PROPORTION
SCIENCE, PHILOSOPHY, ARCHITECTURE
RICHARD PADOVAN
London and New York
CONTENTS
VI
Chapter 9: Vitruvius
9.1.
9.2.
9.3.
9.4.
9.5.
9.6.
Disputed value of the Ten Books on
Architecture
Van der Laan's interpretation of the fundamental
principles
The symmetry of temples and of the human
body
Body, circle and square.
Other proportions prescribed in the Ten Books,
including the square root of two
The system of proportions as a law of
growth
Chapter 10: Gothic proportions
10.1.
10.2.
10.3.
.10.4.
10.5.
10.6.
10.7.
10.8.
10.9.
10.10.
The continuity of Classical culture and the
legacy of Plato and Vitruvius
The practical geometry of the master
masons
The Milan cathedral controversy
The proportions of Chartres cathedral
Otto von Simson
John James
Towards a simpler and more comprehensive
solution
The recovery of Aristotle by the West
Knowing and measuring
Gothic architecture and Scholasticism
156
156
The music of the spheres
Chapter 13:The world as a machine
158
13.1.
162
167
13.2.
13.3.
169
13.4.
13.5.
171
Rudolf Wittkower and the collapse of
universal values
The atomist universe
The changed nature of mathematical
proportion
Science and art
Breaking the bond between science and
art
173
Chapter 14: From the outer to the inner
world
173
14.1.
179
181
184
185
189
14.2.
14.3.
14.4.
14.5.
14.6.
192
197
199
202
14.7.
14.8.
C h a p t e r 1 1 : H u m a n i s m and architecture
207
11.1.
11.2.
11.3.
11.4.
11.5.
207
214
219
225
232
The individual
focus
Proportion in perspective
Alberti on the art of building
San Sebastiano, Mantua
The villas of Palladio
12.7.
Chapter 12: Renaissance cosmology
237
12.1. Empathic and abstract tendencies
12.2. Learned ignorance
12.3. The Copernican revolution
12.4. The infinite universe and the infinity
of worlds
12.5. Johannes Kepler
12.6. The regular polyhedra
237
238
240
244
246
248
Clearing the ground of the obstacles to
knowledge
The duplication of worlds
The dissolution of mind
Passion replaces reason
Berkeley and Hume on proportion
Edmund Burke's attack on the theory of
proportion
The rational imperative
Kant: the understanding as the architect of
nature
Chapter 15:The golden section and the
golden module
15.1.
15.2.
15.3.
15.4.
The rediscovery of the golden section
Adolf Zeising
Gustav Fechner
The statistical approach to the golden
section
15.5. Attempts to explain the phenomenon
15.6. The curves of life
15.7. The golden section in Le Corbusier's early
work
15.8. Origins and aims of the modulor
15.9. The geometry of the modulor
15.10. The modulor's arithmetic
15.11. The anthropometries of the modulor
15.12. The modulor in practice: the Unite
d'habitation
251
253
253
256
258
261
266
273
273
276
280
283
285
290
293
298
304
304
305
307
308
310
313
316
321
323
325
329
332
CONTENTS
Chapter 16: The house as a frame for
living and a discipline for thought
16.1.
16.2.
16.3.
16.4.
16.5.
16.6.
Architecture: a practical or a speculative
art?
Physical versus intellectual functions
The abstract revolution
The necessary and the essential
The search for a starting point
The intrinsic meaning of architecture
336
336
338
343
345
348
351
16.7.
16.8.
16.9.
16.10.
16.11.
16.12.
The first building
Articulate building
What system of proportion do we need?
Knowing by not knowing
Types and orders of size
Conclusion
References
Index
VII
354
356
359
362
364
369
373
383