The Geometry of an Art (eBook)

Contents 7
Introduction 19
Key Issues 19
The Word ' Perspective' 20
Mathematical Terminology, Results, and Techniques 30
Bibliographies 32
Biographies 33
My Text 34
Acknowledgements 24
Notes to the Reader 27
The Birth of Perspective 36
I.1 The First Written Account of Geometrical Perspective 36
I.2 The Origin of Perspective 37
I.3 Four Stimuli 38
I.4 Brunelleschi 46
I.5 Perspective Before the Renaissance? 50
Alberti and Piero della Francesca 51
II.1 The Two Earliest Authors 51
II.2 Alberti and His Work 51
II.3 Alberti’s Model 53
II.4 Alberti’s Construction 56
II.5 Alberti’s Theoretical Reflections and His Diagonal Rule 63
II.6 The Third Dimension in Alberti’s Construction 67
II.7 Alberti’s Construction in History 68
II.8 Piero della Francesca and His Work 68
II.9 The Theoretical Foundation of De Prospectiva 71
II.10 Piero and Alberti’s Construction 74
II.11 Piero’s Diagonal Construction 78
II.12 Piero’s Distance Point Construction 80
II.13 The Division Theorem 84
II.14 Piero’s Treatment of the Third Dimension 84
II.15 The Column Problem 85
II.16 Piero’s Plan and Elevation Construction 93
II.17 Piero’s Cube 98
II.18 Piero’s Anamorphoses 105
II.19 Piero’s Use of Perspective 109
II.20 Piero’s Influence 113
Leonardo da Vinci 115
III.1 Leonardo and the History of Perspective 115
III.2 Leonardo’s Various Concepts of Perspective 118
III.3 Visual Appearances and Perspective Representations 122
III.4 Leonardo on Visual Appearances of Lengths 123
III.5 Leonardo on Perspective Representations 134
III.6 Leonardo and Curvilinear Perspective 141
III.7 Leonardo’s Doubts and Their Consequences 145
Italy in the Cinquecento 148
IV.1 The Italian Sixteenth-Century Perspectivists 148
IV.2 The Architectural, Painting, and Sculpting Traditions 149
IV.3 A Mathematical Approach to Perspective – The Contributions by Vignola and Danti 158
IV.4 Connection Between Perspective and Another Central Projection – Commandino’s Contributions 171
IV.5 Another Mathematical Approach – Benedetti’s Contributions 179
IV.6 An Encyclopedia on Perspective – Barbaro’s Book 185
IV.7 The Italian Pre-1600 Contributions to Perspective 191
North of the Alps Before 1600 194
V.1 The Introduction of Perspective North of the Alps 194
V.2 Viator and His Followers 194
V.3 Cousin 205
V.4 Dürer 216
V.5 Dürer’s German Successors 245
V.6 Vredeman de Vries 263
V.7 The Sixteenth-Century Non-Italian Tableau 269
The Birth of the Mathematical Theory of Perspective Guidobaldo and Stevin 270
VI.1 Guidobaldo and His Work on Perspective 270
VI.2 Guidobaldo’s Theory of Perspective 274
VI.3 Guidobaldo’s Twenty-Three Methods 283
VI.4 New Themes in Guidobaldo’s Work 289
VI.5 Guidobaldo’s Role in the History of Perspective 295
VI.6 Stevin and His Work on Perspective 298
VI.7 The Foundation of Stevin’s Theory 303
VI.8 Stevin’s Practice of Perspective 306
VI.9 Stevin and Inverse Problems of Perspective 312
VI.10 Further Issues in Stevin’s Work 315
VI.11 Stevin’s Influence 320
The Dutch Development after Stevin 323
VII.1 A Survey of the Literature 323
VII.2 The Theory and Practice of Perspective 328
VII.3 The Work by Marolois 329
VII.4 Van Hoogstraten’s Perspective Box 341
VII.5 Van Schooten’s Revival of Stevin’s Theory 349
VII.6 The Problems of Reversing and Scaling 360
VII.7 ’sGravesande’s Essay on Perspective 370
VII.8 Traces of Desargues’s Method in Dutch Perspective 392
VII.9 Jelgerhuis and the Choice of Parameters 395
VII.10 The Dutch Scene 399
Italy after Guidobaldo 400
VIII.1 Waning Interest 400
VIII.2 Perspective in Textbooks on Architecture 401
VIII.3 Perspective in Other Textbooks 403
VIII.4 The Prospettiva Pratica Tradition 406
VIII.5 Pozzo’s Influential Textbook 417
VIII.6 A Special Approach to Perspective – Costa 425
VIII.7 Mathematical Approaches to Perspective 428
VIII.8 The Later Italian Period 430
France and the Southern Netherlands after 1600 431
IX.1 The Early Modern French Publications 431
IX.2 The Theory of Perspective Taught 433
IX.3 The Works of de Caus and Vaulezard 440
IX.4 The Work of Aleaume and Migon 448
IX.5 Desargues’s Perspective Method 457
IX.6 Brouillon project and Perspective 475
IX.7 Perspectivists at War – and the Work of Dubreuil 478
IX.8 The Work of Niceron 482
IX.9 Second Act of the Desargues Drama 487
IX.10 The 1660s and 1670s 495
IX.11 Perspective and the Educated Mathematician 500
IX.12 French Eighteenth-Century Literature on Perspective 501
IX.13 The French Development 515
Britain 518
X.1 Starting Late 518
X.2 British Literature on Perspective Before Taylor 518
X.3 Taylor and His Work on Perspective 523
X.4 Taylor’s Fundamental Concepts and Results 531
X.5 Taylor’s Basic Constructions 537
X.6 Taylor’s Contributions to Plane Perspective Geometry 540
X.7 Taylor’s Contributions to Solid Perspective Geometry 544
X.8 Taylor’s Examples of Drawing Figures in Perspective 548
X.9 Taylor’s Treatment of Shadows 553
X.10 Taylor on Reflections 558
X.11 Taylor on Inverse Problems of Perspective 563
X.12 The Immediate Response to Taylor’s Work 567
X.13 Taylor’s Work in History 569
X.14 Hamilton’s Comprehensive Work on Perspective 570
X.15 Kirby and Highmore 576
X.16 The Taylor Tradition Continued 597
X.17 Perspective in Textbooks on Mathematics 617
X.18 British Individualists 621
X.19 British Mathematicians and Perspective 626
X.20 The British Chapter 627
The German-Speaking Areas after 1600 628
XLI Categorization of the German Literature 628
XL2 Perspective Instruments 628
XI.3 Anamorphoses 634
XI.4 Perspective Presented for Practitioners 643
XI.5 Mathematical Works on Perspective 648
XI. 6 Traces of Lambert 660
XI.7 Perspective in the German Countries 662
Lambert 664
XII.1 Lambert's Special Position 664
XII.2 Life and Work on Perspective 664
XII. 3 Early Approach to Perspective 671
XII.4 The Contents of Freye Perspektive 676
XII.5 Constructing Polygons in the Picture Plane 679
XII.6 Oblique Figures 684
XII.7 Shadows 690
XII.8 Reflections 693
XII.9 Parallel Projections 703
XII.I0 Inverse Problems of Perspective 708
XII. II Lambert's Practice of Perspective 711
XII.12 Ruler Geometry 718
XII. 13 Lambert's Impact 732
Monge Closing a Circle 735
XIII.1 Monge and Descriptive Geometry 735
XIII.2 Monge and Linear Perspective 737
Summing Up 740
XIV.1 Opening Remarks 740
XIV:2 Local Approaches to Perspective 741
XIV.3 Perspective and Pure Mathematics 743
XIV.4 The Theory and Practice of Perspective 746
XlV.5 The Driving Forces Behind the Theory of Perspective 747
On Ancient Roots of Perspective 749
Optics 749
Cartography 753
Scenography 754
The Appearance of a Rectangle à la Leonardo da Vinci 757
’ sGravesande Taking Recourse to the Infinitesimal Calculus to Draw a Column Base in Perspective 761
The Perspective Sources Listed Countrywise in Chronological Order 765
Pre-Nineteenth Century Publications on Perspective 773
Supplementary Literature 796
Index 819