The projective cast : architecture and its three geometries / txt
Robin Evans.
- First MIT Press paperback edition
- xxxvii, 413 p. ill. 29 cm. book
Includes bibliographical references (p. [372]-401) and index.
List of Illustrations ix -- Foreword xix -- Acknowledgments xxi -- Introduction: Composition and Projection xxv -- Part One: Chapter One Perturbed Circles 3 -- Chapter Two Persistent Breakage 55 -- Part Two: Chapter Three Seeing through Paper 107 -- Chapter Four Piero's Heads 123 -- Chapter Five Drawn Stone 179 -- Part Three: Chapter Six The Trouble with Numbers 241 -- Chapter Seven Comic Lines 273 -- Chapter Nine Rumors at the Extremities 337 -- Chapter Eight Forms Lost and Found Again 323 -- Conclusion: The Projective Cast 351 -- Notes 372 -- Illustration Credits 402 -- Index 404 -- List of Illustrations : 1. Sant'Eligio degli Orefici , Rome , Raphael Sanzio , designed 1509 , interior 7 -- 2. Sant'Eligio degli Orefici , plan 8 -- 3. Sant'Eligio degli Orefici , section showing nine centers 10 -- 4. Tempietto , San Pietro in Montorio , Rome , Donato Bramante , 1502 , section 11 -- 5. Leonardo da Vinci , Place for Preaching 12 -- 6. Baptistery , Pisa , section and plan 13 -- 7. Santa Maria delle Grazie , Milan , Donato Bramante , late 1480s , dome 15 -- 8. San Giorgio Maggiore , Venice , Andrea Palladio , 1565 – 1580 , dome 15 -- 9. G. P. Lomazzo , Choirs of Angels , 1565 – 1571 , Foppa Chapel , San Marco , Milan 20 -- 10. Diagram of dual - centered organization implied by sixteenth - century dome frescos 21 -- 11. Francesco Botticini , Assumption of the Virgin , altarpiece , c . 1475 22 -- 12. Giovanni di Paolo , The Creation of the World and the Expulsion from Paradise , 1445 24 -- 13. Sandro Botticelli , illustration for Dante ' s Divine Comedy , Paradiso , canto 23 26 -- 14. San Lorenzo , Florence , Filippo Brunel – Leschi , 1421 , sacristy 28 -- 15. Chigi Chapel , Santa Maria del Popolo , Rome , Raphael Sanzio , c . 1516 , dome 31 – 16. Raphael Sanzio, Disputà, Stanza della Segnatura, Vatican, 1511 32 -- 17. Sallustio Peruzzi , drawing of Sant'Eligio , c . 1560 – 1565 . Page 39 -- 18. Leonardo da Vinci , solid sphere 40 -- 19. Renaissance modification of the Ptolemaic system of celestial orbits 41 -- 20. Leonardo da Vinci , map of Imola , 1502 – 1503 45 -- 21. Marco Fabio Calvo , map of ancient Rome , 1527 46 -- 22. Richard Meier , sketch plan of the Atheneum , New Harmony , Indiana , 1975 – 1979 56 -- 23. Sigfried Giedion , Space , Time and Architecture , 1941 : Picasso ' s L ' Arlésienne and Gropius ' s Bauhaus 58 -- 24. Esprit Jouffret , projections of the pairs of octahedra constituting the hypersolid h2 61 -- 25. Caspar David Friedrich , The Wreck of the " Hope ," 1823 – 1824 64 -- 26. Georges Braque , Mandola , 1909 – 1910 64 -- 27. Pablo Picasso , Guitar maquette , 1912 65 -- 28. Raymond Duchamp – Villon , Maison Cubiste , 1912 65 -- 29. Vergilio Marchi , Model of Futurist House , 1916 66 -- 30. Villa Savoye , Poissy , Le Corbusier , 1928 – 1931 , view out of ramp window 68 -- 31. Walter Gropius , Kapp - Putsch Monument ( Memorial to the March Victims ) , 1920 – 1922 , Weimar 69 -- 32. Baker Dormitory , MIT , Cambridge , Massachusetts , Alvar Aalto , 1947 – 1948 , north side 72 -- 33. Baker Dormitory , plan . Page 72 -- 34. Watts Towers , Los Angeles , Sam Rodia , 1921 – 1945 . Page 77 -- 35. The City of Composite Presence , David Griffin and Hans Kolhoff , from Rowe and Koetter , Collage City , 1978 77 -- 36. Forum des Halles , Paris , C . Vasconi and G . Pencreach , 1972 – 1979 81 -- 37. Humphry Repton , A Design to Exemplify Irregularity of Outline in Castle Gothic 82 -- 38. Parc de La Villette , Paris , Bernard Tschumi , 1982 – 1989 , folie staircase 88 -- 39. Parc de La Villette , Paris , folie in front of J . L . Baltard ' s Slaughterhouse Hall ( 1863 – 1867 ) 88 -- 40. Gordon Matta – Clark , one of the photographs in his contribution to the Idea as Model exhibition , Institute of Architecture and Urban Studies , New York , 1976 90 -- 41. Rooftop Lawyers ' Office , Vienna , Coop Himmelblau , 1983 – 1988 93 -- 42. Hans Scharoun , Kirche als Fels , 1910 95 -- 43. Philharmonie , Berlin , Hans Scharoun , 1956 -1963 , plans 96 -- 44. Philharmonie , exterior from west 97 -- 45. Philharmonie , auditorium 97 -- 46. Philharmonie , foyer 98 -- 47. Philharmonie , foyer 99 -- 48. Philharmonie , foyer 99 -- 49. Pablo Picasso , Weeping Woman , 1937 103 -- 50. The Principles of Parallel Projection , from Daniel Fournier , A Treatise on the Theory of Perspective , 1761 109 -- 51. Alberti ' s perspective construction 110 -- 52. Raphael Sanzio , The School of Athens , 1511 , Stanza della Segnatura , Vatican 111 -- 53. Watercolor of Villa Madama ( anon . ), eighteenth century 112 -- 54. Villa Madama , Rome , Raphael Sanzio , 1517 – 1521 , plan 112 -- 55. Christ Disputing with the Elders in the Temple , fourteenth century , Dragonelli Chapel , San Domenico , Arezzo , detail of tiled floor 113 -- 56. Sant ' Andrea , Mantua , Leone Battista Alberti , designed 1470 , detail of façade 114 -- 57. The Arch of Augustus and the church of San Michele , Fano 115 -- 58. Andrea Palladio , final facade study for San Petronio , Bologna , 1579 116 -- 59. San Giorgio Maggiore , Venice , Andrea Palladio , 1564 – 1580 , detail of façade 117 -- 60. Philharmonie , Berlin , Hans Scharoun , 1956 – 1963 , published sections 120 – 121 -- 61. Bernardino Pinturicchio , one of the series of scenes from the life of Aeneas Silvius Piccolomini 124 -- 62. Snapshot ( author ) 124 -- 63. Albrecht Dürer , perspective machine 128 -- 64. Albrecht Dürer , aids to draw the perspective of a reclining woman 128 -- 65. Jacques Androuet du Cerceau , perspective construction 132 -- 66. Raphael Sanzio , Marriage of the Virgin , 1504 134 -- 67. Leonardo da Vinci , Adoration of the Magi , drawing , 1481 136 -- 68. Leonardo da Vinci , Adoration of the Magi , c . 1481 137 -- 69. Three early methods of perspective construction 138 – 139 -- 70. Solid dodecahedron , from Luca Pacioli , De divina proportione , 1496 143 -- 71. Piero della Francesca , The Flagellation of Christ 145 -- 72. Luca Cambiaso , pen and ink figure study 146 -- 73. Piero della Francesca , De prospectiva pingendi , plan – and – vanishing - point construction of an unaligned octagon 149 74. Piero della Francesca , De prospectiva pingendi , a building projected with the aid of a vanishing point 150 -- 75. Piero della Francesca , De prospectiva pingendi , rotated orthographic projection of a cube 152 -- 76. Piero della Francesca , De prospectiva pingendi , perspective of a rotated cube 152 -- 77. Piero della Francesca , De prospectiva pingendi , orthographic projections of a head 153 -- 78. Piero della Francesca , De prospectiva pingendi , 153 -- 79. L . B . Alberti ' s finitorum , from De statua 155 -- 80. Piero della Francesca , De prospectiva pingendi , orthographic projections of a tilted head ( elevations ) 157 -- 81. Piero della Francesca , De prospectiva pingendi , orthographic projections of a tilted head ( plans ) 157 -- 82. Piero della Francesca , five women from The Proving of the True Cross , San Francesco , Arezzo 160 -- 83. Piero della Francesca , The Baptism of Christ , detail 160 -- 84. Five women from The Proving of the True Cross : schematic rotations 161 -- 85. Five women from The Proving of the True Cross : rotations in detail 162 -- 86. Plan showing orientations of feet , bodies, and heads of the three foreground figures in Piero ' s Flagellation 163 -- 87. Piero della Francesca , Brera altarpiece 164 -- 88. Piero della Francesca , Nativity 165 -- 89. Vanishing points of the stall roof in Piero ' s Nativity 165 -- 90. Piero della Francesca , Dream of Constantine , detail , San Francesco , Arezzo 166 -- 91. Leonardo da Vinci , A Town Overwhelmed by a Deluge , c . 1515 168 -- 92. Peter Paul Rubens , copy of Leonardo ' s Battle of Anghiari , c . 1603 169 -- 93. Paolo Uccello , Subsiding of the Flood , Chiostro Verde , Santa Maria Novella , Florence , 1446 – 1448 170 -- 94. Paolo Uccello , Battle of San Romano : Niccolò da Tolentino at the Head of the Florentines , 1456 171 -- 95. Paolo Uccello , Battle of San Romano : The Counterattack of Micheletto da Cotignola , 1456 172 -- 96. Paolo Uccello , Battle of San Romano : The Unhorsing of Bernardino della Ciarda , 1456 172 -- 97. Paolo Uccello , perspective study of a chalice 173 -- 98. Paolo Uccello , perspective study of a mazzocchio 173 -- 99. Two perspectives of a disk with equal segments 174 -- 100. Hôtel Bullioud , Lyons , Philibert Delorme , 1536 , elevation of courtyard 182 -- 101. Philibert Delorme , perspective of the trompe at Anet , 1549 – 1551 183 -- 102. Philibert Delorme , trait for the trompe at Anet 185 -- 103. Philibert Delorme , the trompe at Anet , relation between the trompe and the trait 187 -- 104. Philibert Delorme , the trompe at Anet , the basic rotation and rabattement 187 -- 105. Philibert Delorme , the trompe at Anet , developed surface of the underside 188 -- 106. Philibert Delorme , the trompe at Anet , perspective 188 -- 107. Trompe under the organ loft , seminary chapel , La Flèche , Jacques Nadreau , 1636 189 -- 108. Francesco Salviati , Bathsheba Going to King David , Palazzo Sacchetti , Rome , 1552 – 1554 191 -- 109. A . F . Frézier , escalier vis de Saint - Gilles suspendu 192 -- 110. Notre Dame de la Couture , Le Mans , suspended stone stair , architect unknown , 1720 – 1739 193 -- 111. Pulpit , Saint - Sulpice , Paris ( second project ), Charles de Wailly , 1789 194 -- 112. Hendrick Goltzius , Job in Distress , c . 1616 197 -- 113. Gérard David , Christ Nailed to the Cross 198 -- 114. Philibert Delorme , frontispiece to the Premier tome , 1567 199 -- 115. Diagram of the first 7 of 11 successive operations in Girard Desargues ' s universal method for stonecutting 202 -- 116. J . B . de La Rue , frontispiece to Traité de la coupe des pierres , first published 1728 204 -- 117. A block of stone and its trait , from Abraham Bosse , La Pratique du trait , 1643 206 -- 118. François Derand , trait for an oblique arch descending through a cylindrical tower into a dome 207 -- 119. Philibert Delorme , rusticated temple 211 -- 120. Hubert Robert , L ' Arc de Triomphe d ' Orange , 1783 212 -- 121. Saint – Paul – Saint – Louis , Paris , François Derand , 1627 – 1641 , interior 215 -- 122. Abbaye de Notre Dame de la Couture , Le Mans , architect unknown , 1720 – 1739 , cloister vaults and pilaster 216 -- 123. Sainte-Geneviève , Paris , J . G . Soufflot , crypt vaults , 1758 – 1764 216 -- 124. Sainte – Geneviève , Paris , J . G . Soufflot , choir vaults , completed 1779 217 -- 125. Halle au Blé , Paris , Nicolas Le Camus de Mézières , 1762 -1766 , section showing suspended double spiral stairs 218 -- 126. Halle au Blé , cross section 219 -- 127. Halle au Blé , section showing grain store vault 219 -- 128. Philibert Delorme , trait for a modern star vault 222 -- 129. Gloucester Cathedral , choir vault , William Ramsey ( ? ) , 1337 – 1367 227 -- 130. Gloucester Cathedral , detail of severy in choir 227 -- 131. Gloucester Cathedral cloister , fan vaulting , begun 1378 230 -- 132. Peterborough Cathedral , retrochoir , John Wastell ( ? ), early sixteenth century , intrados of twenty intersecting fans 232 -- 133. Peterborough Cathedral , retrochoir 233 -- 134. Henry VII Chapel , Westminster Abbey , Robert and William Vertue , 1500 – 1520 , pendant fan vaults 234 -- 135. Extrados of Henry VII Chapel vaults , drawn by Robert Willis , 1842 235 -- 136. François Blondel , harmonically proportioned Attic base with its corresponding chord 242 -- 137. Proportional analyses of Santa Maria Novella , Florence by Wölfflin , 1889 , and Wittkower , 1949 248 -- 138. Proportion in perspective , showing the generation of harmonic ratios when the viewing point O is one bay width distant from the picture plane 252 -- 139. Santo Spirito , Florence , Filippo Brunelleschi , started 1436 , the nave 253 -- 140. Albrecht Dürer , figure from Vier Bücher von menschlicher Proportion , 1538 255 -- 141. Vittore Carpaccio , Birth of the Virgin , 1504 – 1508 257 -- 142. Girard Desargues ' s theorem of four - point involution 258 -- 143. Albrecht Dürer , perspective adaptation of equal measures 260 -- 144. Albrecht Dürer , figure proportioned with the perspective adaptation shown in the previous figure 260 -- 145. Albrecht Dürer , diminishing spiral stair with risers proportioned by perspective adaptation 261 -- 146. Comparison of musical scales visualized as the subdivisions of a monochord 264 -- 147. Notre - Dame du Haut , Ronchamp , Le Corbusier , 1950 – 1955 , view from south 274 -- 148. Le Corbusier , The Modulor , red and blue series 275 -- 149. Le Corbusier, charcoal sketch plan of Ronchamp , June 1950 279 -- 150. Hanning ' s diagram of 1943 and its errors 280 -- 151. Michelangelo ' s Capitol with traces régulateurs superimposed 280 -- 152. Spanish pot , from L ' Art décoratif d'au jourd'hui 282 -- 153. Hans Ern i, Die neuen Ikarier , 1940 283 -- 154. Ronchamp , east end of roof shell 283 -- 155. Ronchamp , view into cowl of red tower 285 -- 156. Le Corbusier ' s revision of Maillart ' s diagram 286 -- 157. Le Corbusier , Apollo and Medusa cameo , first published 1948 288 -- 158. Le Corbusier , plate from Poème de l'angle droit 288 -- 159. Ronchamp , plan 289 -- 160. Church at Lourtier , Switzerland , Alberto Sartoris , 1932 293 -- 161. Ronchamp , interior 294 -- 162. Iannis Xenakis ' s pans de verre ondulatoires , monastery of La Tourette , 1955 – 1959 297 -- 163. Philips Pavilion , Brussels International Exhibition , Le Corbusier and Iannis Xenakis , 1958 299 -- 164. Iannis Xenakis , ruled surfaces of sound in Metastasis , 1954 299 -- 165. Ronchamp , twisted interior surface of south wall 300 -- 166. Ronchamp , the south tower , drawing by Olek , December 1953 301 -- 167. Ronchamp , wire and paper model 303 -- 168. Ronchamp , roof shell , drawing by André Maisonnier , September 1952 304 -- 169. Four projections of Guarini ' s conoid 306 -- 170. The US aircraft carrier Lexington 308 -- 171. Le Corbusier , diagram from sketchbook D17 , 1950 309 -- 172. Antoine Pevsner , Construction dynamique 311 -- 173. André Maisonnier , elevation of the Ronchamp roof as a ruled surface , March 1951 313 -- 174. Interior of Ronchamp showing underside of roof shell 313 -- 175. Woman at prayer , from Le Corbusier , Ronchamp 318 -- 176. Plate from Le Corbusier , Aircraft 319 -- 177. Developing the surface of a cone with base that has been truncated by a sphere , from Gaspard Monge , Géométrie descriptive , 1838 325 -- 178. Courtyards , from JN L Durand , Précis des leçons d'architecture , 1802 – 1805 326 -- 179. AF Frézier , conoidal arrière – voussoirs , from La Théorie et la pratique de la coupe des pierres , 1739 329 -- 180. Ruled surfaces , from Thomas Bradley , Elements of Geometrical Drawing , 1862 330 -- 181. Stern of the Great Eastern , photograph by Robert Howlett , 1857 331 -- 182. Casa Batlló , Barcelona , Antoni Gaudí , 1904 – 1906 , detail of masonry 332 -- 183. Sagrada Familia , Barcelona , Antoni Gaudí , 1884 – 1926 , finial 332 -- 184. Le Corbusier , 1928 sketch of Gaudi ' s 1909 - 1910 roof for the Parochial School of Sagrada Familia 333 -- 185. Theo van Doesburg , Counter - Compositions V , 1924 338 -- 186. Theo van Doesburg , Color Construction in the Fourth Dimension of Space – Time , 1924 340 -- 187. Theo van Doesburg , version of the hypercube 342 -- 188. Alternative axonometric representation of the hypercube 343 -- 189. El Lissitzky , axonometric of the Proun Room , 1923 343 -- 190. Einstein ' s analogy of spherical space , using stereographic projection 345 -- 191. Einstein Tower , Potsdam , Erich Mendelsohn , 1919 – 1921 347 -- 192. Masolino , The Foundation of Santa Maria Maggiore by Pope Liberius 356 -- 193. Chapel of the Santissima Sindone , Turin , Guarino Guarini , 1667 – 1690 , section 361 -- 194. Chapel of the Santissima Sindone , view into dome 362 -- 195. Luigi Moretti , plaster cast of interior of Guarino Guarini ' s Santa Maria della space Divina Providenza , Lisbon 365 -- 196. Santa Maria della Divina Providenza , Lisbon , Guarino Guarini , designed c . 1681 , begun 1698 , section 365 -- 197. Projection and its analogues : The Arrested Image 367 --
Robin Evans recasts the idea of the relationship between geometry and architecture, drawing on mathematics, engineering, art history, and aesthetics to uncover processes in the imagining and realizing of architectural form.
Anyone reviewing the history of architectural theory, Robin Evans observes, would have to conclude that architects do not produce geometry, but rather consume it. In this long-awaited book, completed shortly before its author's death, Evans recasts the idea of the relationship between geometry and architecture, drawing on mathematics, engineering, art history, and aesthetics to uncover processes in the imagining and realizing of architectural form. He shows that geometry does not always play a stolid and dormant role but, in fact, may be an active agent in the links between thinking and imagination, imagination and drawing, drawing and building. He suggests a theory of architecture that is based on the many transactions between architecture and geometry as evidenced in individual buildings, largely in Europe, from the fifteenth to the twentieth century.
From the Henry VII chapel at Westminster Abbey to Le Corbusier's Ronchamp, from Raphael's S. Eligio and the work of Piero della Francesca and Philibert Delorme to Guarino Guarini and the painters of cubism, Evans explores the geometries involved, asking whether they are in fact the stable underpinnings of the creative, intuitive, or rhetorical aspects of architecture. In particular he concentrates on the history of architectural projection, the geometry of vision that has become an internalized and pervasive pictorial method of construction and that, until now, has played only a small part in the development of architectural theory.
Evans describes the ambivalent role that pictures play in architecture and urges resistance to the idea that pictures provide all that architects need, suggesting that there is much more within the scope of the architect's vision of a project than what can be drawn. He defines the different fields of projective transmission that concern architecture, and investigates the ambiguities of projection and the interaction of imagination with projection and its metaphors.
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Architecture--Composition, proportion, etc. Geometry in architecture.