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