.1.5
Prominent figures in the diffusion of astrolabe
knowledge in Latin Europe
. 69
3.1.6
The interplay of modes of communication in the Latin
Middle Ages
. 70
3.1.7
The "rise of literacy' in eleventh-and twelfth-century
Europe
. 72
Contents 7
3.2 Material
and pictorial sources: catalogues, analyses and open
questions
. 73
3.2.1
Arabic-Islamic and European astrolabe artefacts
. 73
3.2.2
The Frankfurt catalogue of medieval astronomical
instruments and previous cataloguing projects
. 74
3.2.3
Difficulties in dating European astrolabe artefacts
. 75
3.2.4
European astrolabe artefacts and astrolabe drawings
used as evidence in this study
. 75
3.2.5
The earliest European astrolabe
(#3042). 76
3.2.6
Early
Andalusi
astrolabe artefacts with additional
non-
Arabic engravings as evidence of cultural
exchange
. 77
3.2.7
Additional pictorial sources
. 79
3.3
Textual sources: research results and open questions
. 79
3.3.1
Extant astrolabe manuscripts
. 79
3.3.2
Astrolabe manuscripts as a source for this study
. 80
3.3.3
Additional textual evidence
. 80
3.3.4
Preliminary remarks on earlier and later Latin texts
on the astrolabe
. 81
3.3.5
The reconstruction of eleventh-century astrolabe texts
. 82
3.3.6
Problems in the philological reconstruction of the
earliest Latin astrolabe texts: the example of
J
. 83
3.3.6.1 Nicolaus
Bubnové
edition of
'de utilitatibus
astrolabii' (J)
. 83
3.3.6.2
André
Van
de
Vyveťs
analysis of the earliest Latin
astrolabe manuscripts
. 85
3.3.6.3
Millas
Vallicrosa's studies on ms. Ripoll
225 . 85
3.3.6.4
Millas
Vallicrosa's edition of early astrolabe texts
. 86
3.3.6.5
Werner
Bergmaruťs
thesis of the two-stages
composition of
J
. 87
3.3.7
The sources of h: the problem of the lost original?
. 88
3.3.8
The problem of relating the earliest Latin astrolabe
texts to Arabic sources
. 89
3.3.9
Paul
Kunitzsclťs
analysis of the relationship of the
text J' to Arabic sources
. 90
3.3.10
Conclusions: the theory of written transmission of
astrolabe knowledge and its problems
. 91
3.4
Medieval mathematical texts and readability: the example of the
"Geometria
incerti
auctoris"
(GIÀ).
92
3.4.1
Catherine Jacquemard's analysis of the GIA and its
relevance for the present study
. 92
3.4.2
The GIA as product of progressive rewriting
. 93
3.4.3
Were the single stages of rewriting of the GIA III an
individual or a collective enterprise?
. 94
Contents
3.4.4
The question of readability and its possible solutions:
the literary and the 'recipe' style
. 95
3.4.5
Conclusions: different criteria for evaluating
eleventh-century astrolabe texts
. 97
Non-written and non-verbal modes of communication in the
diffusion of astrolabe knowledge
. 99
4.1
Memory, notes and geometrical patterns in high medieval
mathematical arts
. 99
4.1.1
The main thesis of the present chapter: astrolabe
manuscripts as written traces of a primarily
non-written transmission
. 99
4.1.2
The medieval craft of memory
. 100
4.1.3
The embodiment of mnemonic patterns in images and
artefacts
. 101
4.1.4
Memory and medieval learning
. 103
4.1.5
Modes of communication in the medieval
mathematical arts
. 104
4.1.6
Thinking numbers as geometrical patterns
. 105
4.1.7
Conclusions: quadrivium, memory and manual crafts
. 108
4.2
Memory and the astrolabe
. 109
4.2.1
Memory in astrolabe-related texts
. 109
4.2.2
Note-taking as a complement to memory
. 111
4.2.3
Fulbert
of
Chartres'
mnemonic verses and the letters
of Radulf of
Liège
and Regimbold of Cologne
. 112
4.3
Drawings as a mode of transmission of astronomical
knowledge
. 113
4.3.1
Astronomy in number and/or in measure
. 113
4.3.2
Diagrams as an independent mode of communication
. 114
4.3.3 Stereographic
projection in ninth-century astronomic
diagrams
. 115
4.3.4
The astronomical diagrams of Abbo of Fleury and
Byrtferth of Ramsey, the astronomical devices of
Gerbert of Aurillac
. 117
4.4
Drawings and knowledge transmission: the construction
of tropics and zodiac
. 118
4.4.1
The sources: texts hi, h2 and h3 and drawings dl and d2
. 118
4.4.2
Relationship between the strictly verbal contents of
hi, h2 and h3
. 119
4.4.3
The construction of tropics and zodiac in the text h2
and in the drawing dl
. 120
4.4.4
The construction of the tropics in h3: a product of
notetaking?
. 124
4.4.5
Comparison of the manuscript tradition of h2 and h3
. 126
4.4.6
The construction of tropics and zodiac in hi
. 126
Contents 9
4.4.7
Conclusions:
transfer
of astrolabe knowledge by means
of memory, drawings and notes
. 128
4.5
The relationship between Ptolemy's 'Planisphaerium'
and early Latin astrolabe texts and drawings
. 129
4.5.1
Greek, Latin and Arabic version of the "Planisphaerium?
. 129
4.5.2
Relevance of the "Planisphaerium' for this study
. 130
4.5.3
What Ptolemy did not say in the'Planisphaerium'
. 131
4.5.4
The contents of the 'Planisphaerium'
. 131
4.5.5
The construction of tropics and zodiac in the
'Planisphaerium'
. 132
4.5.6
The coincidence between dl and the drawing illustrating
chapter
1
of the 'Planisphaerium'
. 134
4.6
The division of the astrolabe's zodiac in eleventh-century
Latin Europe
. 137
4.6.1
The measure of the zodiac
. 139
4.6.2
The division of the zodiac in the text dzl
. 140
4.6.3
The division of the zodiac in the texts dz2, dz3 and dz4
. 143
4.6.4
The division of the zodiac in the text 'Iubet rex
Ptolomeus' (pt)
. 144
4.6.5
The division of the zodiac in the text hi
. 146
4.6.6
The language of proportions in pt and hi
. 147
4.6.7
The division of the zodiac in the treatises of Ascelin of
Augsburg (a) and Herman of Reichenau (h)
. 148
4.6.8
The division of the zodiac in eleventh-century drawings
of astrolabe parts
. 149
4.6.9
Conclusions: the problem of dividing the astrolabe's
zodiac as a focus of natural philosophical discussion
in high medieval astrolabe studies
. 153
4.6.10
The zodiac circle on the astrolabe
#3042. 154
4.6.11
The division of the zodiac on the astrolabe
#3042. 155
The philosophical aspects of the astrolabe
. 158
5.1
Why did medieval Latin scholars study the astrolabe?
. 158
5.1.1
The astrolabe as a new mathematical and philosophical
instrument of the mathematical arts
. 158
5.1.2
The main thesis of the present chapter: the astrolabe as
"architectonica ratio'
. 160
5.1.3
Was there actually an interplay between abstract and
material side in astrolabe studies?
. 162
5.1.4
Evidence on medieval sundials
. 164
5.1.5
Evidence on gnomons and sundials as devices for
astronomical observations
. 165
5.1.6
The analysis of ms. BnF
lat.
7412
as evidence on
the motivation of Latin astrolabe studies
. 166
5.2
The astrolabe as
'
architectonica ratio' of the
"machina
mundi'.
166
10 Contents
5.2.1
The first chapter of the text J: the
'machina
mundi'
and its 'architectonica ratio'
. 166
5.2.2
The Prologue
'Ad intimas'
(pa) and its possible relation
to Vitravius
. 168
5.2.3
The 'architectonica ratio' of the astrolabe as a
forbidden art
. 173
5.2.4
Chapters
J
2-7:
determining temporal hours with the
astrolabe
. 174
5.2.5
Was the gesture of raising the astrolabe a recipe or a
symbolic act?
. 175
5.3
The astrolabe and the measure of time and space
. 176
5.3.1
The measure of time as a philosophical problem
. 176
5.3.2
Chapter
J
8:
the astrolabe and the parts of the hours
. 177
5.3.3
The assimilation of temporal and equinoctial hours
. 178
5.3.4
The order of the sky and its projection on earth:
the seven climates
. 180
5.3.5
The three-dimensional sphere and the measure of
time (J'a)
. 181
5.3.6
Abstract patterns and their embodiment in astronomical
devices and surveying methods
. 183
5.3.7
The sinker and the astrolabe (dpp)
. 184
5.3.8
The traces of the 'Planisphaerium' in ms. BnF
lat.
7412. 187
5.4
Euclid's and Ptolemy's geometric constructions
. 188
5.4.1
The drawings in ms. BnF
lat.
7412
and the knowledge
they conveyed
. 188
5.4.2
Drawings from Euclid's 'Elements' (f.l4v)
. 188
5.4.3
Drawing from the 'Planisphaerium' (f.l4v)
. 189
5.4.4
Drawings of a sphere with sighting tubes and of
a polar sighting tube (f.l5r)
. 192
5.4.5
The universal horary quadrant: text and drawing
(f.lórandf.
Ιδν-^Γ)
. 195
5.5
The equatorial sundial and the
géométrisation
of the flow of time
. 197
5.5.1
The equatorial sundial (f. 19r)
. 197
5.5.2
Material evidence for high medieval equatorial sundials
. 200
5.5.3
Written evidence of high medieval equatorial sundials
. 201
5.6
The astrolabe drawings in ms. BnF
lat.
7412 (#4024). 203
5.6.1
Overview on the astrolabe drawings
#4024. 203
5.6.2
The astrolabe drawings
#4024
and other early European
astrolabe artefacts
. 206
5.6.3
Abraham and his astrolabe in BnF
lat.
12117 f. 106r. 210
6
Summary and outlook: the aspects of the astrolabe in
twelfth-century Europe
. 214
6.1
The aspects of the astrolabe and their interplay
. 214
6.2
Twelfth-century astrolabe treatises and their fortunes
. 216
Contents 11
6.3
The astronomer with astrolabe in Oxf.
Bodl.
614.
f.35r
. 218
6.4
The astrolabe as a symbol
. 219
6.5
Working knowledge in astrolabe lore
. 221
6.6
Working knowledge, forbidden knowledge and the written word
. 222
6.7
The astrolabe as a model to be imitated and the development
of astronomical clocks
. 223
7
Appendix A: Eleventh- and twelfth-century manuscripts containing
astrolabe texts and/or drawings
. 226
8
Appendix B: Thirteenth-, fourteenth- and fifteenth-century
manuscripts containing eleventh- and twelfth-century
astrolabe texts
. 233
9
Appendix C: Abbreviations used in this work to indicate
eleventh-century astrolabe-related texts and drawings
. 238
10
Appendix D: Most diffused twelfth-century astrolabe treatises
. 240
11
Appendix E: Contents of the manuscript Paris, BnF
lat.
7412,
f.lr^vülthc.). 242
12
Appendix
F:
Astrolabe artefacts and astrolabe drawings discussed
in this study
. 244
13
Bibliography
. 246
Name index
. 267
Subject index
.
Tgg |
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| callnumber-first | Q - Science |
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| era | Geschichte 900-1100 gnd |
| era_facet | Geschichte 900-1100 |
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| spelling | Borrelli, Arianna Verfasser aut Aspects of the Astrolabe 'architectonica ratio' in tenth- and eleventh-century Europe Arianna Borrelli Stuttgart Steiner 2008 270 S. Ill., graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Sudhoffs Archiv : Beihefte 57 Zugl.: Diss. Geschichte 900-1100 gnd rswk-swf Astrolabes - 10e siècle - Europe ram Astronomie - 10e siècle - Europe ram Geschichte Astrolabes History Astronomy History Astronomy history Europe History, Medieval Europe Astrolabium (DE-588)4003304-1 gnd rswk-swf Europa (DE-588)4113937-9 Hochschulschrift gnd-content Astrolabium (DE-588)4003304-1 s Geschichte 900-1100 z DE-604 1\p DE-604 Sudhoffs Archiv Beihefte ; 57 (DE-604)BV023551700 57 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016424718&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Borrelli, Arianna Aspects of the Astrolabe 'architectonica ratio' in tenth- and eleventh-century Europe Sudhoffs Archiv Astrolabes - 10e siècle - Europe ram Astronomie - 10e siècle - Europe ram Geschichte Astrolabes History Astronomy History Astronomy history Europe History, Medieval Europe Astrolabium (DE-588)4003304-1 gnd |
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| title | Aspects of the Astrolabe 'architectonica ratio' in tenth- and eleventh-century Europe |
| title_auth | Aspects of the Astrolabe 'architectonica ratio' in tenth- and eleventh-century Europe |
| title_exact_search | Aspects of the Astrolabe 'architectonica ratio' in tenth- and eleventh-century Europe |
| title_exact_search_txtP | Aspects of the Astrolabe 'architectonica ratio' in tenth- and eleventh-century Europe |
| title_full | Aspects of the Astrolabe 'architectonica ratio' in tenth- and eleventh-century Europe Arianna Borrelli |
| title_fullStr | Aspects of the Astrolabe 'architectonica ratio' in tenth- and eleventh-century Europe Arianna Borrelli |
| title_full_unstemmed | Aspects of the Astrolabe 'architectonica ratio' in tenth- and eleventh-century Europe Arianna Borrelli |
| title_short | Aspects of the Astrolabe |
| title_sort | aspects of the astrolabe architectonica ratio in tenth and eleventh century europe |
| title_sub | 'architectonica ratio' in tenth- and eleventh-century Europe |
| topic | Astrolabes - 10e siècle - Europe ram Astronomie - 10e siècle - Europe ram Geschichte Astrolabes History Astronomy History Astronomy history Europe History, Medieval Europe Astrolabium (DE-588)4003304-1 gnd |
| topic_facet | Astrolabes - 10e siècle - Europe Astronomie - 10e siècle - Europe Geschichte Astrolabes History Astronomy History Astronomy history Europe History, Medieval Europe Astrolabium Europa Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016424718&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV023551700 |
| work_keys_str_mv | AT borrelliarianna aspectsoftheastrolabearchitectonicaratiointenthandeleventhcenturyeurope |