Andersen The Geometry of an Art

The History of the Mathematical Theory of Perspective from Alberti to Monge
1. Auflage 2008
ISBN: 978-0-387-48946-9
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 814 Seiten

Key Issues ver since the late 1970s when Pia Holdt, a student of mine at the time, and Jed Buchwald, a colleague normally working in another field, made E me aware of how fascinating the history of perspective constructions is, I have wanted to know more. My studies have resulted in the present book, in which I am mainly concerned with describing how the understanding of the geometry behind perspective developed and how, and to what extent, new insights within the mathematical theoryof perspective influenced the way the discipline was presented in textbooks. In order to throw light on these aspects of the history of perspective, I have chosen to focus upon a number of key questions that I have divided into two groups. Questions Concerning the History of Geometrical Perspective • How did geometrical constructions of perspective images emerge? • How were they understood mathematically? • How did the geometrical constructions give rise to a mathematical theory of perspective? • How did this theory evolve? Inconnectionwith the last question it is natural to takeup the following themes.

Autoren/Hrsg.

Andersen, Kirsti

Inhaltsverzeichnis

1;Contents;7
2;Introduction;19
2.1;Key Issues;19
2.2;The Word ' Perspective';20
2.3;Mathematical Terminology, Results, and Techniques;30
2.4;Bibliographies;32
2.5;Biographies;33
2.6;My Text;34
3;Acknowledgements;24
4;Notes to the Reader;27
5;The Birth of Perspective;36
5.1;I.1 The First Written Account of Geometrical Perspective;36
5.2;I.2 The Origin of Perspective;37
5.3;I.3 Four Stimuli;38
5.4;I.4 Brunelleschi;46
5.5;I.5 Perspective Before the Renaissance?;50
6;Alberti and Piero della Francesca;51
6.1;II.1 The Two Earliest Authors;51
6.2;II.2 Alberti and His Work;51
6.3;II.3 Alberti’s Model;53
6.4;II.4 Alberti’s Construction;56
6.5;II.5 Alberti’s Theoretical Reflections and His Diagonal Rule;63
6.6;II.6 The Third Dimension in Alberti’s Construction;67
6.7;II.7 Alberti’s Construction in History;68
6.8;II.8 Piero della Francesca and His Work;68
6.9;II.9 The Theoretical Foundation of De Prospectiva;71
6.10;II.10 Piero and Alberti’s Construction;74
6.11;II.11 Piero’s Diagonal Construction;78
6.12;II.12 Piero’s Distance Point Construction;80
6.13;II.13 The Division Theorem;84
6.14;II.14 Piero’s Treatment of the Third Dimension;84
6.15;II.15 The Column Problem;85
6.16;II.16 Piero’s Plan and Elevation Construction;93
6.17;II.17 Piero’s Cube;98
6.18;II.18 Piero’s Anamorphoses;105
6.19;II.19 Piero’s Use of Perspective;109
6.20;II.20 Piero’s Influence;113
7;Leonardo da Vinci;115
7.1;III.1 Leonardo and the History of Perspective;115
7.2;III.2 Leonardo’s Various Concepts of Perspective;118
7.3;III.3 Visual Appearances and Perspective Representations;122
7.4;III.4 Leonardo on Visual Appearances of Lengths;123
7.5;III.5 Leonardo on Perspective Representations;134
7.6;III.6 Leonardo and Curvilinear Perspective;141
7.7;III.7 Leonardo’s Doubts and Their Consequences;145
8;Italy in the Cinquecento;148
8.1;IV.1 The Italian Sixteenth-Century Perspectivists;148
8.2;IV.2 The Architectural, Painting, and Sculpting Traditions;149
8.3;IV.3 A Mathematical Approach to Perspective – The Contributions by Vignola and Danti;158
8.4;IV.4 Connection Between Perspective and Another Central Projection – Commandino’s Contributions;171
8.5;IV.5 Another Mathematical Approach – Benedetti’s Contributions;179
8.6;IV.6 An Encyclopedia on Perspective – Barbaro’s Book;185
8.7;IV.7 The Italian Pre-1600 Contributions to Perspective;191
9;North of the Alps Before 1600;194
9.1;V.1 The Introduction of Perspective North of the Alps;194
9.2;V.2 Viator and His Followers;194
9.3;V.3 Cousin;205
9.4;V.4 Dürer;216
9.5;V.5 Dürer’s German Successors;245
9.6;V.6 Vredeman de Vries;263
9.7;V.7 The Sixteenth-Century Non-Italian Tableau;269
10;The Birth of the Mathematical Theory of Perspective Guidobaldo and Stevin;270
10.1;VI.1 Guidobaldo and His Work on Perspective;270
10.2;VI.2 Guidobaldo’s Theory of Perspective;274
10.3;VI.3 Guidobaldo’s Twenty-Three Methods;283
10.4;VI.4 New Themes in Guidobaldo’s Work;289
10.5;VI.5 Guidobaldo’s Role in the History of Perspective;295
10.6;VI.6 Stevin and His Work on Perspective;298
10.7;VI.7 The Foundation of Stevin’s Theory;303
10.8;VI.8 Stevin’s Practice of Perspective;306
10.9;VI.9 Stevin and Inverse Problems of Perspective;312
10.10;VI.10 Further Issues in Stevin’s Work;315
10.11;VI.11 Stevin’s Influence;320
11;The Dutch Development after Stevin;323
11.1;VII.1 A Survey of the Literature;323
11.2;VII.2 The Theory and Practice of Perspective;328
11.3;VII.3 The Work by Marolois;329
11.4;VII.4 Van Hoogstraten’s Perspective Box;341
11.5;VII.5 Van Schooten’s Revival of Stevin’s Theory;349
11.6;VII.6 The Problems of Reversing and Scaling;360
11.7;VII.7 ’sGravesande’s Essay on Perspective;370
11.8;VII.8 Traces of Desargues’s Method in Dutch Perspective;392
11.9;VII.9 Jelgerhuis and the Choice of Parameters;395
11.10;VII.10 The Dutch Scene;399
12;Italy after Guidobaldo;400
12.1;VIII.1 Waning Interest;400
12.2;VIII.2 Perspective in Textbooks on Architecture;401
12.3;VIII.3 Perspective in Other Textbooks;403
12.4;VIII.4 The Prospettiva Pratica Tradition;406
12.5;VIII.5 Pozzo’s Influential Textbook;417
12.6;VIII.6 A Special Approach to Perspective – Costa;425
12.7;VIII.7 Mathematical Approaches to Perspective;428
12.8;VIII.8 The Later Italian Period;430
13;France and the Southern Netherlands after 1600;431
13.1;IX.1 The Early Modern French Publications;431
13.2;IX.2 The Theory of Perspective Taught;433
13.3;IX.3 The Works of de Caus and Vaulezard;440
13.4;IX.4 The Work of Aleaume and Migon;448
13.5;IX.5 Desargues’s Perspective Method;457
13.6;IX.6 Brouillon project and Perspective;475
13.7;IX.7 Perspectivists at War – and the Work of Dubreuil;478
13.8;IX.8 The Work of Niceron;482
13.9;IX.9 Second Act of the Desargues Drama;487
13.10;IX.10 The 1660s and 1670s;495
13.11;IX.11 Perspective and the Educated Mathematician;500
13.12;IX.12 French Eighteenth-Century Literature on Perspective;501
13.13;IX.13 The French Development;515
14;Britain;518
14.1;X.1 Starting Late;518
14.2;X.2 British Literature on Perspective Before Taylor;518
14.3;X.3 Taylor and His Work on Perspective;523
14.4;X.4 Taylor’s Fundamental Concepts and Results;531
14.5;X.5 Taylor’s Basic Constructions;537
14.6;X.6 Taylor’s Contributions to Plane Perspective Geometry;540
14.7;X.7 Taylor’s Contributions to Solid Perspective Geometry;544
14.8;X.8 Taylor’s Examples of Drawing Figures in Perspective;548
14.9;X.9 Taylor’s Treatment of Shadows;553
14.10;X.10 Taylor on Reflections;558
14.11;X.11 Taylor on Inverse Problems of Perspective;563
14.12;X.12 The Immediate Response to Taylor’s Work;567
14.13;X.13 Taylor’s Work in History;569
14.14;X.14 Hamilton’s Comprehensive Work on Perspective;570
14.15;X.15 Kirby and Highmore;576
14.16;X.16 The Taylor Tradition Continued;597
14.17;X.17 Perspective in Textbooks on Mathematics;617
14.18;X.18 British Individualists;621
14.19;X.19 British Mathematicians and Perspective;626
14.20;X.20 The British Chapter;627
15;The German-Speaking Areas after 1600;628
15.1;XLI Categorization of the German Literature;628
15.2;XL2 Perspective Instruments;628
15.3;XI.3 Anamorphoses;634
15.4;XI.4 Perspective Presented for Practitioners;643
15.5;XI.5 Mathematical Works on Perspective;648
15.6;XI. 6 Traces of Lambert;660
15.7;XI.7 Perspective in the German Countries;662
16;Lambert;664
16.1;XII.1 Lambert's Special Position;664
16.2;XII.2 Life and Work on Perspective;664
16.3;XII. 3 Early Approach to Perspective;671
16.4;XII.4 The Contents of Freye Perspektive;676
16.5;XII.5 Constructing Polygons in the Picture Plane;679
16.6;XII.6 Oblique Figures;684
16.7;XII.7 Shadows;690
16.8;XII.8 Reflections;693
16.9;XII.9 Parallel Projections;703
16.10;XII.I0 Inverse Problems of Perspective;708
16.11;XII. II Lambert's Practice of Perspective;711
16.12;XII.12 Ruler Geometry;718
16.13;XII. 13 Lambert's Impact;732
17;Monge Closing a Circle;735
17.1;XIII.1 Monge and Descriptive Geometry;735
17.2;XIII.2 Monge and Linear Perspective;737
18;Summing Up;740
18.1;XIV.1 Opening Remarks;740
18.2;XIV:2 Local Approaches to Perspective;741
18.3;XIV.3 Perspective and Pure Mathematics;743
18.4;XIV.4 The Theory and Practice of Perspective;746
18.5;XlV.5 The Driving Forces Behind the Theory of Perspective;747
19;On Ancient Roots of Perspective;749
19.1;Optics;749
19.2;Cartography;753
19.3;Scenography;754
20;The Appearance of a Rectangle à la Leonardo da Vinci;757
21;’ sGravesande Taking Recourse to the Infinitesimal Calculus to Draw a Column Base in Perspective;761
22;The Perspective Sources Listed Countrywise in Chronological Order;765
23;Pre-Nineteenth Century Publications on Perspective;773
24;Supplementary Literature;796
25;Index;819