The document discusses architectural principles of proportion and symmetry from antiquity through the Renaissance. It provides examples of how proportion was seen as key to beauty and harmony in buildings from Vitruvius to Alberti and Palladio. Specific structures are discussed like Bramante's San Pietro in Montorio to show how Renaissance architects designed central-plan churches based on classical precedents but also innovated on the forms. The document examines the shift from medieval to Renaissance perspectives through treatises and buildings.

1. Architectural Analysis
The legacy of Antiquity
Alberto Iacovoni, Marialuisa Palumbo | Cornell in Rome

2. Proportion is a due adjustment of the size of the different parts to each other and to
the whole; on this proper adjustment symmetry depends.
1. On Principles and Foundations

4. Effetti del Buon Governo, Palazzo Pubblico, Siena,1337-1340 | Ambrogio Lorenzetti

5. Merchants' meeting | miniature XIV century

6. Proportion is a due adjustment of the size of the different parts to each other and to
the whole; on this proper adjustment symmetry depends.
Man is the measure of all things
Protagoras, c.450 BC

7. Annunciation, 1344 | Ambrogio Lorenzetti

8. Proportion is a due adjustment of the size of the different parts to each other and to
the whole; on this proper adjustment symmetry depends.
It is not too much to claim that a pattern of tiles used in this sense
represents the modern 'systematic space' in an artistically concrete
sphere, well before it had been postulated by abstract mathematical
thought… Once again this perspectival achievement is nothing other
than a concrete expression of a contemporary advance in epistemology
or natural philosophy... abandoning the Scholastic idea of a cosmos with
the middle of the earth as its absolute center and with the outermost
celestial sphere as its absolute limit; the result was the concept of
infinity. The vision of the universe is detheologized.
Erwin Panofsky, Perspective as Symbolic Form

9. The Geocentric model or Ptolemaic system

10. Della Pittura (On Painting), 1435 | Leon Battista Alberti

11. Della Pittura | Leon Battista Alberti

12. Proportion is a due adjustment of the size of the different parts to each other and to
the whole; on this proper adjustment symmetry depends.
To make clear my exposition in writing this brief commentary on
painting, I will take first from the mathematicians those things with which
my subject is concerned.
Leon Battista Alberti, Della Pittura

13. Ludi mathematici, 1450 | Leon Battista Alberti

14. Ludi mathematici | Leon Battista Alberti

15. Ludi mathematici | Leon Battista Alberti

16. De revolutionibus orbium coelestium (On the Revolutions of the Heavenly Spheres)
1543 | Nicolaus Copernicus

17. Proportion is a due adjustment of the size of the different parts to each other and to
the whole; on this proper adjustment symmetry depends.
People gave ear to an upstart astrologer who strove to show that the
earth revolves, not the heavens or the firmament, the sun and the
moon... This fool wishes to reverse the entire science of astronomy; but
sacred Scripture tells us [Joshua 10:13] that Joshua commanded the
sun to stand still, and not the earth.
Martin Luther

18. Astronomia Nova, 1609 | Johannes Kepler

19. Sidereus Nuncius (Starry Messenger) , 1610 | Galileo Galilei

20. Cartesian coordinate system, 1637 | René Descartes

21. Philosophiæ Naturalis Principia Mathematica, 1687 | Isaac Newton

22. Proportion is a due adjustment of the size of the different parts to each other and to
the whole; on this proper adjustment symmetry depends.
02. On Beauty

23. De Re Aedificatoria (On the Art of Building in Ten Books), c.1450 | Leon Battista Alberti

24. De Re Aedificatoria | Leon Battista Alberti

25. Proportion is a due adjustment of the size of the different parts to each other and to
the whole; on this proper adjustment symmetry depends.
Ut sit pulchritudo quidem certa cum ratione concinnitas universarum
partium in eo cuius sint: ita ut addi, aut diminui, aut immutari possit nihil,
quam improbabilius reddat.
[Beauty is] the harmony and concord of all parts achieved in such a
manner that nothing could be added or taken away or altered except for
the worse.
Alberti, De re aedificatoria, Book VI

26. Proportion is a due adjustment of the size of the different parts to each other and to
the whole; on this proper adjustment symmetry depends.
Aedium compositio constat ex symmetria, cuius rationem diligentissime
architecti tenere debent. ea autem paritur a proportione, quae graece
ἀναλογία dicitur. proportio est ratae partis membrorum in omni opere
totiusque commodulatio, ex qua ratio efficitur symmetriarum.
The design of Temples depends on symmetry, the rules of which
Architects should be most careful to observe. Symmetry arises from
proportion, which the Greeks call ἀναλογία. Proportion is a due
adjustment of the size of the different parts to each other and to the
whole; on this proper adjustment symmetry depends.
Vitruvius, De Architectura, III, 1

27. Santa Maria Novella, Florence, 1458-78 (facade) | Alberti

28. Proportion is a due adjustment of the size of the different parts to each other and to
the whole; on this proper adjustment symmetry depends.
All the new elements introduced by Alberti in the facade, the columns,
the pediment, the attic, and the scrolls, would remain isolated features
were it not for the all-pervading harmony which formed the basis and
background of his whole theory. Harmony, the essence of beauty,
consists in the relationship of the parts to each other and to the whole,
and, in fact, a single system of proportion permeates the facade, and the
place and size of every single part and detail is fixed and defined by it.
Proportions recommended by Alberti are the simple relations of one to
one, one to two, one to three... which are the elements of musical
harmony and which Alberti found in classical buildings...
The whole facade of S. Maria Novella can be exactly circumscribed by a
square. A square of half the side of the large square defines the
relationship of the two stories. The main story can be divided into two
such squares, while one enclose the upper storey. In other words, the
whole building is related to its main parts in the proportion of one to
two...
Rudolf Wittkower, Architectural Principles in the Age of Humanism

29. Santa Maria Novella, Florence | Alberti

30. Proportion is a due adjustment of the size of the different parts to each other and to
the whole; on this proper adjustment symmetry depends.
If Nature, therefore, has made the human body so that the different
members of it are measures of the whole, so the ancients have, with
great propriety, determined that in all perfect works, each part should be
some aliquot part of the whole; and since they direct, that this be
observed in all works, it must be most strictly attended to in temples of
the gods, wherein the faults as well as the beauties remain to the end of
time.
Vitruvius, De Architectura, III, 1

31. I sette libri dell'architettura, c.1537 | The Five Orders

32. Proportion is a due adjustment of the size of the different parts to each other and to
the whole; on this proper adjustment symmetry depends.
Beauty will result from the beautiful form and from the correspondence
of the whole to the parts, of the parts amongst themselves, and of these
again to the whole; so that the structures may appear an entire and
complete body, wherein each member agrees with the other and all
memebrs are necessary for the accomplishment of the building”
Palladio, Book 1, chap. 1

33. Homo ad circulum, c.1490 | Leonardo

34. First illustrated edition of De Architectura, Venezia, 1511 | Giovanni Giocondo

35. Studies of proportions | Francesco di Giorgio

36. Studies of proportions | Francesco di Giorgio

37. Studies of proportions | Francesco di Giorgio

38. Trattato di Architettura Civile e Militare, c.1470 | Francesco di Giorgio Martini

39. The Antiquities of Rome | Andrea Palladio

40. I Quattro Libri dell'Architettura, 1570 | Andrea Palladio

41. The Four Books of Architecture | Dell'Atrio Corinthio

42. The Four Books of Architecture | Pantheon

43. The Four Books of Architecture | San Pietro in Montorio

44. 03. On the Central-plan Church

45. De Re Aedificatoria | Leon Battista Alberti

46. Proportion is a due adjustment of the size of the different parts to each other and to
the whole; on this proper adjustment symmetry depends.
Deus est sphaera infinita, cuius centrum est ubique, circumferentia
nullibi.
God is an infinite sphere whose center is everywhere and circumference
nowhere.
Nicolò Cusano, De Docta Ignorantia, 1440

47. S. Maria degli Angeli, Firenze, 1434 | Brunelleschi

48. Pantheon | Rome

49. Temple of Vesta | Rome

50. Santa costanza | Rome

51. Temple of Minerva Medica or Nymphaeum at the Horti Liciniani | Rome

52. Proportion is a due adjustment of the size of the different parts to each other and to
the whole; on this proper adjustment symmetry depends.
Le più belle, e più regolate forme, e dalle quali le altre ricevono le
misure, sono la Ritonda e la Quadrangulare...
la Ritonda... sola tra tutte le figure è semplice, uniforme, eguale, forte e
capace, faremo I Tempij rotondi.
...è attissima a dimostrare la Unità, la Infinita Essenza, la Uniformità, et
la Giustizia di Dio.
The most beautiful and most regular forms and from which the other
receive their measure are the round and the quadrangular. The round...
it is the only one among all the figures that is simple, uniform, equal,
strong, and spacious. Therefore let us make our temples round”
Palladio, Book I, chap 1

53. Sketches for central plan church, c. 1484 | Leonardo

54. Santa Maria delle Carceri, Prato, 1485 | Giuliano da Sangallo

55. Santa Maria delle Carceri, Prato, 1485 | Giuliano da Sangallo

56. San Pietro in Montorio, Roma, 1502 | Bramante

57. Proportion is a due adjustment of the size of the different parts to each other and to
the whole; on this proper adjustment symmetry depends.
This building is a reconstruction by Bramante of an ancient Roman
circular temple – or so it seems at first.
He mounts it [the theme of the circular temple] on three steps and sets a
continuous moulded plinth under the order. This plinth gives the little
building a sudden and auspicious 'lift' – enough to ratify its sanctity. And
each Doric column has an answering Doric pilaster on the wall of the
inner building – what is called the cella. This cella rises higher than the
colonnade and is covered with a hemi-spherical dome. Now, is this a
literal reconstruction of a Roman temple or is not? Clearly not. It is an
extension of an idea borrowed from the Romans. The plinth and the
vertical penetration of the central cylinder up and through to a hemi-
spherical dome are Bramante's inventions and highly successful ones to
judge by the numbers of times they have been imitated.
John Summerson, The Classical Language of Architecture

58. San Pietro in Montorio | Palladio's drawing

59. Bramante's design for St Peter Cathedral, 1506 | Serlio

60. Foundation medal for St Peter's, 1505 | Cristoforo Caradosso

61. Tempietto Barbaro, Maser (Treviso), c. 1570 | Andrea Palladio

62. St Paul Cathedral, London, 1696-1708 | Christopher Wren

63. Santa Agnese in Agone, Rome, 1652 - 1672 | Borromini

64. San Carlo alle Quattro Fontane, Rome, 1641-1667 | Borromini

65. Sant'Andrea al Quirinale, Roma, 1658 - 1678 | Bernini

66. Proportion is a due adjustment of the size of the different parts to each other and to
the whole; on this proper adjustment symmetry depends.
04. On the Church's Facade

67. Medieval churches | Rome

68. Proportion is a due adjustment of the size of the different parts to each other and to
the whole; on this proper adjustment symmetry depends.
Far from leaving the orders out when they [the Romans] built vaulted
amphi-theatres, basilicas and triumphal arches, they brought them in, in
the most conspicuous way possible, as if they felt that no building could
communicate anything unless the orders were involved in it. To them the
orders were architecture... The Romans took this highly stylized but
structurally quite primitive kind of architecture and married it to arched
and vaulted multi-storey buildings of great elaborations. And in doing so
they raised architectural language to a new level...
...all major Roman buildings other than temples were designed on the
basis of arches and vaults, whereas the orders belong strictly to the
more primitive system of 'trabeation'. To marry the two in the sense of
giving the old types of temple column the job of carrying arches could
work up to a point but it was never satisfactory... So what did the
Romans do? The Colosseum at Rome answers the question at once...
every row of arches is framed inside a continuous colonnade. The
colonnades have no structural purpose – or very little. They are
representations of temple architecture carved, as it were, in relief on a
building which is not a temple, which is multi-storeyed and is built as a
system of arches and vaults.
John Summerson, The Classical Language of Architecture

70. Sebastiano Serlio, I sette libri dell'architettura, c.1537 | The Colosseum

71. San Francesco, Rimini, 1450 | Alberti

72. Arch of Constantine | Foundation medal for St Francesco

74. Sant'Andrea, Mantova, 1470 | Alberti

75. San Satiro, Milano, 1480, Bramante | Sagra di Carpi, 1515, Peruzzi

76. San Francesco della Vigna, Venezia, 1562 | Palladio

77. San Giorgio Maggiore, Venezia, 1566-1610 | Palladio

78. The Four Books of Architecture | Andrea Palladio

79. Chiesa del Redentore, Venezia, 1576-92 | Palladio

80. Chiesa del Gesù, Roma, 1575 | Giacomo della Porta

81. Santi Vincenzo e Anastasio, Rome, 1646 | Martino Longhi

82. Val-de-Grâce, Paris, 1645 | Francois Mansart

83. San Carlo alle Quattro Fontane, Rome, 1641-1667 | Borromini

84. Santa Agnese in Agone, Rome, 1652 - 1672 | Borromini

85. Santa Maria della Pace, Rome, 1656-58 | Pietro da Cortona

86. Sant'Andrea al Quirinale, Roma, 1658 - 1678 | Bernini

87. Panthéon, Paris, 1758-90 | Jacques-Germain Soufflot

88. San Rocco, Rome, 1832 | Giuseppe Valadier

89. Proportion is a due adjustment of the size of the different parts to each other and to
the whole; on this proper adjustment symmetry depends.
05. On Cities as Monuments

90. Ideal City, c.1480 | Luciano Laurana / Piero Della Francesca

91. Ideal Piazza | Luciano Laurana / Piero Della Francesca

92. Architectural Perspective | Luciano Laurana / Piero Della Francesca

93. Consegna delle chiavi, Roma, Cappella Sistina 1481 | Perugino

94. Pienza, 1459 | Bernanrdo Rossellino

95. Urbino, Palazzo ducale, 1454 | Luciano Laurana

96. Ferrara, Herculean Addition, 1492 | Biagio Rossetti

97. Piazza San Marco, Venezia | Jacopo Sansovino

98. San Marco's Library, 1537, Venezia | Jacopo Sansovino

99. Scuola di Atene, Palazzi Vaticani, 1509 | Raffaello

100. Capitoline Hill, view c. 1555 | Anonymous

102. Campidoglio, 1534-38 | Michelangelo

103. Michelangelo's Campidoglio, 1568 | Étienne Dupérac

105. Cosmological schema | Isidore of Seville

106. Proportion is a due adjustment of the size of the different parts to each other and to
the whole; on this proper adjustment symmetry depends.
The ancient Romans moved the umbelicus mundi figuratively from
Delphi to the Forum, where it remained until medieval legend shifted it
once more to the Campidoglio. Here it was permanently fixed in
Michelangelo's pavement, which combined its zodiacal inferences with
its mound-like forme. Marcus Aurelius, mounted at the center, might
have been a foreign element if iconic tradition had not permitted his
association with the umbelicus. As Kosmokrator, he succeeded to
Apollo's position upon the mound, and since the ancient sculptor had not
equipped him with the requisite attributes, Michelangelo placed around
his base the corona of Apollo: the twelve pointed rays which also serve
as the starting-points of the zodiacal pattern.
James Ackerman, The Architecture of Michelangelo

107. Piazza del Campidoglio, 1547 | Michelangelo