The Art of Building in the Classical View of the World Craftsmanship and the Linear Perspective in Greek and Roman Architecture - VSIP.INFO (2023)

The Art of Building in the Classical World This book examines the application of design to the creation of classical architecture and examines how design tools and techniques developed for architecture later shaped theories of vision and representations of the universe in science. and philosophy. Based on recent studies examining and reconstructing the design process in classical architecture, John R. Senseney focuses on technical drawing in building construction as a model for expressing visual order and shows that drawing techniques from ancient Greece actively shaped concepts about the world. He argues that unique Greek innovations in graphic construction determined the principles that shaped the mass, the special qualities and refinements of buildings, and the way in which order itself was conceived. John R. Senseney is an assistant professor of ancient architectural history in the School of Architecture at the University of Illinois at Urbana-Champaign. A historian of ancient Greek and Roman art and architecture, his current and future articles and chapters appear in Hesperia, Journal of the Society of Architectural Historians, International Journal of the Book, The Blackwell Companion to Roman Architecture (edited by Roger Ulrich and Caroline Quenemoen ) and Sacred Landscapes in Anatolia and Surrounding Regions (edited by Charles Gates, Jacques Morin and Thomas Zimmermann).

The Art of Building in the Classical Worldview, Craftsmanship, and Linear Perspective in Greek and Roman Architecture John R. Senseney University of Illinois at Urbana-Champaign

Cambridge University Press Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo, Delhi, Tokyo, Mexico City Cambridge University Press 32 Avenue of the Americas, New York, NY 10013-2473, USA www Information in this title: © John R. Senseney 2011 This publication is protected by copyright. Subject to the legal exception and the provisions of the relevant collective license agreements, no part may be reproduced without the written permission of Cambridge University Press. First published 2011 Printed in the United States of America A catalog entry for this publication is available from the British Library. Library of Congress Cataloging in Publication Dates Senseney, John R. (John Robert), 1969 - Architecture in the Classical World: Vision, Craft, and Linear Perspective in Greek and Roman Architecture / John R. Senseney. Includes references and index. ISBN 978-1-107-00235-7 1. Architectural Design. 2. Architectural Design. 3. Classical Architecture. I. Title. NA2750.S45 2011 722′.8–dc22 2010049728 ISBN 978-1-107-00235-7 Hardcover Cambridge University Press is not responsible for the persistence or accuracy of any URL to any external or third-party website referenced in this publication and does not warrant that all content on such websites will or will remain accurate or appropriate.

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Table of Contents List of Figures Preface Notes on Dates and Translations Abbreviations Introduction: Challenges of Analysis and Interpretation 1 The Ideas of Architecture 2 Vision and Spatial Representation 3 The Genesis of Drawing to Scale and Linear Perspective 4 Architectural Vision Tour: Imagining the cosmic mechanism in Plato and Vitruvius Appendix A Analysis of the design dimensions for Entasis at Didyma Appendix B Analysis of the hypothetical working design for the curvature of the platform at Segesta Appendix C Analysis of the hypothetical working design for the curvature of the platform at the Parthenon Notes Reference Index

List of Figures 1. Pantheon, Rome. to demand 120s 2. Classical Parthenon, Athens. 447–438 a. C. 3. Miron of Athens (fifth century b.c.). Discobolus (Lancellotti Discobolus) 4. Miron of Athens (5th century BCE). Discobolus (Lancellotti Discobolus) 5. Horse and Jockey. Hellenistic, about 150-125 B.C. 6. Sleeping hermaphrodite. Copy by Antoninus (AD 138-192) from a Hellenistic original of the second century a. C. 7. Hellenistic Poetry 8. Hellenistic Poetry 9. Hellenistic Poetry 10. Hellenistic Poetry 11. Leonardo da Vinci (1452–1519). The "Man of Vitruvius," 12. Theater of Dionysos, Athens 13. Caesar's Forum, Rome 14. Whole Proportions in Greek Temples of the Classical Period 15. Temple of Juno Lacinia, Agrigentus 16. Temple of Concordia, Agrigentus 17. Temple of Segesta 18 .Hephaisteion, Athens 19. Hephaisteion, Athens 20. Parthenon, Athens 21. Parthenon, Athens 22. Anta Building, Didyma and East Building, Didyma 23. Hermogenes (3rd and 2nd centuries B.C.). Temple of Artemis Leukophryne at Magnesia-on-the-Maeander 24. Old Parthenon, Athens. Modified by M. Korres 25. Acropolis, Athens 26. Schematic comparison of the typical plans of hexastyle Doric and octastyle Ionic temples with the Parthenon. The symbol of the Tetraktys

31. Temple A, Asklepieion, Kos 32. Temple A, Asklepieion, Kos 33. Hellenistic Didymaion 34. Diagram of Euclid’s proof of a geocentric universe 35. The zodiac as a circular construction with twelve equal sectors for the signs 36. The zodiacal cosmos in rotation according to the Model of Eudoxus 37. The zodiac as a construction of twenty-four parts 38. Tholos on the terrace of Marmaria, sanctuary of Athena Pronaia, Delphi 39. Tholos on the Asklepieion, Epidaurus 40. Circular temple, Rome, here . . . . 100 a.C. 41. The Latin theater described by Vitruvius 42. The six-petalled rosette 43. Diagram of Aristoxenus (4th century B.C.) for the placement of the vessels of resonance in the theater 44. Cycles of revolutions of the moon, the sun and the planets through the zodiac 45. Markets of Trajan, Rome 46. Theatre, Asklepieion, Epidaurus 47. Theatre, Asklepieion, Epidaurus 48. Theatre, Acropolis, Pergamum 49. Greek theater after Vitruvius 50. Lower theater at Cnidus. Modified by I.C. Love 51. Diagrams of Greek theaters with their geometric bases 52. Diagrams of Greek theaters with their geometric bases 53. Theater at Priene 54. Hypothetical Greek conveyor or "curve rule" showing angular divisions of 15 degrees 55. Pnyx, Athens, phase III 56 Pnyx, Athens, Phase III 57. Graphic form of the Analem according to Vitruvius 58. Hellenistic Didymaion 59. Hellenistic Didymaion 60. Hellenistic Didymaion 61. Temple of Segesta 62. Hellenistic Didymaion. Modified by L. Haselberger 63. Parthenon, Athens

64. Proposals for graphic constructions for the curvature of the platform on the north flanks of the Temple of Segesta and the Parthenon 65. Archaic Didymaion. Restored capital 66. Hellenistic Didymaion 67. Stoa, Agora, Kos. Unfinished Ionic column drum preserving the radial construction for the fluting of its Ionic columns 68. Artemision, Sardis. Column detail 69. Hellenistic Didymaion 70. Hellenistic Didymaion 71. Suggested order for flute drums in Hellenistic Didymaion based on design analysis 72. "Rosette-based" method of identifying flutes in a design like the Didyma 73. Didymaion hellenistic. Fountain on the surface of the north wall of the Adyton of Didymaion 74. Hellenistic Didymaion. Plan for fluted columns 75. Hypothetical methods for making twenty equal divisions of circumference for Doric fluting 76. Hypothetical methods for making fluted columns with a protractor 77. The zodiac as a circular construction with twelve equal sectors for the signs; the Greek Theater after Vitruvius 78. Artemision and Agora, Magnesia on the Meander 79. Human form defined by modules of pattern, proportions and geometry as described by Vitruvius 80. Temple of Athena Polias, Priene. Restored drawing of a cornice and incised pediment on a block erected in Temple 81. Temple of Athena Polias at Priene by Pytheos and Temple of Artemis Leukophryne at Magnesia on the Hermogenes Meander 82. Temple of Athena Polias, Priene 83. Temple of Dionysus in Teos 84. Asklepieion, Kos 85. Upper terrace with Temple A, Asklepieion, Kos 86. Temple A, Asklepieion, Kos 87. Shrine of Juno, Gabii 88. Temple of Juno, Gabii, circa 160 B.C. 89. Temple of Juno, Gabii 90. Sanctuary of Aphrodite, Kos

91. Several fragments of the marble plan showing the Porticus Octaviae (Porticus Metelli, renamed and rebuilt under Augustus), Rome, superimposed on modern urban elements 93. Forum of Trajan, Rome 94. Octagon of Nero's Golden House on the Aisle , Rome 95 Pantheon, Rome

Foreword This book examines the importance of Greek thought and construction in the creation of architecture as Vitruvius understood it in the Roman context. Focusing on the central role of Greek drawing practices in terms of scale and linear perspective, he considers the influence that Roman architecture had on Greek architectural and craft concepts. In addition, however, he examined the influence of the tools and techniques of the Greek architects on the classical understanding of the forms and mechanisms of nature and how they are perceived by the eye. Rather than show how classical architecture simply reflects features of its broader cultural context, he attempts to show how the practices of Greek architects actively shaped concepts about the world. In addition to classicists, art and architectural historians, this book is intended for readers interested in the history of philosophy and science, as well as architects who draw inspiration from the classical world. I would like to thank only a small part of those who were directly involved in the realization of this work, and first of all I would like to thank my mentor, Fikret K. Yegül, who not only trained me in ancient art and architecture, but also read the complete manuscript of this book Has. His experience provided the comments, critiques, and insights necessary to elevate it beyond the simplicity of his first draft. Credit for this project goes to Beatrice Rehl, Director of Humanities and Social Sciences Publications at Cambridge University Press. Beatrice's editorial assistant, Amanda Smith, provided invaluable assistance in the creation of this book. My wife, Megan Finn Senseney, read and edited later drafts of the manuscript, enhancing it with her gift of language and mastery of sources like a true information scientist. I would also like to thank the especially thoughtful anonymous reviewers of my manuscript who encouraged me and gave me much-needed perspectives on details and larger questions. The architects Sarang Gokhale and Erin Haglund provided excellent support with my drawings that illustrate many of the points in this book. The ideas in this book have benefited at various stages from discussions with various classicists and historians of art and architecture. james and christina

Dengate has always been generous with his enthusiasm, his comments, and the sharing of sources. Diane Favro challenged my ideas with direct questions. Erich Gruen took the time to meet with me and share his thoughts on the Hellenistic and Roman historical contexts of my research on ancient architecture. Richard Mohr gave me invaluable feedback on my interest in Plato. Robin Rhodes generously discussed the details of my research and invited me to participate in his panel on scale in Greek architecture. David Sansone provided important feedback on my interest in Aristophanes. Phil Sapirstein provided insightful insights and questions about engineering and design, particularly in archaic times. Both in person and by email, Andrew Stewart asked me powerful questions about my ongoing research on Greek architectural design, which led me down several of the paths I took later in this book. Phil Stinson gave me his thoughts and encouragement on a variety of topics. I also benefited from my colleagues who researched historical architectural design in later periods, including Robert Bork, Anthony Gerbino, Raffaela Fabbiani Giannetto, Ann Huppert, and Heather Hyde Minor. In addition to Heather Hyde Minor, this study simply would not have been possible without the incredible support of my colleagues Dianne Harris and Areli Marina. Ultimately, the ideas and approaches in this book are grounded in art history shaped by my amazing teachers C. Edson Armi and Larry Ayres. Any questionable errors of fact or interpretation in the final work are the result of my own disagreement with the helpful suggestions of these eminent scholars. The concepts were also developed with the help of numerous friends and family, including Jonathan Banks, Brent Capriotti, Heidi Capriotti, Barbara Cohen, Lawrence Hamlin, Dan Korman, Geza Kotha, Paolo Maddaloni, Rick Mercatoris, Madhu Parthasarathy, Donna Senseney, Megan Finn Senseney. , Debbie Senseney-Kotha, Kevin Serra, Leonore Smith, Smitha Vishveshwara and many others. Finally, the following awards provided invaluable support to the research and writing of this book: a William and Flora Hewlett International Research Travel Grant; Funding for travel, research grants, partial faculty credit, and image copyrights from the University of Illinois at Urbana-Champaign Campus Research Council; travel funding through the Laing Endowment of the University of Illinois at Urbana-Champaign School of Architecture; and travel financing for two

Separate Creative Research Awards from the College of Fine and Applied Arts at the University of Illinois at Urbana-Champaign. John R. Senseney Heraklion, May 2010

Note on dates and translations All dates are B.C. unless given as AD or in obvious post-ancient contexts like the Renaissance. Classical with a capital "C" specifically denotes the Classical period of ancient Greece (479-323 BCE), while Classical with a lowercase "c" describes Greek and Roman antiquity more generally. An exact or even relative chronology of Plato's works (ca. 427-347 BC) is perhaps impossible to establish with certainty. For the purposes of this study, it is sufficient to consider Plato as a late classical writer of the early to mid-4th century BCE. recognize. and they follow the indisputable chronological order of the Republic before the Timaeus. Unless otherwise indicated, the source is provided in the author's translation.

Abbreviations Abbreviations not listed in this section follow the standard abbreviations established in the American Journal of Archaeology. German Archaeological Institute, publisher (no date). Architectural Planning and Theory of Antiquity. Report on a colloquium organized by the architectural department for construction planning of the German Archaeological Institute (DAI) with the support of the Volkswagenwerk Foundation on November 16-18, 1983 in Berlin. Sedan. Almagro-Gorbea, M., ed., 1982. The Sanctuary of Gabii Juno in Gabii. Italic Library 17. Rome. Hoepfner, W., 1990 edition. Hermogenes and the High Hellenistic Architecture. International symposium in Berlin from July 28 to 29, 1988 within the framework of the XIII. Hermogenes International Congress of Classical Archeology organized by the Department of Architecture of the DAI in collaboration with the Classical Archeology Seminar of the Freie Universität Berlin. Mainz on the Rhine. Vollkommer, R., editor 2001. Lexicon of ancient artists. Kustlerlexikon Munich and Leipzig. Neils, J., 2005 edition. The Parthenon: From Antiquity to Today's Parthenon. Cambridge. Haselberger, L. 1999. Appearance and character. Refinements of classical architecture: the curvature. Proceedings of the Second Williams Symposium on Classical Architecture Refinements, held at the University of Pennsylvania, Philadelphia, 2-4. April 1993. Philadelphia. Geertman, H. and J.J. deJong, editor. 1989. Munus non ingratum: Proceedings of the International Symposium on Vitruvian Hellenistic and Republican Architecture by Vitruvius = BABesch,

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Introduction: challenges of analysis and interpretation When Renaissance architects such as Bramante or Alberti made or wrote about architectural drawings in linear perspective and scale, they engaged in practices and discourses that were already well established when Vitruvius took up his pen at the end of the 20th century. . 1st millennium BCE C. .3 More than just a fact of the design process, the application of geometry to scale drawings, particularly during the imperial period, may have produced precisely the curve- and polygon-based aesthetic that characterizes Roman vaulted buildings, perhaps best appreciated today in the Pantheon (Figure 1). This observation, which is not new, underscores the formative role of small-format drawings not only in the creation of buildings, but also in formative approaches to their production.4 In a direct emphasis on technical determinism, fluidity, and plastic. The potential of Roman concrete can be recognized as the main driving force, which transcended the prismatic shapes dictated by traditional Greek construction with rectilinear blocks. Perhaps we can better understand Roman concrete as the material used to reflect in three dimensions the forms first explored in iconography (the art of the plant), elevation drawing, and linear perspective.6 Recognition of this generative aspect of ancient drawings underline their function as models rather than mere architectural representations.7

1 Pantheon, Rome. 120 d. C. Plan III view with radial pattern of the revelation. Author's drawing, adapted by B.M. Boyle, D. Scutt, R. Larason Guthrie, and D. Thorbeck, in MacDonald 1982: Plate 103.

Of course, the idea that drawing to scale precedes construction does not seem revolutionary. At least until recently, students of architecture generally learned to think of buildings in terms of parts, or the geometric foundations that make up the composition of a whole person and the interrelationships of its parts. This

2 Classical Parthenon, Athens. 447–438 BCE C. Floor plan BC. Author of the drawing, modified by M. Korres, in Korres 1994: Figure 2. The design approach results in a sequential process that directly links the final constructed form to the first moments of small-scale drawing. Scale cannot arise solely from forms of design by architects, but also by institutionalized ways of thinking about buildings. After the first publication of Sir Banister Fletcher's A History of Architecture on the Comparative Method in 18969, historians of art and architecture began to understand works from all periods holistically, through illustrations comparing buildings, through often at a strictly typological level. This type of representation, in turn, often serves to form part of the modern image of a particular historic building. Relatively few introductory level students are lucky enough to experience the Parthenon for the first time while walking outdoors on the Acropolis of Athens, rather than in a darkened textbook or classroom, viewing the temple through a series of small miniatures. black lines (Figure 2). This graphic representation of

a plan then becomes part of a new generation's image of the Parthenon, showing how architectural space is organized in a way that compares or contrasts Iktino's supposed drawing board with that of Brunelleschi, Mies or Zaha Hadid. family and culturally neutral act of universal application in buildings that express very different forms and purposes over time. Focusing on the gulf that separates the tools, methods, and applications of technical drawing in classical and modern architecture, this study examines how craftsmanship conditions vision in the classical world. As an argument, common design habits in architecture and in the sciences became a central element of the unit that in Roman times acquired the designation "architecture" that was passed on to Western building traditions. The formation of order according to artisan tools and techniques directly affected the way the Greeks viewed the structures and mechanisms of nature, as well as their understanding of vision itself articulated in philosophy and optical theory. It is in this context that I present the Greek invention of linear perspective as a reflection of existing drawing procedures and as an influence on the increasing role of scale drawing in the organization of architectural space from the Classical period (479-323 BCE). c.). In this exploration, I approach the Greek theatron—the “place of seeing”—as the first space explicitly designed to shape sight, and highlight the rituals of performance associated with Greek practices of seeing, known as Metaphors of “ theory” itself as a new way of explaining the universe in an abstract and internally coherent way. The resulting "architectural vision" sought to define how sacred and urban spaces were planned through iconography, which in turn grew out of linear perspective in Greek painting. Therefore, this book considers the effects of architecture on classical buildings and worldviews. For good reason, the centrality of graphic representations to scale as an art historical approach in the sense of this book has been questioned in recent decades. Kevin Lynch's groundbreaking sociological study of how Westerners understand their cities as collectives of landmarks, nodes, roads, districts, and edges, proposed an alternative analytical model that corresponds to an experiential level of knowledge that urban architecture it has the integrated nature of Roman architecture.

Cities perceived at eye level by walking subjects responding to partial, oblique, and gradually unfolding views.12 Researchers have sparked interest in the interaction of Roman observers with the everyday experience of their cities through Sequential three-dimensional "armatures" emerging from fragmented aggregations of structures over time, rather than just city plans or individual buildings studied as isolated plans, elevation drawings, and sections that do not correlate with actual perceptions of ancient buildings . This methodology provides a good dose of imagination needed to bring a humanizing sense of life, movement, and even emotion back to the functioning of buildings in antiquity.13 In this way, a new historical narrative has classical architecture in a kind of transposed real space. , enabling the apprehension of its ancient potential to be perceived in time by the senses of the people who lived and moved in it, moved by desire and necessity. Unlike buildings, complexes, and cities, sculptures need not involve a similar degree of moving perspective changes on the part of the viewer. A classic example of rigid frontal perspective, even a dynamic circular sculpture like a mid-fifth-century Roman copy of Myron's Diskobolos (Figures 3-4) disappoints rather than rewards alternative perspectives of the viewer's shifting position. , revealing flattening and imbalance

3 Myron of Athens (5th century BC). Discus thrower (Lancellotti Discus thrower). Roman copy of Myron's bronze original from around 460–450 BC. Front view of the CB. Marble. National Roman Museum (Palazzo Massimo alle Terme), Rome, Italy. Vanni/Art Resource, New York. on the side doing little to break even the static pose of an archaic kouros.14

The processual and developing element of classical architecture gains in importance, especially when it comes to Hellenistic sculpture. A defining feature of Hellenistic art is the extension of the work's inherent dynamism to the viewer's interaction with the work. As can be seen in the bronze horse and jockey from an ancient shipwreck off Cape Artemision, this quality transcends the mainstream view that is usually presented in published photographs (Figure 5).15 The boy turns his gaze to an unseen opponent , with whom he appears to be running head-to-neck, head-to-neck towards a "photo finish", with his horse dedicating every muscle, fiber and vein to the momentum and energy of the final push. Regarding the height of its original location and its accessibility,

4 Myron of Athens (5th century BC). Discus thrower (Lancellotti Discus thrower). Roman copy of Myron's bronze original from around 460–450 BC. Side view of the CB. Marble. Museo Nazionale Romano (Palazzo Massimo alle Terme), Rome, Italy. Vanni/Art Resource, New York. It is not known how this work relates to the perspective of ancient observers, but it seems unlikely that it would differ significantly from its current display at the National Archaeological Museum in Athens. Driven by curiosity, the engaged viewer may be drawn to a frontal view where the

The effect of the horse's speed can be felt with adrenaline-pumping intensity and, indeed, at personal risk. only a sculpture internalizes the experience of the viewer by breaking the space that otherwise separates the viewer from the work, somewhat in the manner of Diskobolos. Perhaps one of the most daring Hellenistic expressions of vision in motion centers on Roman copies that depict a far from dynamic figure (Figure 6). Seduced by the erotic qualities of the sleeping figure, the experience that unfolds

5 horses and jockey. Hellenistic, around 150-125 B.C. Side view of the CB. Found at Cape Artemision, Greece. Bronze. Restored horse racing parts, modern tail set. National Archaeological Museum, Athens, Greece. Vanni/Art Resource, New York. Seeing the male genitalia of a hermaphrodite provokes bewilderment and amazement, "a typically Hellenistic theatrical surprise."

The gradual, spatial, and temporal qualities of the classical view show a kinship in the various sculptural and architectural media that seem to emerge in the Hellenistic period.

6 sleeping hermaphrodite. Antoninus (AD 138–192) copy of a 2nd century BC Hellenistic original. C. BC Rear view. Marble. Museo Nazionale Romano (Palazzo Massimo alle Terme), Rome, Italy. Vanni/Art Resource, New York.

Architectural design and invention Beyond this very general classical context, however, there is a significant difference between the creative methods that produced the visual experience in sculpture compared to architecture. In this sense, the special case of architecture is reduced to fundamental questions of definition. Strictly speaking, architecture as an institution in its own right, as Vitruvius acknowledges, is difficult to isolate in ancient Greek culture during the Hellenistic period. In ancient Greek, the construction techne as a category with its own nominal designation (κ δ μικ) seems to have suggested the art of the architect in the sense of “master builder” (κ δ μ).18 Vitruvian architecture, a Hellenized Latin term of the late Republic, rather carries the explicit authority of the architect in the sense of "master craftsman" (ρχιτ κτων). the greek

Adjective 'architectural' (ρχιτ κτ νικ), describing not only the art of the builder (Plato Statesman 261c; Aristotle Politics 1282a3), but also the concept of authoritative mastery, at the service of the people and processes it dictates. For Vitruvius, architecture consists of a set of Greek concepts, given mainly by Greek terms with which Hellenistic builders before him would surely have identified (De architectura 1.2.1–9).20 Despite the close ties between builders and sculptors,21 these concepts are closely related to drawing and would presumably represent an important difference between the arts of construction and sculpture. In addition to financial and natural resource considerations, the architecture consists of a graphic ordering process based on a modular quantity approach and a design process in terms of a correct graphic placement in accordance with the whole of the work. Finally, the principles of pleasant form and modular adequacy that these design processes contribute to form the architecture. As indicated in Vitruvian's definition of architecture in terms of what it is, it may be important that architecture be fully identified with planning issues. More specifically, these processes and principles are embodied in three approaches to small-scale drawing: ichnography (the planes of art), elevation or orthography, and linear perspective. This reliance on graphic representation obviously differs from the classical sculptural process, which uses a variety of models and forms. models In Vitruvian architecture, the three-dimensional construction of buildings, which convey the qualities and principles sought by the architect, occurs through a monumental imitation of the authoritative vision of the architect as a graphically constructed idea (De architectura 1.2.2 ). Notwithstanding the observable similarities in the unfolding of the spatial and temporal spectacle created in classical sculpture and architecture, the process by which this visual and kinesthetic experience was formalized is different. However, it is not simply different in terms of the nature of a particular medium. Rather, the different design process is central to what architecture consists of at the time of its first institutionalizing definition in Vitruvius's writings. Appropriation of graphic construction as a domain of cogitatio (analysis) and inventio (invention) to model

of space according to good form and number (De architectura 1.2.2) has important implications for the classical understanding of seeing itself. As the present study suggests, technical drawing and performance were linked in a way that had a profound impact on the awakening of consciousness an individual discipline and separate from architecture. In addition, this study explores the relationship between drawing, seeing and the birth of theoretical philosophy as an internal vision associated with knowledge ("insight"), the ways of visualizing nature and even the very nature of seeing. or multiple unified perspectives on the experience of Hellenistic sculptural works such as those cited here (Figures 5, 6) could well represent a plastic exploration of a notion found first in Greek drawing as an activity and later as an integral part that was labeled with "the architecture".

Vision, Philosophy and the Art of Building Vitruvius' description of architecture suggests an important link between design and the experience of knowledge and vision. According to him, the Greek term is ideal for the three types of small-scale drawings that define design (ichnography, elevation drawing, and linear perspective).23 These drawings therefore have the same term (δα) that Plato uses in his famous Theory of Forms to describe the transcendent ideas underlying objects in the phenomenal realm, seen internally by the rational mind and not externally by the eye.24 In other words, there seems to be a correspondence between A) the idea as a graphical construction in contrast to the materialized construction that imitates it, and B) the idea as an immaterial object that imitates the material object. This constructive and philosophical correlation between the graphic and the transcendent (or 'mental') image, together with an etymological connection between idea and vision (δν, aorist infinitive of ράω), extends, as in Marsiglio, through the centuries until Ficino's Early Modern Age. Neoplatonic Thought Commentary on Plato's Banquet in the 15th century AD: From the first moment the architect captures reason in his soul and broadly speaking the idea of ​​the building. He then he makes the house (the best he can) as it occurs to him. Who will deny that the house is a body? And that this is very similar to the incorporeal

Handmade idea in imitation of who was made? Certainly it must be judged more by a certain incorporeal order than by its matter. 25 As Heidegger points out for Kant's critique, the association between pure reason and architectural design is, however, explicit in the notion of the "internal structure" of a building as a projection of the rational graphic construction of the building plan. 26 It doesn't have to be. it would be unfounded to consider the existence of a parallel and interdependent "architectural idealism" with philosophical discourse in the Western tradition, going back to Plato and the architects of his time. According to this understanding of the Platonic model, the privilege of drawings as fixed and eternal ideas seems to suggest to them a higher ontological status than their imitations as corporeal buildings that underlie their always incomplete, unfolding and multi-perspective experience. To approach the experience of buildings again sculpturally, Plato himself offers some reflections on the matter. In his discussion of mimesis in colossal sculpture in the Sophist (235d-236e), he mentions an older way of recreating "the approximations of the model" (τ τ παραδ γματ σ μμ τρ α, 235d) to "assure the true approximation of beautiful shapes" (τ ν τ ν καλ ν λη ιν σ μμ τρ αν, 235e). This ancient method and its beautiful result contrasts with the spirits of its time, altering its proportions to give a more correct appearance to the height of the eyes of the beholder. J. J. Pollitt correctly links this distinction of an older and newer style of carving with a first-century reference by Diodoros Sikeliotes, who distinguished between the Egyptian method of working by a formula of proportion and the Greek interest in approximating to visual appearance.27 Another suggestion that the evidence this time from studies of Egyptian rather than Greek art is that Plato's idealism, as articulated in the Allegory of the Cave (Republic 514-517), has parallels with the natural hieroglyphic piece of art, possibly reflecting the view that characters in Egyptian writing, sculpture, and painting serve as archetypes uniting eternal essence and appearance. As such, Egyptian imagery denies the partial or multi-perspective view of reality in a way that anticipates Plato's devaluation of visual appearances as shadows on a cave wall, and locates knowledge in the immutable idea grasped by the mind.

The implications of these connections for art and philosophy raise questions for architectural ideas. As rationally fabricated geometric shapes with no three-dimensional presence, did the Greeks consider scaled architectural drawings to correlate with Plato's archetypal ideas with their intelligible, immaterial existence? Could these designs rank higher for Greek thinkers and architects than their imperfect and derivative appearances in the physical world, as Ficino suggests for ideas during the Renaissance? In contrast to the sensory experience of buildings and cities emphasized by more recent studies of ancient architecture, Vitruvius' description of ideals and related passages reflects part of Greek architectural theory, which in contrast emphasized geometry, proportion, and modular adequacy that graphically set in a flat, planar realm far removed from vision embodied in three-dimensional space? In addressing such questions, an important caveat in correlating philosophical idealism and architecture is that it is best to properly understand the former before examining its purported implications for the latter. If Vitruvius' witness to drawing as an ideal is supposed to reflect a Plato-dating tradition of leveling architecture according to a supposed privilege of graphic construction, care must be taken not to level Plato in the process.29 However , Plato's leveling may, in fact, to be an unwanted, albeit longstanding, stand-alone project whose principles are poised to help reduce architecture to intellectually oriented graphical exploration. Vitruvius's discussion of ideals as products of a highly rational process involving numbers, calculus, and geometry seems to recall Plato's emphasis on arithmetic and plane geometry, the latter serving as a means of directing the soul's vision to the idea. that good is eternal (República 526e, 527b). However, the experience of this type of vision is not only a rational grasp of abstract relationships and archetypal forms drawn with a compass and straightedge. A recent study by Andrea Wilson Nightingale assesses Nietzsche's critiques of classical philosophy by postmodern and contemporary thinkers and challenges the reiterated claim that classical thought involves a kind of objective knowledge that is directly and universally accessible to the mind, free of constructions. cultural and emotional Factors.30 The existence of Plato's ideals as objects of truth, unifying essence and appearance, fully available to the subject regardless of perspective, certainly bears resemblance to his

he privileges flat geometry, the two-dimensional realm of architectural design, and the timeless, objective Egyptian hieroglyphs presented frontally on the flat surface of a tomb wall. But in the allegory of the cave only the shadows are flat, seen through the eternally fixed panoptic perspective of the captivated spectators: a play of shadows as perverse spectacle. Breaking free of its chains, the philosopher's journey toward truth is anything but mere intellectual contemplation. Rather, it is highly emotional, erotic, and driven by lust.31 Leaving the cave and returning, the philosopher experiences pain and irritation, rising and falling, narrowing and expanding space, and even temporary blindness due to the contrasts of darkness. . and light. More than the distant thinker of the Modern Age

7 Hellenistic Didimaion. Go up towards Stilobato. Author of the photo. A figure like Descartes, Plato's philosopher, can think of the inhabitant or visitor to ancient Athens, or even any city at any time, and pave the way.

among monuments, huts, shops, taverns and temples to find food or drunkenness, seek physical satisfaction and company, confront and see the divine. The difference between the internal effort of the philosopher and the wandering of non-philosophers is not a degree of experiential awareness during the progression of the movement. Rather, it is the supreme level of emotional intensity that drives and shocks the philosopher when he meets his intended goal: the state of tauma as a kind of awe or overwhelming wonder and bewilderment.32 Ultimately, it is not a panoptic or frontal view. . , which confronts in the form of a flat hieroglyph or elevation drawing, but only a partial vision of an individual perspective, depending on the preparation and purity of the viewer's soul.33 Beyond the sensual experience in Roman urbanism Already well analyzed by others , a similar spirit is expressed in the Hellenistic architectural conception.34 To cite just one example, the Hellenistic Didymaion is a masterpiece in terms of sensitivity to manifest transitions towards the sacred. The tour begins with an ascent up the front staircase to the high stylobate (Figure 7), where the warmth and brightness of the sun are left for the shadow and density of the 'forest of columns' that rises 20 meters to the ceiling. From this transition space, continue straight through one of the two vaulted passages (Fig. 8). Now progression becomes descent as space transitions from outside world to outside world.

8 Hellenistic Didymaion. View from the Stylobate of the North Passage to Adyton. Author of the photo. The density of the portico narrows, the body is now wrapped in the coldness of the marble, and the view is left in almost total darkness, except for the backlight (Figure 9). Once the ground is reached, the transition is a sudden and dramatic burst of blindingly hot light as one enters the Holy of Holies,

9 Hellenistic Didimaion. Looking down the North Passage to the Adyton. Author of the photo. the adyton or inner sanctuary open to the sky (Figure 10). Here, as the eyes adjust to the bright light of the sacred space, he is confronted with the divine, albeit in a vague way and indirectly experienced through an oracular message. The variety of perspectives of this type of wandering is, in turn, characteristic of sculpture. In Plato's Phaedrus, Socrates makes an analogy of desire with a horse race which, when confronted with the face of a child as the object of desire, causes the driver to pull on the reins and stop suddenly (254b-c). In the Horse and Jockey Diagram (Figure 5), the thrilling sense of wonder and fear confronted with frontal perspective may remind us of the same passage (254b) where Socrates, in the vision of beauty, describes fear and fear. fear that affect desire and make it fall. backward. Like the spectator of Hellenistic sculpture, the charioteer remains motionless. In this relationship, it is the boy who

the being is projected forward through a flow of beauty captured by the eyes of the one who desires. The lagging behind position is also the “looking up” position described in the Republic (τ νω ρ ν, 529a), which metaphorically represents the “correct” contemplation of beauty through geometry (527b) or astronomy. (529a). It is also the position of reception that Socrates metaphorically describes as the copula that leads to the birth (γ νν σα) of reason and the truth that leads to knowledge (490b). Speaking of the horses and the boy in the Phaedrus, Socrates curiously characterizes this experience of earthly beauty as a statue whose luminous emission reflects the idea of ​​beauty (251a, 252d), allowing the viewer a distant memory of the pre-experience. embodied soul of ideas, displayed as cult statues in a sanctuary (254b). To be clear, I am in no way suggesting that some Hellenistic sculptor or patron had any intended correlation between the horse and rider and Plato's texts. Instead, I bring text and image together to offer a culturally relevant reading of this sculpture, acknowledging that his experience, ancient and modern, can never be reduced to a set of textual references. At the same time, and more importantly for the present study, I hope to illustrate the qualities of the experience of seeing described by Plato and its relation to knowledge and spirituality. In this way, one can begin to approach the role of geometry and astronomy in a particular perspective relevant to the question of the ideal in the realm of art and construction. Pollitt's characterization of the developmental experience of the sleeping hermaphrodite (Figure 6) as a "theatrical surprise" is a particularly suggestive observation for the classical understanding of visual experience. is that this work "can express a complex psychological and philosophical vision of the psyche, the Platonic idea that on a spiritual plane the natures we call feminine and masculine become one."

Hellenistic 10 Didymaion. View of the Naiskos from Adyton. Author of the photo. and later in this book, this interpretation is compelling and relevant to the theme of theater as a kind of Greek visual experience that generates truth and knowledge. with the "truly real" and the subsequent birth of intelligence and truth - is particularly significant because it is based on a more originally related metaphor. By this I mean a way in which, in esoteric thought, the primary metaphors themselves can generate additional metaphors that reinforce the essential image. In this step, the message becomes extraordinarily subtle and requires careful consideration of the nature of things like gender and sexuality outside of their usual cultural associations. As an analogy, it may be helpful to recall the Tao Te Ching, the ancient Chinese sacred text that invites the reader to open up to the Tao, a linguistically indefinable force or presence.

expressed through the flow metaphor. This metaphor is enriched with yin, the feminine principle associated with earth, darkness, and cold, and yang, the masculine principle associated with sky, heat, and light.38 It would not make sense to make this distinction in relation to constructions. cultural thinking about gender roles. Rather, there is something poetic and primal at play in that both the sage and the earth embrace yin and play the role of a woman, "the spirit of the valley" who lies still and deep and opens to the flow of the Tao from within to inside. receive... to produce the universe.39 As with yang, there is a repeated metaphor in Plato of a creative flow of light. However, the idea of ​​the good is not limited to illuminating the intelligible realm. It also gives birth to the sun in the phenomenal realm. Likewise, the philosopher must maintain a flow of ideas to give birth to truth through his own actions in daily life. As in the unfolding vision of the sleeping hermaphrodite, the desire that drives the person must finally cease and give way to the reception of the idea that plays both roles. However, for both Plato and the Chinese text, the gender metaphor of emission, reception, and birth refers to a primary metaphor, rather than adding a new concept that must be considered separately. In both cases, the metaphor on which the act of receiving love rests and builds is that of flow, which at least for Plato is a feature of seeing. In other words, Plato does not discard the metaphor of seeing in favor of copulating once the ideas are found. The active journey of the soul, driven by eros from the process of conception and development, leading to the idea of ​​the good, must imply a passive and paralyzed reception of its flow.40 However, the colored sexual character of this encounter remains what Plato calls "the Vision of the Soul" (τ ν τ ψ χ ψιν, Republic 519b). Like seeing beauty in the realm of appearances, it is an intrusion into the eyes, which also occurs in the "eye of the soul" (τ τ ψ χ μμα, 533d). The sex metaphor, therefore, heightens the reader's awareness of the experience of seeing and reinforces the eye's dual function as an organ, going in and out like the dual parts of the hermaphrodite. For Plato, the light of the inner eye flows and merges with the light of the outer world in one body (Timaeus 45b-c). In this way, seeing implies an intimate and even tactile relationship between the subject

and object This experience in the phenomenal realm is similar to the encounter with the intelligible ideal, but for Plato the metaphor is reinforced by a particular institutionalized activity. The way we talk about "theory" originates from Plato's metaphor of theoria, the journey of a theoros, or envoy, to see performances related to religious festivals in another city-state and then return home to tell what had happened. seen, 41 as well as in the allegory of the cave, where the escaped prisoner, upon seeing the light of the sun, recounts his experiences to his fellow prisoners still trapped in the dark, rather the inner journey of the philosopher, the which culminates in the vision of the ideal, his generation of knowledge and truth, and returning home to describe his experience. Significantly, however, this ideal and intimate experience of the ideal is beyond the reach of incarnated philosophers in the world, including Socrates. The real philosopher in the world (as opposed to the ideal philosopher) can only achieve, at best, a partial vision of the ideal. In his dialectic, therefore, Plato makes extensive use of analogies and metaphors borrowed from the phenomenal world, and writes in a way that the reader can relate to through common experience. A tantalizing reference in The Republic (529c-e) suggests that the philosopher should treat spinning astral bodies as paradeigmata ("patterns"). As a paradigm, they are comparable to what one would see "if one were to find diagrams (διαγράμμασιν) drawn and worked with precision by Daedalus or some other craftsman or painter". approaching transcendent reality through sight, even if such models cannot embody truth itself in the phenomenal realm. In the later Timaeus, Plato describes the cosmos as the creation of a divine craftsman according to a paradigm (28c-29a), again in the terminology of construction and painting. In this study I argue that Plato may have drawn a second metaphor for craft, the idea which, except in the late Vitruvian text, remains largely untested due to the decline of Greek architectural writing. Plato relates the term to the trade (Republic 596b), but in the construction trade it acquires a special meaning as an object susceptible to design.

convey the architect's vision to be realized on site by various craftsmen. What made Plato's metaphor (rather than invention) of the idea significant was that these architectural ideas were related to cosmic order through an affinity with astronomical diagrams, for reasons I will understand later. In this kinship, these two uses of drawing, architectural and astronomical, emerge together as an expression of the order created by existing engineering drawing tools and practices first explored at an earlier stage in building design and construction. . Whether as iconographies, spellings, perspectives, or even graphic images of the spinning mechanisms of the cosmos, for Plato these drawings would have presented to the eye beautiful if distant imitations of the underlying sense of order that the divine craftsman, metaphorically speaking, created in the universe. Echoing this view in Plato's discussion of the philosopher's ideal encounter with ideas, seeing itself is a metaphor for a kind of direct, complete, and penetrating contact with ultimate transcendent realities. By visualizing and imitating this geometric order of the cosmos in one's embodied body in the physical world, one raises one's vision of the soul in the manner described above in preparation for receiving the ideas. Finally, the metaphor theoria expresses the entire sequence from the journey to ideas to the account of that experience. The following chapters trace the genesis of "theory" in the combination of knowledge and vision, which was first realized in architecture for theater rituals. More specifically, this connection belonged to what would come to be called 'architecture' in the late Republic at the end of the Hellenistic period, but which began as a turn towards a type of construction oriented towards representational space through reduced drawing. Technical drawing as such was a common practice of architecture and other crafts, astronomy and geometry, and the related field of optics, and together these fields formed an inseparable network of instruments, methods, and representations that visually determined order. of the world. . Terms. Through this development, architecture broadened its focus from massive sculptural representations to spatial constructions as three-dimensional projections of principles of order or ideas explored with ruler and compass: axes, radial lines, circles, archetypal polygons (Pythagorean triangles, squares, and squares) , other equilateral shapes) and so on. In the age of architecture in the Roman world, these ideas of order became

they eventually became formal principles that defined the spatial experience in three dimensions in ways previously unimaginable. Rather than simply maintaining form, ideas became forms in the concrete sense when Roman architects mastered opus caementicium as a medium whose fluidity could emphasize the curvilinear and polygonal character of straightedge and compass drawing. Without doubt, this development represents a uniquely Roman creative achievement, which was anything but a mere plastic translation of earlier Greek graphic practices, and it is far from my intention to claim the primacy of Greek culture in what could be said to be the invention of the possibility of a European era. architectural tradition. Nor is it within the scope of this brief study to examine any aspect of this "Roman architectural revolution", a subject so admirably treated long ago by the Greeks that it can be compared to Vitruvius' criticism of the Greek architect Pytheos, who created the own work of the. with the reasoning, ratiocinatione, on which he relies. Following Plato's adaptation of the term theoria, this reasoning is the vision and presentation of ideas shared by many disciplines, underlying the actual production according to the capabilities of a single discipline. As Vitruvius explains: ... Astronomers and musicians discuss certain things in common: the harmony of the stars, the intervals of squares and triangles, that is, the [musical] intervals of fourths and fifths, and with geometers they speak of see. which in Greek is logos optikos, the science of optics, and in the other disciplines many - or all - things are common knowledge as far as the argument is concerned. But as for the creation of works brought to an elegant conclusion... that is left to those trained in the exercise of a single skill.45 (De architectura 1.1.16) The perimeter, polygon and polyaxial geometry that drove the design of Greek and Hellenistic buildings and complexes were theoretical, existing as support for the reduced form in the area of ​​the drawing board. With the important exception of the Greek theater, this style of design, which also shaped technical design in astronomy and optics, only "came to an elegant conclusion" in the Roman Imperial period with the aid of concrete, a liquid medium that builders they could throw in the environment,

monumental shapes that reflect drawings produced by manipulations with a compass and ruler (as in Figure 1). Moreover, the genius of Roman architecture implies not only a new kind of spatial experience, but also a new kind of institutional space in the invention of architecture itself as a separate sphere worthy of the Emperor's attention (the Ten Books of Vitruvius are offer to Augusto) . along with astronomy, music, geometry, and the related field of optics and other similar disciplines. Regardless of whether Vitruvius intended to improve his own position and that of the architectural profession through his detailed theoretical description of architecture,46 there is one additional possibility that I will examine below. This is the possibility, what it means, that the theory itself arose as a set of ideas that could be shared across disciplines: that these ideas or principles were captured as an ideal with an explicitly visual nature, a claim to be alien to them. he can be consoled by the realization that the ideas are related to what it means to see (δ ν) and that this vision was discovered largely through drawing for the purpose of building. To be explained in the present study, thea (seeing or spectacle) acquires a "theoretical" quality through a vision of theoria (vision of truth through a messenger) according to geometric and optical models that first appeared. in the graphic planning of the standard architecture. of theatron (the place of sight) as early as the fifth century. Among the many implications of this circumstance is one that would doubtless have been forgotten long before the first century, art. In the construction of this theory, Vitruvian's elevation played a part in the actual emergence of the theory. Perhaps most importantly, the ideas of the Greeks, described by Vitruvius as nature and the underlying buildings (Figure 11), became enduring figures to be reinterpreted throughout the history of Western visual culture. More than that, they shaped the notion of architecture and the transformation of the built environment that gained prominence in the Roman Empire. As I explore later in this book, this reformulation may have begun in the classical period of the fifth century and, centuries later, laid the foundation for a complete reformulation of the architectural vision of space (Figure 1). Exploring the subject of Greek technical drawing, then, means engaging with the transcendent guiding principles that governed the conception and construction of Greek spaces and the experience of seeing oneself, including linearity.

Perspective. Penetrating into such an unlikely realm requires detailed analysis and synthesis of different types of barely surviving evidence (metrological, mathematical and textual) from different contexts associated with different types of buildings that hold the potential to shed light on a separate disembodied process. of us. . connected to us for two millennia and little more

11Leonardo da Vinci (1452-1519). The "Man of Vitruvius" defined by modules of pattern, proportions and geometry as described by Vitruvius (De arch. 3.1.2-3). Academy, Venice, Italy. Alinari/Art Resource, New York.

than our common humanity. More than a description of evolving approaches to architectural design, our recovery of even a semblance of this process allows us to engage with a fundamental change in the perception of form that would alter the classical experience in sacred and urban settings. With this in mind, I propose what may seem improbable to some in order to approach the subject of geometry in classical architecture. Geometry and classical architecture can evoke a

12 Theater of Dionysus, Athens. Started around 370 author of the photo.


View of the Acropolis.

Characterized as "cerebral". It is commonplace to see how Mannerism or the Baroque introduced unexpected combinations of elements or fusions of media (architecture, figurative sculpture, stucco, painting, etc.) and formulas from the classical tradition into early modern architecture. As for the ancient material, we have no evidence, with the exception of later antiquarian references and descriptions, of how the Greeks of the classical period generally responded to the crystalline perfection and subtle refinements of the stonework in a building like the Parthenon.47 We I meet such monuments individually with polite admiration or respect,48 it is not

It is hard to imagine that the vast majority of classical Athenians and visitors would react to these new forms in a way that tended toward the former. The earliest associations of such viewers with geometry would not have been simply arcane theorems and diagrams, but rather the general details and forms of the building itself, from the fluted columns of the Erechtheion to the unprecedented, sinuous, monumental curvature of the Theater of Dionysus. . (Figure 12). Plato's emphasis on the beauty of geometry, discussed in Chapter 1, may indicate that such forms in the built world were not only "rational" but also deeply moving expressions. According to the forms that he analyzes in this book, the geometric form, which has its origin in architecture, could have allowed Plato to glimpse a glimpse of cosmic order, which as an object of contemplation leads to the confrontation of the spirit with the divine. . Geometry in the sacred space of temple, theater, or (in Plato's writings) the architectural product of the cosmos itself was arguably anything but cerebral, and there is little justification for treating it as somehow remote from our interests. broader humanities. . . in philosophy and art.

Target group, structure and approach There are, however, analytical challenges such as B. an interdisciplinary investigation that requires the reader to deal with different types of evidence. By making consistent connections to the history, philosophy, and science of art and architecture, the audience for this book will be diverse. While primarily intended for historians of art and architecture and classical archaeologists, it will also appeal to a wide range of classical scholars and students interested in the history of philosophy and science, as well as architects interested in the classical world. In today's interdisciplinary environment, there is notable overlap between these fields, and students who are primarily concerned with visual objects are generally just as comfortable with texts as classical literature students with works of architecture, sculpture, and painting. . However, the challenge of considering these different types of evidence is real, and by providing a detailed analysis of buildings and texts, the following chapters truly address two separate investigations that have traditionally been the domain of separate disciplines. in the house

For readers who may be equally familiar with both approaches, there is also always a matter of bias for the individual reader, who sometimes fluctuates back and forth periodically. The implications of this study for art and thought therefore require accessibility for readers with different habits and inclinations. This is particularly the case in Chapter 1, where in-depth analyzes of buildings and texts infer connections between architecture, philosophical inquiry, optical theory, and cosmic representation that cut across a nexus of Greek cultural productivity, creating the possibility of architecture as defined by Vitruvius was defined. As these connections form the basis for the rest of the book, limited technical terms and numerous illustrations accompany discussions of buildings, and the extensive use of parenthetical translations allows for a critical examination of the analysis presented. The heavy emphasis on buildings and text in Chapter 1 needs clarification. As I hope is clear, an analysis of the material evidence in the first part of this chapter causes a turn to the literary sources. This transition is far from perfect. However, the evaluation of texts opens up new approaches to the analysis of buildings and radically changes the questions about architecture and the other types of evidence that are required to address classical architectural theory and practice. At the end of the book, a digression examining the evidence from Plato and related sources for our understanding of classical architectural drawing complements the arguments of Chapter 1. In Chapter 2, I identify the historical connections and technical drawing practices shared by Greek craftsmanship. . Construction, astronomy and optical theory. Furthermore, I discuss how these three areas provided important precursors to the roles of craft, astral movement, and vision in Plato's metaphorical discussions of truth. More importantly, this chapter argues that Plato's use of the term idea in the metaphysical sense may actually have followed an existing non-philosophical application of the term along with reduced architectural drawings that predate Vitruvius. Based on a reading of Aristophanes, I evaluate the textual evidence of the invention of linear perspective as a backdrop to approach the reformulation of the Theater of Dionysus in Athens. I also interpret the implications of what can be learned from Greek drawing in the service of

Painting and Construction for our understanding of the metaphors used by Plato in his Republic. Chapter 3 examines the invention of small-scale architectural drawing as a descendant of traditional practices of single-element full drawing, the techniques and principles of which influenced drawing and the associated modeling of orders on craft and engineering diagrams. Building on the discoveries and theories of Lothar Haselberger, to whom this research is indebted, Chapter 3 identifies two dominant approaches to protraction by engineering drawing, one for entasis and curvature refinements and one for columns, and how to explain the relationship between them is . As part of this projection of the practice of discrete feature design into an expansive architectural space, I advocate a simple design apparatus in which the primary application of compass and straightedge has evolved a third indispensable tool, the "curved ruler" or protractor. , which extends graphics . Algorithms in the field of vision as a principle of protraction. The resulting invention of linear perspective for theatrical landscape painting is then evaluated as a tool after which the same projection of visual rays into space now shapes architecture through ichnography. Chapter 4 looks at how repeated drawing habits in architecture have created new ways of looking at nature, which in turn have changed the way buildings and environments are formed. The focus of this chapter is on the writings of Vitruvius as a reflection of the Greek theory of design applied to the iconography of Hellenistic sanctuaries. The center of this analysis is the “Vitruvian Man” (Figure 11) as a model for iconography in the temple design process. Chapter 4 also provides further support for my suspicion that reduced architectural designs arose from repeated design practices in the geometric construction of architectural elements and refinements. This final chapter concludes with the subsequent application of iconography to architectural ensembles, configuring both complete environments and isolated buildings. Exploring this latter approach to design would be of great importance for the future development of architecture in the Roman context. Caesar's Forum (Figure 13) initiated the Imperial Forums, perhaps representing the culmination of ongoing Axis and closing trends,

Completing the transformation of Rome in a succession of porticos that extend from the Circus Flaminio and the Field of Mars to the center of the city. other than that

13 Forum of Caesar, Rome. It started after 48 B.C. Restored plant. Original design, modified by C. Amici, in Amici 1991: Plate 160. In addition to the curvilinear and polygonal aesthetics made possible by Roman concrete, these porticos also bring potential for the construction of space that first appeared on the Drawing Boards. explored by architects in Greek Language World. Once again, creativity in applying such approaches to design in a Roman urban context to specifically address Roman needs was more of a Roman phenomenon than the inevitable telos of an originally Greek practice. On the contrary, the very institution of architecture, capable of its own set of images and the Vitruvian corpus theorizing them, is a Roman invention. However, tracing the underlying threads of Roman architecture through graphic considerations of its Greek genesis involves immense interpretive challenges that go beyond even the paucity of surviving Greek architectural drawings and writings. Instead of remaining connected to each other and to the meaning they generate, these threads are lost in torn fragments that are scattered and buried in a varied landscape. Nor does this dilapidated state result solely from the destruction or falsification of evidence over time; In the realm of art and thought, even well-preserved evidence rarely, if ever, leaves clear traces of the intended influences that creators and writers actively or consciously draw on for their own expression. Furthermore, our interpretations are open to the dangers of anachronism in the study of architecture at a time when builders lacked our post-Vitruvian (much less postmodern) conception of the canon of their methods of production. However, given all these pitfalls and many others, perhaps the biggest challenge in role-playing is actually role-playing. I submit that recent studies of Greek buildings and the evidence of their architects' design processes have simply been too strong and the material itself too important not to attempt to reconnect the broken threads in their interstices to penetrate what Romans like it. Vitruvius may have seen in this the possibility of architecture: a discipline that relied on drawings as a guiding principle to create a sense of order in the built world, similar to the sense of order built in the cosmos.

1. Architectural Ideas This chapter discusses how temple buildings were created during the Archaic and Classic periods. Moving through the challenges of understanding building construction processes before the Late Classic in the fourth century, the following observations and arguments direct you to specific design problems in standard and innovative temples. As a result of this research, this chapter particularly emphasizes the contradiction between natural vision and the abstract concept of ichnography.

Drawing on a reduced scale Since the relationship between scale drawing and architecture is also natural to us, we cannot expect the same case to occur in Hellenic architecture. For materials from the pre-Hellenistic period, there is no scholarly consensus as to whether Greek buildings were products of scale drawings.1 Vitruvius' writings reflect an understanding of architectural drawing as held in the Hellenistic world, but beyond that of writers not architects. like Plato and Plato, others lack evidence of the planning methods common to architects of the classical period and earlier.2 Metrological and proportional studies confirm the difficulties in recognizing classical temples as products of scale drawings. The relatively recent critique of earlier scholarly assumptions about the design process (in regards to architectural writing) in the poorly documented fifth century helps us to see that the temples of the classical period were expressions of an extremely rational planning process, and the focus need not have been graphical exploration on the drawing board. Instead, the process seems to have been largely driven by integral number relations translated arithmetically.

14 whole number ratios used in classical Greek temples. Design author based on an analysis by D. Mertens and adapted from Mertens 1984b: Figure 1. in metric specifications. Temple after temple, the architects repeated the shared proportions that produced the visual forms of the individual elements, the relationships between the elements and the general features, such as the rectangle of the façade defined by the selected features, which required irrational proportional relationships rediscovered by individual architects through drawings or models (Figure 14). ).5 These integer proportions are found in several examples from the Archaic and Classical periods, both in elevation and in plan, in Magna Graecia (Figures 15 and 16) and mainland Greece, suggesting that a widespread method of design involving the small-scale drawing to make superfluous.6

Another caveat to the display of reduced-scale designs in pre-fourth-century temples stems from the realization that the integral proportions underlying a building like the Temple of Segesta (Figure 17) is not an ancient method of producing a design that represents an obligation. seek. It does. Mark Wilson Jones correctly distinguishes between visual and schematic proportions, adopting and repeating the latter more for convenience in the design process than for its experimental qualities.7 This distinction finds more support

15 Temple of Juno Lacinia, Agrigento. Here. 455 BC Plan showing a 4:9 integral ratio between the width and length of the stylobate. Design author, modified from D. Mertens, in Mertens 1984b: Figure 3. where classical building locations require special design considerations for the viewing experience. As in the Temple of Segesta and many other contemporary examples, the integral relationship guides the design of the elevation of Hephaestus in Athens. A ratio of 1:3 establishes the level of order in terms of the distances between the centers of the columns, and for the main rectangle of the façade a ratio of 1:2 (Figure 18).8 Due to the limited space of the location of the temple however, only oblique views of the façade are possible at the eastern edge of Kolonos Agoraios. From this restricted perspective, it turns out that only four metopes are engraved on the eastern end of the flanks (Figure 19), suggesting that the main view of the temple is from the front, and therefore from the plane of the agora occupied below. . 9 This perspective, however, creates a vertical compression, changing the visual consistency with the proportions of the whole number.

16 Temple of Concordia, Agrigento. Here. 435 BC B.C. Plan showing integral proportions of 3:7 and 1:2 between the width and length of the stylobate and the inner cell, respectively. Author of the design, modified from D. Mertens, in Mertens 1984b: Figure 3. In the Parthenon, the 4:9 ratio of the main rectangle of the façade acts on its eastern front but not on the lower point of view of the “first good view”. of the Parthenon” below the great steps on the terraced level of Chalcotheke to the west.10 The clear view from the still lower vantage points of Propylaia or Pnyx Hill no longer corresponds to ancient experience. 11 If the visual experience was fitted on the Parthenon or Hephaisteion, it is in the greater height of the columns in relation to their slender diameters, as well as a relatively tall entablature.12 Another indication of the schematic rather than visual nature of such integral proportions is the presence of visual "refinements" in features unrelated to proportions such as 1:2, 1:3, and 4:9.13 Refinements such as convex curvatures in horizontal elements and columns (their slight swelling of

17 Temples of Segesta. 5th century BC (before 409). Height with integer proportions. Author of the drawing, modified according to M. Schützenberger, in Mertens 2006: Figure 705.

18 Hephaestion, Athens. Here. 450-445 proportions. designer author.


Altitude sample integral

19 Hephaestion, Athens. Looking towards the southeast corner (now side). Author of the photo. wells known as entasis) and the inward inclination of the columns (Figure 20) may have been intended to correct erroneous optical impressions.14 In addition to these deviations, the "refinements of refinements" on the Parthenon created a subtle play of height and curvature, as intended, at eye level and full scale for the viewer's perspective, reflecting an incredibly keen awareness in design (Figure 21). Originally an important northwest vantage point while at the level of the Sacred Way, the temple's sloping location would cause an optically derived convergence of the lower crepis and their eclipse towards the west stairway if it were built without curvature (Figure 21.1). By refining the curvature of the stylobate, the diagonal view of the Via Sacra makes the curved lines appear not parallel but converging in two places (Fig. 21.2). to avoid these

In conflict, the architect refined this curvature by slightly raising the northwest and southwest corners. edge), resulting in the visually pleasing appearance of a parallel linear composition (Figure 21.3). the smallest

20 Parthenon, Athens. Refinements with horizontal curvature and extrapolated column tilt. Author of the drawing, adapted from M. Korres, in Korres 1999: Figure 3.29. The perspective from which it was normally viewed and Hephaistaion's 1:2 and 1:3 proportions actually fall short of its ideal vertical dimensions, despite the fact that the main vantage point is on the Agora.19 This lack of correction for experiential optics suggests that architects intended integral proportions not as visually imaginable harmonies, but as arithmetic structures within which a mass sculptural play can be created

Considerations such as the thickness of the column expressed by the tangible relationship between the diameter and the height. The notion of classical temple buildings as products of reduced design also contradicts evidence suggesting that Greek architects traditionally conceived of these buildings as sets of well-defined repetitive parts, rather than as unified concepts that can be reduced to small-scale representations. The masons made each piece, such as a capital or triglyph, made of wood, clay, stucco or stone from a 1:1 model called an anagraph, or a 1:1 prototype or model called a paradeigma and which was presumably the responsibility of the architect. to approve these models.20 To summarize, the architect did not provide or refer to drawings as our own graphical reconstructions (Figures 15 and 16), but rather written specifications, called syngraphai, detailing the exact measurements of individual elements and the spaces between them. provided 21 Along with this lack of need for reduced-scale drawings, there was probably little interest in further developing tools to aid in the actual creation of drawings. No measuring ruler survives, and certainly no measuring ruler existed.22 Measurement on the drawing board depended on the skillful use of a divider, and to produce accurate orthogonal and perpendicular lines, a ruler connected intersections drawn with a compass. in circumference .23

21 Parthenon, Athens. Analysis of the viewer's perspective of the northwest platform showing possible visual conflicts (1 and 2) and their adjustment through refinements (3). Author of the drawing, adapted from M. Korres, in Korres 1999: Figure 3.12. With these simple tools, Greek technical drawing undoubtedly reached a level of sophistication that has been largely lost to us today. Nevertheless, the relative lack of surviving textual and physical evidence of the development of Greek sign practices probably reflects a lack of urgency in helping such

Developing. The reasons for this fact are obvious. With few exceptions, drawn plans would be of little or no help in planning or visualizing such simple traditional Greek forms as rectilinear temples, columnar temples, stoas, and portals.24 As J. J. Coulton has suggested, simple rules of thumb (with variations) suffice. to determine the relationships between such prominent elements in Doric design as the stylobate and the columns. related to creating and adjusting shapes in a view drawing. In addition to the issue of the prescribed proportional relationships of column width, height, and distances between centers (De architectura 3.3.1-8), since the Archaic period, monuments have repeated features of fixed sizes, separated by fixed distances along their lengths. the width or length of the building. . The potential for much of the creativity of ancient Greek buildings resides, therefore, in the sizes and proportions of the typological forms, repeated in friezes, column tops, etc. Of course, such designs could theoretically be carried out using detailed elevation drawings as in the fine art tradition, but this need not be the only effective method. Well-documented use of individual element-scale prototypes (paradeigmata) and written specifications (syngraphai), or even simple in-situ intuition as construction progressed, would suffice for the full height of elements such as columns or an entablature. Ultimately, what gives Greek buildings their unique character and presence is the plastic expression of their masses in three dimensions.26 To develop such effects and convey them to builders and masons, only sculptural models of the features would suffice. Perhaps anyone who has seen firsthand the subtly bulging top of the capitals, the curvature of the column shafts, and the crystalline projection of the triglyphs in a mid-fifth-century building like the Hephaisteion (Figure 19) would agree. in that elevation drawings, let alone flat terrain, would add little to the aesthetic appeal of your final product.27 However, traditional Greek buildings are believed to have evolved from iconography, a view that even includes works from the Archaic period. Discovery of extensive full-size chalk traces in the foundations of the 6th century Temple D at Heraion on Samos 'proves' that the architect had previously drawn on a reduced scale first

Transfer your design to the actual dimensions of the foundation.28 It is not clear, however, why the presence of a scaled chalk drawing, specifying the location and dimensions of the walls, would indicate the use of a reduced-scale drawing instead of a temple, as such markings are not used. A full 1:1 drawing would serve as a guide for equal spacing and wall thickness as construction progressed, but the drawing itself could follow the written specifications at least as well as a reduced floor plan.29 Assuming the Although common, metrological analyzes of two other 6th-century buildings, on which no chalk survives, are cited as evidence for this tripartite process of iconography, complete remodeling, and construction: the so-called Anta building and the East building at Didyma. 30 Here the thicknesses of the walls and almost all other dimensions obey rational measurements in Ionic cubits and feet, so much so that one can follow his bulldozer as he displays his restored plans with superimposed grids showing these measurements (Figure 22). The addition of such grids can increase that

22 Anta Building, Didyma (top) and East Building, Didyma (bottom). 6th century BC Restored floor plans with metrological analysis and associated grid overlay. Author of the drawing, modified after P. Schneider, in Schneider 1996: Figs. 15 and 31. I am under the impression that the practice of ichnography has established these floor plans, but in fact the grids are superfluous for any purpose other than to show us metrology at work in the x and y dimensions. The impression of ichnography given by these finely gridded plans is perhaps related to our familiarity with the T-square as a tool of modern engineering drawing. Certainly squares were used in ancient carpentry,31 but there is no evidence of their use in ancient architectural drawing. Our attempt to see drawings to scale on these archaic buildings at Didyma is also undermined by minimal integration, not just conformity, of their proposed foundations and full designs. In both examples, there is a striking lack of systematic integration of all interior features with the orthogonal grid, what might be termed an "empty grid" that seems out of place with the expectation that a geometric base will serve for concrete placement. . Items. Again, this expectation is not necessarily modern; As our sole surviving authority on Greek architectural design practices, Vitruvius proposes a similar idea (De architectura 1.1.2-4). He describes ichnography as the use of compasses and rulers to measure taxis (lat. ordinatio) as a process of ordering giving postotes (lat. quantitas) or "quantity" in the creation of modules within the work, as well as design or diathesis (Lat. dispositio) as a process aimed at elegance through the graphic placement of resources in the work. Together, this ordering and positioning result in the principles of symmetry (modular measure) and eurythmy ("good form"). While Didyma's buildings do not reflect anything contrary to this description, their simplicity does not readily suggest a unification of features and principles through the Greek design processes known to Vitruvius. In contrast, the Hellenistic Artemisia at Magnesia by Hermogenes (late 3rd century) and the Late Classical Temple of Athena Polias at Priene of Pytheos (c. 340) show extensive and consistent integration with latticework as a

graphic support (Figures 23 and 81).32 In both examples, the grid expresses the modular set used for the systematic placement of columns and walls. In addition, the grids of Magnesia and Priene are reduced to a minimal number of partitions compared to restored plans of archaic buildings, a construction that seems more aligned with straightedge and compass than with a square, although here too its agreement with the ancient drawing. it is anything but conclusive. In Chapter 4 I consider additional literary, epigraphic, and archaeological evidence to analyze these last two temples as possible products of iconography. For the moment, this brief comparison should underscore the relatively weak argument in favor of the ichnography represented by the archaic buildings at Didyma.

The Curious Case of Iconography Despite its ubiquity in the modern world, the limited utility of small-scale architectural drawings in the Greek world may give us an opportunity to reflect specifically on the fundamental peculiarity of iconography. Arguably, there is an important conceptual distinction between elevations or perspective drawings, on the one hand, and floor plans, on the other. exactly this

23 Hermogenes (3rd and 2nd centuries BC). Temple of Artemis Leukophryne at Magnesia-on-the-Maeander. It began around 220 B.C. Low level. Author's drawing modified by J.J. Coulton, in Coulton 1977: Figure 23. The concept of orthographic projection in eye drawing is quite artificial as it tends to flatten all features into one plane without the foreshortening that occurs in the usual visual experience. However, one must appreciate the imagination of the invention of ichnography as the concept of a building represented not in part as seen by the eye, but in its entirety as seen on a unified and consistent scale from an almost unfathomable vantage point. . from directly above, while only showing the resources that touch the support plan. Simple justifications for the practice can be made, albeit with caveats. Aerial photography was certainly part of the viewing experience in all eras of the ancient Greek world, such as tracking mountain peaks during military campaigns. Still, it's hard to reconcile a temple design with a natural view, where walls and ceilings form invisible barriers. While one can imagine a scenario where builders came up with the idea of ​​ichnography while looking at the relationships between the interior and exterior features of a temple while standing inside partially built walls, this scenario itself contemplates the construction of the temple, the construction of the temple builders fear in the factory. Of course, one could also postulate that such a "eureka moment" occurred relatively early and was used early in later building designs. On the other hand, one might question the value of deferring this defense to the early practice of iconography. A rigorous and skeptical approach to the question of iconography can help us identify instances of its use with greater certainty, and thus allow a fuller understanding of what these individual instances can tell us about the rise and nature of the practice. . The emphasis on this contradiction between natural vision and iconography does not intend to exclude the possible existence of the latter at any time in the chronology of ancient Greek architecture. The earlier practice of iconography in other ancient cultures is a well-established fact, and the Greeks were in regular contact with the world as early as the Ionian military and commercial periods.

Involved in Egypt in the seventh century.33 Furthermore, a small bird's-eye sketch of a building, showing its internal and external features, can at no time exceed the abilities of a highly creative child. However, applying this imaginative vision to the construction of a real building would require both a motivation for its use and an application method in keeping with the tools and procedures used by Greek architects. Given the sculptural emphasis of Greek temples and the effectiveness of syngraphai, the motivation for iconography would not be easy to sustain in most cases. In addition to their inherent strangeness as aerial views, there is an obvious, albeit important, quality that distinguishes iconographies from the other types of small-scale drawings practiced in classical architecture.34 Other drawings approach experience on a sculptural level, depicting the composition of masses seen from a certain point of view (perspectives) or

24 Ancient Parthenon, Athens, 490–480 B.C. C. (in progress if destroyed). Design. Author's drawing, modified from M. Korres, in Korres 1994: Figure 1. Generalized frontal view (elevations). Ichnographies, on the other hand, overlook the optical qualities of architecture. Instead, they are limited to determining the relative flat positions of the edges and centers of features such as B. walls, doors, and columns to fix. Its functioning refers to the establishment of an abstract spatial order through purely two-dimensional relationships.

Such a planar conception of space, constructed with straightedge and compass, is clearly necessary for designing buildings with complex circular or polygonal outlines, as in Byzantine or Roman imperial architecture, but the utility of its application to simple prismatic Greek buildings seems difficult to justify. 35

The Plan of the Parthenon To deal with this difficulty, it may be useful to cover a whole range of complications by looking at the classical Parthenon of 447-438, whose plan at the stylobate level may be the most innovative and complex. of a Greek temple of the classical period.36 Its architect, Iktinos, faced the particular challenge of creating a truly monumental (more than 72 × 33 m at Krepis) and spacious temple of the Doric order, incorporating the foundations and marble columnar drums of the Archaic hexastyle Parthenon (Figure 24), destroyed by the Persians in 480 (drums and ashlar blocks too damaged to be reused on the north wall of the Acropolis have recently been built - see Figure 25).37 Despite the restriction to accommodate column drums of a predetermined diameter, Iktinos designed a floor plan (Figure 2) with a remarkably large cell housing 1) the monumental chryselephantine cult statue of Athena Parthenos by Phidias, surrounded on three sides by an inner colonnade in the shape of a unprecedented pi; 2) unprecedented but geometrically pleasing proportions between the respective latitudes of the ship and the general plain; and 3) precise alignment of the antae of the pronaos with the external columns.38 In addition

25 Acropolis, Athens. Column drums and ashlars from the crepis of the archaic Parthenon, built into the north wall after the Persian destruction of 480 BC. Author of the photo. The architect achieved all of this by maintaining rational proportions in the selected flat masses and their spacing (the familiar 4:9 ratio between the smallest diameters of the columns and their center distances), as well as the full width-to-length size. dimensions of the stylobate (in turn a ratio of 4:9).39 Does this combination of innovation and visual clarity indicate that Iktinos worked on the composition of the Parthenon's stylobate and supporting features through iconography? A justified rejection of this possibility was the limited size of the available drawing surfaces, such as papyrus, clay tablets, or whiteboard (λ χωμα). in the case of Didymaion (Figure 33), however, this objection is no longer tenable.41 Theoretically, Iktinos could have drawn planes on the large surfaces

available from the blocks of the ancient Parthenon destroyed on site. In terms of the ratio of its naos to its overall width, the Parthenon represents a marked departure from earlier temples (see Figure 26). Traditional Doric temples are hexagonal with a 1-3-1 ratio of three lateral ptera and naos, divided according to the five axial distances from the front. Three-way ratio 3-2 after seven wheelbases. However, despite its Doric order, the Parthenon adopts the octastyle layout of the Ionic.

26 Schematic comparison of the typical plans of the hexastyle Doric and octastyle Ionic temples with the Parthenon. Author of the design, modified from M. Korres, in Korres 1994: Figure 35. Temples while expanding the relative width of their naos to create a

unprecedented 1-5-1 ratio, or about 70% of the total width.43 At the same time, this correspondence between the naos and the columns is given an almost graphical clarity by the alignment of the antae of the pronaos with the axes of the second and third columns from the corner, the so-called “second column rule” (Figure 27).44 Finally, these proportional and axial features preserve the precision of whole number ratios. Although Iktinos worked with the predetermined column diameters of the Archean Parthenon, these diameters form a ratio of 4:9 with respect to the center distances. It even seems that the same 4:9 ratio is reflected in the overall width-to-length dimensions of the stylobate.45 Although these flat features indicate careful design considerations, they would in no way depend on the reduced-scale drawing. As mentioned above, proportional relationships, such as the 4:9 ratio of columns to center distances, were common schemes that could easily have been communicated orally or in writing. Arguably, visually representing this relationship on a reduced scale would be a step that would unnecessarily complicate the design process. Regarding the correspondence of this same proportion with the general rectangle

27 Parthenon, Athens. The so-called "second column rule" leads to the axial alignment of the antae with the second and third columns. Author of the drawing, modified according to M. Korres, in Korres 1994: figure 38. of the stylobate, a simple procedure independent of the drawing makes it possible: the strong contraction of the distances between centers of the corners to solve the famous “problem of the triglyphs from the corners” (Vitruvius 4.3.2).46 In addition to

By correcting for possibly excessive widths of the lateral metopes that would otherwise result from the placement of the corner triglyphs beyond the axis of the corner columns, contraction controls the length and width of the stylobate to maintain the ratio 4 :9. A flat drawing of this 4:9 rectangle would not even be helpful in visualizing what the stylobate would look like, since the stylobate as a whole would never become part of the viewer's viewing experience due to the colonnades and walls. Furthermore, despite the suggestion of a graphic sensibility in the 'second column rule' (Figure 27), this feature is actually a common element of fifth-century design and may be based on non-planar, three-dimensional, optics. considerations: the orientation of the antae with the axes of the third columns on the north and south flanks increasing the density of the columns in the corners and placing the second column on each flank so that its mass gives a feeling of closed space in the east or western ptera. For an observer inside the western pteron, the second column visually confirms the continuity of the space framed by colonnades around the cella (Figure 28).47 Also this canonical alignment of the antae with the axes of the columns

28 Parthenon, Athens. Restored perspective view of the Western Pteron. Author of the drawing modified by A.K. Orlandos in Korres 1994: Figure 40. controls the latitude of ships without the need to graphically examine the relationship to the full scale latitude. Considerations like these do not prove that the architect of the Parthenon did not draw plans to scale. However, they show that even the most complicated and imaginative temples of the Classic period make a weak argument for their necessity in the creation of the final building.

Alternative justifications for ichnography Still, it could be considered a separate possibility. Assuming that the visual experience alone justifies a design method, it could be assumed that the value of the experience outweighs the value of other possible motivations in the creation of a building. For example, for us there is a particular value on which the construction of the architectural space does not necessarily depend, which justifies the iconography and makes it seem natural. Instead, it is beset by the very tradition of institutionalized formal education: the value of expectation. In reviews of design studios in modern architecture schools, one often finds the mechanical expectation that students submit floor plans alongside other scale drawings and models. Through this kind of nonsensical reinforcement, the practice of presenting floor plans continues in professional practice, particularly in architects' presentations to clients. Was there a similar motivation for iconography in the classical period, not just design? Given the apparent cultural differences between modern and ancient Greek architectural practices, one possibility worth exploring is the value of iconography for contemporary Greek thought. Consistent with the moral and spiritual value of classical Greek art advocated by Pollitt,48 such value can be derived from creating works that address concerns on an abstract level through their fidelity to truth or reality as opposed to experience or bodily perception.49 Corresponding to Vitruvius, the Greeks called his architectural drawings ideali (δ αι),50 a term that shows a parallel with

the Platonic conception of transcendent, universal, and archetypal ideas imperfectly imitated in the images of nature.51 Such ideas refer ultimately to "the idea of ​​the good" (τ γα δα, Plato's Republic 508e), which illuminates the kingdom intelligible. In the phenomenal realm, the idea of ​​the good is the source of the sun itself and its luminosity and all that is right, beautiful and true (517b-c). This kind of philosophical idealism is far removed from the Kantian notion that the cognitive apparatus sees the world through space as a mode of perception separate from pure objects (or nouns). a physical object emerges from the craftsman's apprehension of the abstract and incorporeal form of δ α or δ, which he then imitates in physical form: "For it is clear that no craftsman creates the idea by himself" ( γάρ π τ ν γ δ αν α τ ν δημι ργ δ τ ν δημι ργ ν, 596b).53 Plato’s inclination to craft when trying to explain the character of transcendent ideas indicates that they need not have no precedents as a concept. Significantly, Plato has Socrates say, "And are we not accustomed to say (αµ ν λ γ ιν) that the craftsman... things we use?" (Republic 596b). Here Plato seems to indicate that it is generally accepted that the ideal also belongs to craft and that in the world of manufacture the term conveys the more direct meaning of 'idea' (with a lowercase 'i') which survives as its common meaning. Meaning in modern Greek.54 In other words, Plato’s ideal can use the assumption of a common concept as a metaphor to describe his metaphysically charged conception of a transcendent and intelligible reality. Especially when ideals were introduced into the republic, their common meaning as mental images or images was not separated from ideas (with a capital "I"), it is possible that they imagined their product and executed it accordingly. However, in the specific case of architects who required their clients to see their ideas, it makes sense for the term to be adapted to include drawings. As analyzed later in this chapter, this possibility could account for Vitruvius’ reference to reduced architectural drawings as ideals.

If such drawings existed before Plato, one might wonder if there was any tradition that might have understood them to contain an essential good value, beauty, or truth, and thus a significant precedent for Plato's conception of created ideas. In fact, there is an example from the late sixth century that should draw attention to this possibility. Analysis of the Temple of Athena at Paestum, in southern Italy, revealed interesting arithmetic and geometric features both in plan and elevation (Figure 29).56 In plan and plan, the Pythagorean triangles support the design of the temple. of the three sides of the plane is equal to 240, which is the product of ten times twenty-four. In Pythagorean thought, ten is the teleion,58 the perfect number because it is the sum of one, two, three, and four, the first four integers that make up the sacred tetractys (or decade), which is easily formed from ten. pebbles (Figure 30). . This was the symbol upon which the adepts swore by Pythagoras.59 Likewise, twenty-four is the product of the integers of the Tetraktys. A recent analysis of Temple A in the Asklepieion on Kos from around 170 shows analogous results in a Doric temple from the Hellenistic period (Figures 31, 32).60 As demonstrated by AutoCAD and analytical geometry, the integral relationships are established both circumferentially and orthogonally. With an overall width to length ratio of 6:11, the circles share a ratio to the diameters

29 Temple of Athena, Paestum (Posidonia of ancient Greece). late 6th century B.C. Retrieved elevation and simplified plan (not omitted) using basic Pythagorean triangles. Author of the drawing modified by R.A. Baldwin, in Nabers and Ford Wiltshire 1980: Figs. 1, 2

30 The symbol of Tetraktys, upon which the Adepts swore by Pythagoras, expresses the sacred sum of 10 (the Teleion) of the first four integers, here formed of pebbles. designer author.

31 Temple A, Asklepieion, Cos. It began around 170 B.C. Restored plan showing the geometric support of the Pythagorean triangle ABC 6:8:10 and the ratio of diameters 6:10 to establish the positions of cells and pronaos. designer author.

ab 6:8 locates prominent corners and walls corresponding to a Pythagorean triangle 6:8:10.61 Again, the sum of the sides of the triangle equals twenty-four, the product of the integers of the tetractys. A key difference between these archaic and Hellenistic examples is their relationship to design. By systematically arranging architectural features through circles and whole sets defining a regular polygon, Temple A also anticipates Vitruvius' conception of temple design (3.1.2-3) through the analogy of the creation of the human body by nature (Figure 11). such as his exposition of architectural ideas related to taxis, the ordering process based on quantities and diathesis, the process of positioning resources after taxis (1.2.1–3).


Temple A, Asklepieion, Kos. floor plan with geometry

Support for circles with radii of four and five units, centered on the x-x' baseline, with points of intersection specifying perpendicularity and the positions of Euthyntia and Antae. designer author. from the Ionic order of Pytheos and Hermogenes (Figure 81), in which the modular grid controls the placement of key elements, although the non-orthogonal nature of Temple A's circular-diameter booths further emphasizes the practice of curves drawn with a compass , as to find the Didyma plants for example (Figure 33). Although the perimeter relations of Temple A demonstrate a conception that could only result from the tools of technical drawing, the architect of Paestum could have conceived his floor plan using numbers instead of the drawn geometry already seen. However, if skepticism is removed for a moment, the Temple of Athena may suggest that geometric patterns, as "ideas" for plans and views, may have conveyed meaning and beauty since archaic times, existing independently of the bodily constructions they projected. . . This chapter's analysis of just a handful of Greek buildings leads to a consistent conclusion. Temples from before the 4th century may indicate the use of iconography in their designs. Ultimately, however, our difficulty in determining the need for iconography in his creations undermines our firm identification of the craft of drawing to scale at work. The plan of the classical Upper Parthenon certainly shows sophistication and

Hellenistic 33 Didymaion. Restored working drawings for pulling pillar drums and constructing pillar stasis discovered in the walls of Adyton. Author of the drawing, modified according to L. Haselberger, in Haselberger 1980: Figure 1. Complexity. However, like the archaic Didyma buildings, it differs in the interdependence of concrete features and theoretical underpinnings expressed through the latticework that graphically unifies, for example, the walls and columns of the Late Classic Temple of Athena Polias. in Priene. Likewise, the geometry of a Pythagorean triangle in the Temple of Athena at Paestum offers the intriguing hint of graphic support in the Archaic period. However, this proposal lacks the power of Temple A on Kos in the Hellenistic period, where the Pythagorean triangle refers to circles that seem to locate features according to the compass and straightedge, the tools of architectural design. Thus, it must be admitted that a correlation between final form and the hypothesized role of design discernible in Late Classic and Hellenistic temples is less evident in sixth- and fifth-century temples, and therefore less convincing of value. of the drawing to scale in Creation. of Greek temples before the fourth century. Despite the search for outstanding reflections on drawing tools or the adaptation of the understanding of ichnography to the procedures of taxis and diathesis described by Vitrúvio, an important link between the

Archaic and Hellenistic temples have survived at Paestum and Kos: both seem to have a base of a Pythagorean triangle with the tetractys. One might wonder if the more complete level of integration of geometry, number, and built form exemplified in the works of Pytheos, Hermogenes, or the anonymous architect of Temple A on Kos is also a litmus test for the advent of scale drawing. in the Late Classic. be a development of the older drawing traditions. In other words, the requirement that practices observed in relatively late Greek buildings and described by Vitruvius demonstrate the earlier existence of scale drawings would depend on two unverifiable assumptions: that the integrated correspondence between taxis and diathesis is not direct was a later innovation . The purpose of architectural ideas has always been the modeling of buildings rather than any other motivation.63 Thus, the possibility exists that a longstanding primary value of ideasi in at least some examples of architecture may be whether it is associated with Views that had their origins in Pythagorean thought or some other interest in numbers and archetypal geometric shapes. In fact, there is an attractive reason to consider this alternative possibility. On the basis of good evidence, Coulton argues eloquently that archaic and classical architects were not master craftsmen who learned their trade through an apprenticeship and rose through the ranks of masons.64 Rather, they were educated men from independent backgrounds who learned the art of building by reading technical documents, which of course they also wrote. Motivated not by the need to earn a salary, they designed buildings and aligned their construction to gain prestige by contributing to their respective communities. This characterization of Greek architects is consistent with Plato's statesman's observations that architects direct workers even if they are not themselves workers, that they produce knowledge rather than manual labor, and that they belong to an appropriate intellectual milieu (259e). It would then be conceivable that ichnography had emerged not only as a practical starting point for building planning, but also as an expression of scholarship, perhaps combined with qualities such as beauty and truth, and had endured for a longer period of weather. time. In this setting, where iconography arose from concerns other than pure craftsmanship, it would also be questionable whether scale plans later achieved more than being mere embodiments of number and geometry.

the hallmark of craftsmanship in the expression of the tools and techniques that have shaped them and the buildings they design. At temples like Priene, Magnesia, and Kos, then, the clear integration of underlying graphic constructions, concrete forms, and formal contexts would be a remarkable development, not a recent invention, of iconography in the late classical and Hellenistic periods. . Thus, the possibility remains that the Archaic and Classical antecedents of these later buildings reflect practices of iconography. However, when examining the merits of this possibility, we have probably hit a dead end if we are only looking at buildings. Rather, it would be better to turn to the literary record to answer the following questions. Could iconography have been born from abstract thought and reflect an intellectual or spiritual value of architects who, as educated people, cultivated it by engaging in philosophical questions instead of building concerns? Could the architects of the sixth and fifth centuries, together with the thinkers of the Pythagorean tradition, have anticipated Plato's ideas? If we consider the possibility that ideas like architectural design reach traditions that predate Plato, we can begin to analyze Plato's writings as a reflection of architectural traditions.

Number, Geometry, and Vision As with Pythagorean creations, the use of number and geometry in design may have anticipated Plato by bringing a spiritual dimension to the process of creation.65 Plato writes that numbers lead the person to the light of truth and that “geometry brings knowledge is of eternal being” (τ γ ρ ντ γ ωμ τρικ γν σ στιν, Republic 527b).66 Elsewhere, Socrates draws geometry as a demonstration of innate and universal truth (Minus 82b-86c). The qualities of number and geometry, then, involve considerations not only of form but also of the element of disembodied truth verifiable by reason. (μ τρι τη) and the appropriate (σ μμ τρ α) are identified with beauty and excellence (Philebus 64e),68 and Plato explicitly describes geometric forms as beautiful (Timeo 53e–54a) or even exemplars of absolute beauty in the sense of beauty itself (κα α τά) without dependence on a functional or

aesthetic relation to anything else (Phileibus 51c-d).69 In fact, this sense of beauty is not easily conveyed or experienced in paintings, sculptures, and buildings.70 Rather, it is problematic for bodily experience. For example, I previously discussed the value of a drawing that helps visualize the 4:9 proportions of the Parthenon's stylobate, as the presence of colonnades and walls obscures the viewer's perception of this plane as a distinct spatial entity. For Plato and his Pythagorean precursors, the value of such proportions in this context may not even have been in his visual experience. After all, Plato clearly distinguishes between two types of mimesis: 1) colossal sculptures and paintings from Plato's time, which are mere ghosts (φαντάσματα) showing proportional adjustments for the sake of correctness of appearance from the lower point of view of the spectator; and 2) those older works that were images ( χ ) imitating "the measurements of the model (or ideal)" ( τ τ παραδ γματ σ μμ τρ α , Sophist 235d) ideal. Art of the "true approximation of beautiful forms" (τ ν τ ν καλ ν λη ιν σ μμ τρ αν, 235e), metaphorically challenging the sophist's deception. The beauty does not lie in the visual perception of the large-format work, but in the pure geometry of the model, a preference that Plato also takes up in his preference for geometric shapes over paintings and organic objects (Phileibus 51c). For Plato, then, beauty centers on the truth of geometry and number rather than on ordinary visual experience, a concept that has important implications for the potential value of the idea as a graphic model.72 On the one hand, beauty can be present in a work because of its accuracy ( ρ τη ) in imitating its model, which refers to the pedagogical function of art to suggest the existence of ideas.73 On the other hand, beauty and virtue can exist independently due to to the very internal nature of the work ( κατά φ σιν , Republic 444d) and as a Product of measurement and adaptation in its constituent parts (Philebus 64e, Republic 444e) that define its order or taxis (or κ κ σμ , Gorgias 506e). 74 Along with music, dance, poetry, painting and embroidery, for Plato the art of architecture can imitate ideas directly through good form or eurythmy (Republic 400e-402b).75

In examining this relationship between beauty and truth, it is important to distinguish between what might be called ordinary visual experience and the experience of seeing correctly directed at or associated with appropriate objects. Plato clearly says that ideas cannot be seen (ρ σ αι, Republic 507b). However, he repeatedly describes the apprehension of ideas in terms of seeing (α or ψι) and as objects that the soul sees or can see (δν, βλ π ιν, π βλ π ιν, κατιδ ν). In words, embodied vision and the understanding of this type of vision serves as a metaphor for Plato's description of the soul's encounter with ideas, just as the artisan of sofas or tables serves as a metaphor for Plato's divine artisan of the universe (Republic of 596b). The craftsmen's insights provide a model for understanding the transcendent archetypes. Describes "soul vision" (τ ψ χ ψιν, 519b), or a type of vision that can be correctly guided by numbers, which enables the soul to see abstract qualities as small and great in itself (δ ν) (524c) . 525c). Geometry will also prepare the soul to see (κατιδ ν) the idea of ​​good (526e), and in this way both arithmetic and geometry direct vision to the intelligible realm of the soul and not to the phenomenal area caught by the eye. However, even in the material world of buildings, statues, and the like, vision can be related to specific objects that take us beyond ordinary visual experience. Plato's characterization of geometry as beautiful (Timaeus 53e-54a) or exemplary of absolute beauty (Philebus 51c-d) separates his perception from ordinary vision, but it is the eye that perceives the geometry. Among the organs of perception, Plato grants the eyes a special status.78 In the Timaeus, sight is given by God (47a), and in the Republic, the eye is an expensive expense created by the divine craftsman (507c). 79 Turn your eyes like the sun to the "light-bearers" (φωσφ ρα), who carry within them a pure fire related to the light of the sun (Timaeus 45b). Like the sun, light radiates from the eye. After this light has left the eye, its kinship with sunlight enables it to form a body (σ μα) with daylight (45c). In this way, the sight is related (but not the same) with the deity of the sun, since the light reaches the viewer and connects it with the object seen, and also the sun is the cause of the sight (Republic 507e-508a). . The sun in turn owes

Presence of a superior and transcendent being that is the cause of the light of the sun itself: the idea of ​​good illuminating the intelligible realm as a source of truth, knowledge, justice and beauty (508e, 517c). As an art that exemplifies the beautiful, the relationship of geometry to sight can be of great importance in how Plato's concept of the ideal is anchored in existing thought and practice. What the beauty of geometry means can be understood through Plato's discussion of beauty through the viewer's experience of beautiful bodies. Just as an influx (π ρρ τ ν) of sunlight into the eye strengthens sight (508b), so "the lover, seeing the handsome body of a boy, "absorbs the flow of beauty through his eyes" ( δ ξάμ ν γ ρ τ κάλλ τ ν π ρρ ν δι τ ν μμάτων, Phaedrus 251b). In addition to the emission of light from the eyes, there is also an influx. Furthermore, beauty itself behaves like the light emitted by the eye or the sun Just as the sun, as an idea of ​​the good that illuminates the truth, has its counterpart in the intelligible realm, so beautiful things resemble the idea of ​​beauty, which, unlike other ideas80, shines with light. light that the soul receives (Phaedrus 250b-d) In the guise of a child in the phenomenal realm, beauty shines in the eyes of her lover with a ray reminiscent of the radiant radiance of good, while the lover plays the part receptive or even feminine.81 Similarly, in the intelligible realm the good plays the role of Feminine giving birth to the sun (τ κ σα) radiating in the phenomenal realm. nico (Republic 517c). The lover of knowledge also plays the feminine role, since the rational part of his soul "approaches and copulates with the really real" (πλησιάσα και μιγ τ ντι ντω), so that through the birth (γ νν σα) of the spirit and from truth he attains knowledge (490b).82 This birth of mind or intelligence (ν) and truth (λ ια) is the end of an arduous journey driven by desire towards the beautiful (and therefore penetrating) geometry that philosophers prepared by directing the vision of the soul towards the blissful reality that is crucial for it to see (δν, 526e). As Heidegger acknowledges, birth also characterizes doing, as in his general reading of truth (λ ια) itself as "revelation" through work. ) es, which is related to tiktein-giving birth.84 Of course, a carpenter can make a sofa or a table incorporating the idea he sees in his own head. A master builder, on the other hand, must build according to the idea of ​​the architect or master builder. In order for the builders to see the idea of ​​​​him, the architect can provide

Paradeigmata or models, perhaps in the form of drawings made with a straightedge and compass. By observing them, builders can use mimesis to highlight their incarnation as buildings. Both construction and truth follow after looking at a model. Against this backdrop of geometry, birth, and beauty, one can explore the possibility that poetic understanding of Plato's (and ultimately Heidegger's) ideas might have grown out of existing architectural practices. As I will discuss later, Plato's similar metaphorical use of paradeigmata may reinforce this possibility. If the potential connection between Plato's respective philosophical and graphical ideas and architecture seems too tenuous to grasp, remember that "architecture" simply did not exist in the fourth century. To see architectural metaphors at work in this period, then, one must consider a number of references that Plato and his Greek readers would find difficult to separate conceptually, including craft, construction (as in Philebus 56b-c), and even the astronomy. and clock.

Geometry, Craftsmanship, and Cosmic Mechanism In response to the unconvincing argument that the Parthenon relies on iconography as an experiential value, I have asked up to this point whether contemporary architectural theory might have emphasized some other ideal value that might justify its use. As a contemporary treatise on sculpture said to have been influenced by lost architectural thought, the lost canon of Polykleitos, the celebrated fifth-century Argive sculptor, may be relevant. Texts from the Hellenistic and Roman Imperial periods purporting to represent the views of Polykleitos (Philo Mechanikos On Artillery 50.6, Galen On the Doctrines of Hippocrates and Plato 5.48) seem to indicate that beauty or "the good" seems to have resulted in The Pythagoreans. desired by the motives depend on a mathematically grounded proportionality, which is then adjusted.85 According to this later statement, "the good" represents the calculation as an important step in a design process oriented to the perception of the viewer, considering that the Numbers they they themselves produce "good" to mikron, "except for a little".

to your right. Rather, later evidence appears to be merely consistent with the notion of architectural design as a calculation of dimensions based on integer proportions, as found in the repeating ratio of 4:9 in the dimensions of the Parthenon. Understood in this reading from Polikleitano's point of view, however, the "good" of the Parthenon may have arisen from the adjustments in tilt and curvature (Figure 20), as well as the planes (Figure 21) aligned with the eye. of the viewer. on a very refined sculptural level. The value of iconography as a transcendent concept responding to epistemological rather than practical and experiential considerations remains unclear in this case, and the Parthenon project is perhaps best explained as the result of simple calculations and sophisticated optical refinements. Therefore, the iconographies of the Parthenon (Figure 2), however natural they appear to us today, may well be the only products of modern science that would have seemed irrelevant to the temple's designers for their purpose of attracting the viewer's attention. If this interpretation of classical architecture's primary experiential agenda holds up, it may support an approach to the question of ancient Greek iconography from a strictly architectural-archaeological point of view, rather than a method that also takes philosophical concerns into account. The Pythagoreans saw numbers as a kind of ultimate reality underlying nature. Linked to an anti-sophist agenda87, Plato lamented the changes in perceptions of the truth of straight lines and proportions and the beauty of geometry. Whether the architects and sculptors adhered to the Pythagorean mysticism of numbers or something like Plato's idealism, these visual artists were concerned with perception, not with numbers, ideas, or fear of deception. This last statement, however, stimulates further reflection on the relationship between manufacturing and philosophy as Greek activities marked by an awareness of differences in approach to number and geometry. In addition to the possible connections between Polyklet's theory and the Pythagorean interest in measurement, the role of measurement in fabrication is central to Plato. In addition to his comments quoted earlier in this chapter, Plato sees the craft as a model for cosmology. In creating the world, God is a divine creator (π ιητ) or craftsman (δημι ργ) who sets ideas as norms and imitates them in the realm of appearances in such a way that

it aims for accuracy according to these standards.88 Plato's cosmology draws on notions of actual creation to explain it, and in doing so necessarily brings actual creation and its strategies into the epistemological concerns of philosophy. Moving from philosophy to art, Polykleitos and the Greek architects may have translated the Pythagorean value of number into a visual and sculptural experience, and they may have distorted the purity of number into an artistic expression of beauty and goodness. As Walter Benjamin argues in his classic essay on translation, this element of corruption is a defining feature of the translator's job. Justice as pure and true but duly subject to sensory distortions. For Plato, beauty in sculpture depends on the sculptor adhering to true and unrefined proportions (Sophist 235d-e), making the connection between truth and beauty, elevating geometry and ideas into the realm of beauty. Furthermore, according to Derrida's reflections on translation, there is a covert contractual interdependence between an original and its translation, which neither recognizes inevitably. while truth acquires the beauty of art. Looking back to an earlier period, before sculptors adjusted the proportions of their works for the sake of perception (Sophist 235e), Plato's project aimed to establish an alectic element in the ancient approach to sculpture, faithfully imitating the adjustments of his paradeigmata. Plato also grants this element to architecture, which occupies a privileged place over minor arts such as music, medicine or agriculture because its work tools (compass, ruler, square, plumb line and peg) allow a "scientific" interpretation ( τ χνιχωτ ραν) on the precision of measurement (Filebus 56b-c).91 Plato's recognition of this precision in architecture may therefore call attention to the question of what measurement embodies. Unlike the Pythagoreans, for Plato it is not the numbers that make up the essential reality of a person, a sculpture or a building. Rather, the numbers encompass both eternal elements that transcend phenomenal experience and an important one

model imitation operations in arts such as sculpture and construction that draw our attention to the underlying truth of the things we see in our everyday world.92 In this sense, I have up to this point underestimated a perhaps remarkable and Platonic thought. While the former seems to have seen numbers as concrete elements in space, Plato sees each number as an individual and transcendent idea separate from phenomena. As immutable individuals, numbers are not subject to computation in the ideal domain, which occurs more in the phenomenal domain between countable and commensurable objects. Intervals, just as astronomers use visual observation as a basis for measuring time (530d-531c). A problem for Plato in both music and astronomy is the orientation of the senses towards phenomena and not the application of reason to "the beautiful and the good" (531c). Simultaneous with this problem is the measurement of such phenomena as astral movements only against each other and without reference to any idea as an absolute standard or model. But with regard to Plato's assessment of the metaphorical value of architecture, which is expressed in Filebo, by what standards do architects measure their buildings with their precision tools? Plato can answer this question in a discussion of vision, truth, and models in astronomy and craft. In an important passage in the Republic, the difference between what astronomers see and measure and the underlying truth of such optical recording and calculation is again captured through metaphors. Consequently, we must treat astral bodies and the quantifiable rates of their velocity in the spinning cosmos as models or paradigms of ultimate reality, much like the geometric diagrams of Daedalus or some other craftsman or painter (529c-e). This direct reference to the mythical architect Daedalus' diagrams may have a significant impact on Plato's understanding of design in architecture. However, if Plato intended here to refer to graphic templates in the sense of the Vitruvian ideal (drawing to scale and linear perspective), there is nothing in his text that directly confirms this intention. On the most direct reading of the passage, it is clear that Daedalus's diagrams have some affinity with the rotational motions of celestial bodies. More specifically, Plato argues that by visualizing cosmic bodies, their

movements do not provide truth per se, but models of truth in the same way as diagrams drawn by daedalus or some other craftsman or painter. Plato sees the full implications of this discussion in the Timaeus, where seeing patterns in the phenomenal realm leads to a higher way of seeing in the transcendent realm.94 Plato's reference to the drawings of the mythical architect does not give an idea of ​​his character. and function, but offer the interesting point that such drawings are somehow appropriate in a discussion of cosmic order. In the Timaeus, this connection becomes clearer when Plato reports on the divine craftsman's reliance on "eternal models" in his construction of the order of the universe. One might wonder what, in the experience of Plato and his readers, allowed this metaphor of models by a craftsman to work in a discussion of cosmic order. It is clear that there is something in the designs of a craftsman, such as those envisioned for Daedalus, that does not contradict the ideas of cosmic mechanisms. In other words, it is possible that the differences between ship diagrams and diagrams of cosmic mechanisms were not so great that the former would not be out of place in a philosophical discussion of celestial motion. Metaphorically speaking, a graphic representation of the cosmic mechanism can be a model, much like a craftsman's diagram, especially when a divine craftsman uses a model in the construction of cosmic order. Thus, along with the philosophical metaphors of craft, the Republic's reference to Daedalus' diagrams serves as a useful entry point for a deeper study of the nature and purposes of drawing in architecture, along with the astronomical representation. Among other topics, in Chapter 2 I discuss what can be understood by diagrams of cosmic mechanisms in the classical period. What would these drawings be like? How do they relate to Plato's emphasis on geometry and his importance to beauty and truth? How would the drawings relate to the kind of vision Plato is talking about? Such questions will open up a set of related, though separate, considerations that support a new theory for the genesis of ichnography and linear perspective in a vision context applicable to representations of cosmic order.

Summary and Conclusion: Architectural Ideas

We can briefly summarize the implications of this chapter for the question of architectural representation. Vitruvius' use of the Greek term idea for architectural models as reduced-scale architectural drawings suggests a possible correspondence with Plato's philosophy in the classical period. If one can look to Plato for insights into the details of architectural theory before him, the common notion opens up the further possibility that Plato knew ideas as models in terms of iconography, orthography, and perspective drawings. However, on closer inspection, Plato's discussion of drawings in his reference to Daedalus becomes particularly relevant to the type of drawings that his contemporary Greek readers had in mind. Plato's focus in this reference is not to describe the shapes or purposes of Daedalus's diagrams, but to address the relationship between them and the movements of the cosmos to discuss the relationship between vision and ultimate truth. At first, Plato's interest here seems to belittle the evidence of scaled architectural drawings before Plato. Coupled with the difficulty of defending the contingency of the Parthenon and other classical buildings in iconography, the question of whether the architects of these buildings used such designs must remain unanswered for the moment. But again, this question probably misses the point. The strange connections we find between building, astronomy, and philosophy give rise to additional considerations that may enhance our understanding of how classical architects thought about their buildings, from what sources they might have drawn and influenced, and what these were. knowledge domains. that could encompass what would later be called architecture. The day the world began to build was probably not the day a Greek architect drew the first iconography. Even more convincing was the day that iconography became architectural. Whether there was iconography for cases where its use did not significantly characterize a building is of limited interest to architecture. By saying that ichnography is architectural I mean something more than what can be achieved computationally by the integer proportions of a Pythagorean triangle or 4:9 rectangle. "Architecture" in the context of Vitruvius

Arguably, it can encompass an embodiment not only of graphic arrangement (taxis) and positioning (diathesis), but also of the three parts of architecture: construction, time, and mechanisms, all of which are linked by geometry.95 A Complete unification of these parts is found in the Pantheon (Figure 1), where geometry frames a vision of cosmic movement in time through the Roman application of concrete, bringing the compass and ruler marks to a monumental presence. Focusing on this holistic vision of architecture should not evoke a mystical tone, like the emergence of the cosmic being. Instead, from a classical perspective, architecture may have more to do with the element that allows its appearance in the built world and the recognition of the structure and mechanisms of nature by the classical viewer. This element can be understood as something tangible: the flat geometry of the compass and the ruler of the classical architect. These simple tools are the means to order the idea of ​​building and visualizing the order of the universe. In approaching ichnography as the flat construction of architectural space on a large scale, one must first consider the simple but surprisingly sophisticated applications of the compass and straightedge in Greek technical drawing. In the next chapter, I examine the emergence of small-scale drawing in the context of seeing, which as a skill etymologically expressed by the term idea came to shape an underlying sense of order in the universe through tools and methods. shared with architects. This investigation will show that if Plato had diagrams of cosmic mechanisms in mind in his reference to Daedalus, these drawings may reflect something completely different: the existence of linear perspective and iconography.

Two points of view and spatial representation Even with Plato's later elaboration of the relationship between craft and cosmic mechanism in the Timaeus, the comparison of the Republic with the diagrams of Daedalus (or other craftsmen or painters) and the movements of the celestial bodies may seem strange, perhaps excessive. . . By examining the formal and conceptual connections between the Greek diagrams of cosmic mechanisms and the graphic underpinnings of circular and part-circular Greek buildings, this chapter seeks to demonstrate the naturalness of Plato's comparison in the broader context of classical visual culture. In particular, I try to show how in the classical period the design of the Greek theater as a circular and radial construction is related to the theories of vision, the recent invention of linear perspective and astronomical drawings that represent the revolutions of bodies in space. space and currently dying. The discovered connections help to find an early application of iconography in theatrical design as a container of the community vision. They also demonstrate a nexus of conceptual associations available to Plato when he referred to Daedalus' diagrams. Finally, they demonstrate that the relationship (or, just as importantly, a simple lack of separation) between the construction, the mechanism, and the astronomical clocks that together define Vitruvian architecture is found in remarkably earlier Greek traditions. This background serves to delve into the origins of linear perspective and iconography in Chapter 3.

Viewing the Universe In his work On the Revolutions of the Celestial Spheres, Copernicus found little to convince him of Euclid's proof of a geocentric universe.1 Illustrated by a ruler-and-compass demonstration (Figure 34), Euclid combined

34 Diagram for Euclid's proof of a geocentric universe, showing the observer's position on Earth at the center of the horizon circle (D), the exit point of Cancer (C) and Leo (B), and the points Fixed Goat Horn (A) and Gargoyles (E). designer author. Experiment with reason in this first theorem of your phenomena from the end of the fourth century. Copernicus' problem with the theorem was not nearly as fundamental as Lobachevsky's challenge to the underlying assumptions of Euclid's parallel postulate, which laid the foundation for non-Euclidean geometry in the 19th century. Instead, he limited himself to concluding this one theorem, that the earth occupies the center of the cosmos. It takes little skill in mathematics or astronomy to immediately understand what Copernicus is missing in Euclid's chain of arguments. Euclid begins with a theoros ("observer") placed on the earth's surface and an observation tube (the diopter), possibly equipped with a protractor to measure angles. The crab spawns in the east, it can reverse its position and

Look west through the tube and find the goat horn placement point in the same line of sight. If you keep this view to the west and aim the sighting tube at the set point of the water spout, you can reverse your position again and find the lion's rising point along a second common axis. Euclid illustrates this experiment by drawing the circle of the horizon (Figure 34) along which appear the rising points of Cancer (C) and Leo (B) and the setting points of Goat's Horn (A) and Waterweed (Y). . The two axes corresponding to the direction of the viewing tube converge at D, the point where the observer is on Earth. Both ADC and BDE describe the diameter of the circle drawn by the caliper. Therefore, according to Euclid, the astronomical diagram proves that the earth is at the center of the cosmos. Obviously, this evidence is supported by the assumption that each of these constellations is a priori equidistant from Earth. Surprisingly, then, the pie chart seems to demonstrate nothing more than circular reasoning itself. However, contrary to this negative assessment, something much more interesting could also be interpreted than the erroneous justification of Euclid's theorem. In Elements of him, Euclid shows a remarkable consistency in his theorems, which provide proofs for a series of postulates embedded in premises. The first set of his phenomena is no different in this respect, and here is one of the assumptions handed down to Euclid, that the earth appears within the larger sphere of the cosmos on whose surface all the stars are fixed.4 Hence the assumption that the compass and the ruler prove not simply an existing explanation for the structure of the universe. Furthermore, the drawing theorizes an experience in perspective with its lines of sight projected through space through a reduced representation of the universe from an abstract point of view that no observer can observe. In the drawing, Theoros' own earthly point of view is represented by the center of a circle from which the axial lines of sight emanate. By placing the viewer of the drawing outside of this perspective, he is able to theorize perspective itself in relation to the revolving cosmos as an ontological and panoptic whole. In this way, the compass and ruler allow us to take the theorem (ρημα) as a speculation. In addition to revealing the structure and order of the rotating cosmos, this graphic construction clearly refers to the viewer's perspective.

another interest of Euclid. In optics, Euclid theorizes vision in terms of rays that form the geometry of a cone with its vertex in the eye and its circular base at the maximum visible distance.5 In reality, the contour of the base would depend on the shape of the object that is being treated observed. But, to cite Euclid's own example of phenomena, the concave inner surface of the sphere of the cosmos as observed from Earth would form the circular base itself, just as in the case of the spheres described in Propositions 23-27 of Optical Perspective. From the eye of the terrestrial observer, the cone-shaped view of the sky would theoretically have the same circular shape as the line-of-sight diagram in the rotating cosmos (Figure 34). Another similarity between this theoretical perspective and his diagram can be seen by considering two important passages from Vitruvius that John White convincingly linked to Euclid's visual cone. , where, after his introduction to iconography and elevation drawing, he describes linear perspective or skenographia ("scene painting"). Here his involvement in the process of adumbratio or 'shading' may reflect the connection between an origin in painting and its current context of types of architectural drawing.8 In the second passage (7.praef.11) he presents perspective as linear as that of a painter invention in fifth-century Athens named Agatharkhos, who painted the theater stage and later wrote a commentary on the subject, which later informed the accounts of Democritus and Anaxagoras. In both passages, Vitruvius describes the geometric construction of linear perspective as radial lines projecting or receding toward the circini centrum, with the center of a circle as the vanishing point.9 Classical linear perspective, as described by Vitruvius, is thus refers to that of Euclid and may derive from his Theory of Optics10, but apart from Vitruvius' unconfirmed testimony about the painter Agatharkos, it cannot currently be confirmed whether linear perspective existed before it appeared in surviving first-century frescoes in Campania. .11 In this chapter and the next I consider evidence related to optics, philosophy, astronomy, painting, and the building trades to provide a new interpretation of the rise of perspective and iconography in the Athens of the fifth cosmos.

Theorizing Vision In the history of the Greek theories of vision, the ideas underlying Euclid's geometric study of optics were not entirely new. Geometric features such as circles, radials, angles, and cones created with compass and ruler create for Euclid small-scale, highly streamlined representations of visual qualities in free space. As discussed in Chapter 1, Plato describes sight as the emission of rays from the eye, which has a sun-like fire with which it merges (Timaeus 45b-c). After forming a body, the rays or streams of light return to the eye (Republic 508b, Phaedrus 251b). Plato's metaphors on the transmission of light and copulation do not define any form of this emission and influence. In the previous century, Empedocles may have set an influential precedent for Plato with his description of vision as physical contact between particles in the eye and the object (Aristotle's De sensu 437b23–438a5),12 and perhaps with Alkmaion's Pythagorean model of Croton 6th century. of a visual stream radiating from an eye composed of water and fire.13 Far from proposing a purely abstract geometric analysis, Euclid's optics conveys the physiological properties and processes of visual experience expressed by Plato and his predecessors. In Theorem 1, Euclid emphasizes that the spaces between rays associated with the eye prevent full visibility of an object at any given viewing moment. In Theorem 2 he states that a distant object can fool the eye if it is placed entirely within a space between visible rays, and that the clarity of a visible object is proportional to the number of angles (and therefore rays) that coincide with it. the. sight. From that. As these features show, Euclid's rays are not simply lines connecting other lines and points according to the conventions of geometry. Rather, they are visual guides in a way not unlike the rays of light in Plato's account, represented by Euclid with the geometric clarity of the eye as a point at the apex of a cone.14 The role of geometry in representation of structure and order Vision is similar to how it works in drawings of astronomical phenomena, and the relationship may not be accidental. It is necessary to consider the common tools and practices of technical drawing in the sciences, not to mention that, as in the case of Euclid, sometimes it is the same draftsman who applies these approaches.

for different research areas such as astronomy and optics. A proper understanding of the background to the application of geometry in visual theory, together with the formal similarity shared between Vitruvius' construction of linear perspective and Euclid's own construction of the geocentric cosmos (Figure 34), may require further insight. exploration of astronomical representation. Vitruvius reflects another point of similarity with Euclid, or at least an assumption on which Euclid is based. Here, too, Euclid's theorem on the geocentric structure of the universe assumes a rotating cosmic sphere. the fourth century.16 In the earlier work, Autolycus formulates the horizon in Euclid's theorem as a circle dividing the sphere of the cosmos with respect to the position of the observer on the sphere of the earth. Not relative to Autolycus is the fixed position of the axis of the sphere around which the cosmos revolves, resulting in the perpetual circular pattern drawn by the stars when one holds the horizon perpendicular to the axis, and their sunrises and sunsets, when the horizon is parallel to the axis axis.17 In both cases, the motions of the stars around the Earth can be graphically imitated by the orbit traced by a compass, as in Euclid's geocentric diagram. But there is something emphatically three-dimensional about the rotating spherical cosmos imagined by Autolycus, anticipating Vitruvian's cosmic machine, which perpetually rotates on its axis, making constellations visible or invisible depending on the location of the terrestrial observer and the time of year (De Arquitectura 9.1 .2-3). As discussed in the digression to this book, the progenitors of the Vitruvian cosmic machine may have been quite ancient, possibly dating back to the spinning machines of Khersiphron and Metagenes, archaic architects of Artemision at Ephesus, as well as related machines. of Anaximander. Rotating model of the cosmos. Like these machines and clocks based on the movement of celestial bodies, the cosmos that Vitruvius model emulates is, according to Vitruvius, architectural and, in fact, the creation of the force of nature as architect. From this Vitruvian perspective, Euclid's graphic demonstration of the rotating cosmos would certainly be architectural. The importance of this continuity between astronomy and construction for the question of linear perspective and vision

Iconography, we must consider some of the qualities of geometry in the representations of the cosmos.

Geometry and cosmos This common quality of making in nature and representation is already found in Plato. Significantly, the diagrams by Daedalus (or some other craftsman or painter) mentioned in the Republic (529c-530c) serve to underscore Plato's emphasis on distinguishing between the "most beautiful" (κ λλιστα) pattern of stars on the surface of the heavens and their visible Revolutions on the one hand, and on the other hand the true intelligible velocity of the movement underlying the stars. This true speed cannot be captured by sight, but only by reason and contemplation. Plato claims that both the stars in the sky and the diagrams are the creations of a craftsman, anticipating the divine craftsman of Timaeus, and combining the stars and geometry as products of art. The same superlative "most beautiful" applies to the Daedalus diagrams, whose spatial measurements, like the temporal measurements of moving stars, embody no truth. Continuing with Euclid, the spatial measures of angles and lengths in such drawings (as in the 30-degree angles and equidistant radial lines showing the rising or setting of the relevant sea crab, goat's horn, lion, and waterweed with respect to the represented observer) correspond to the movement of the constellations in time; In fact, Euclid's theorem not only applies to rotational motion, but also to the necessary synchronous display of the constellations as they move across the sky. For reasons that I will develop in the rest of this chapter, I propose here that Euclid's geocentric diagram preserves for us a later example of the type of geometric design that Plato knew about and possibly reflected in his passage on Daedalus' diagrams. Along with astronomy, these designs reflect a type of craft similar to what Vitruvius would later describe as architecture. Regarding the question of his personification of truth, other comments in the Republic on geometry and later details in the Timaeus reinforce Plato's apparently inferior appreciation of geometric diagrams. Although geometry alone cannot complete the journey to absolute truth, geometry and astronomy direct the soul's eye to a higher realm (Republic 527b, 529b) where one can better understand the idea of

the good (Republic 526e). The power of geometry does not lie in its practical capacity (Republic 527a-b), as in the measurement of real space, but in its character of pure "knowledge of eternal being." What Plato advocates is a kind of eternal geometry, similar to what he would call in the Timaeus the eternal model, on which the divine artificer builds the cosmos (Timaeus 48e-49a). Likewise, it is the eternal model, not the generated model, that the philosopher in astronomy must pursue.

35 The zodiac as a circular construction with twelve equal sectors for the signs. designer author. (Republic 529c-d). Plato can find a cosmic diagram or the "most beautiful" astral bodies themselves, but it is the role of these images in the transformation

the soul's vision for this idea of ​​good, which captures the true value of such visualization in the phenomenal realm. In this binary representation of drawings and the actual mechanisms of the bodies they represent, there is good reason to believe that the former had the greatest influence on Plato's representation. In the Timaeus, Plato emphasizes that in the cosmos of the divine craftsman, the ordered movements of bodies are similar to the movements of our own mind and are driven by divine reason (ν) itself.18 As we contemplate and theorize the orbits of these celestial movements, our kindred reason absorbs the quality of the divine order that they embody and elevates our own soul so that we can perceive intelligible reality. Plato attaches particular importance to the relationship between geometry and reason, but his connection between circular geometry and astronomy is not apparent when observed without the aid of astronomers and their diagrams.19 This is particularly true of the theories of the contemporary astronomer and mathematician Eudoxus. of Cnidus, to which Plato's emphasis can be attributed

36 The rotating cosmos inspired by Eudoxus. designer author. Circle.20 In the lost but still known writings of Eudoxus, the circle described the movements of stars and planets.21 His Zodiac (Figure 35), whose equal sectors treated the constellations as if they were uniform signs of 30° longitude, in instead of distinguishing between signs as part of an equal division of twelve sectors (δωδ κατημ ρια) and the variable width of the constellations in the later form led to errors that Hipparchus criticized two centuries later.22 In Euclid's drawing (Figure 34) these became equal sectors, in which the lines of sight intersect at the Theoros, underlining the central position of the land by six equal sectors above and below the opposite

ascending and descending pairs (crab - goat's horn, algae - lion). In addition to the zodiac, three other main circles describe the equator and the northern and southern tropics of Eudoxus. Together with the inclined drawing band, these circles form the sphere of the cosmos as a geometric construction, which is made by technical drawing with a compass (Figure 36). In this scheme, a feature of the Eudoxus zodiac that would not be included in the canon is what can be understood as the bisection of the signs/constellations, as indicated by its intersection of the Tropic of Cancer and the Tropic of Cancer with the center, and not the beginning of the constellations. (Figure 36).23 This recognition of the centers and not only of the edges of the constellations could indicate a division of the zodiac into 24 parts instead of 12 (Figure 37). From a visual studies perspective, one might reconsider what was formulated as a philosophical rather than a scientific basis for the circular nature of the Greek cosmos. Eudoxus is the first known astronomer to explain cosmic motions in terms of the mathematical properties of circles, and from Plato to Ptolemy in the 2nd century AD. and furthermore, the circular and spherical model of the celestial movement continues to be a doctrine in both philosophy and science. More likely than just patiently observing the night sky, for Plato this geometry influences the image or "generated model" that graphically reveals the circular order of the revolving universe for the philosopher's soul to emulate. According to a teleological view of scientific development, this philosophical model prevented a more modern understanding of astronomy. An opposing scientific point of view argues the merits of the circular/spherical model as a developmental aid and, more important here for our aesthetic concerns, the naturalness of the circle in astronomical representation as fully consistent with perceived appearance: "The stars they move in circular orbits in the sky, the sun appears to move in circles around the earth..."24 However, if seeing circles working in the sky is merely natural, one might wonder why this happened. the Greeks, and only the Greeks, who created this detailed circular pattern. Given the seriousness and antiquity of the Babylonian tradition, why did the Babylonian astronomers content themselves with a system of arithmetic progressions? Form, the graphic models that represent what is seen.26

If Plato and Eudoxus forged a particular geometric view of the universe that should be shared by philosophy and science, was there something in their shared cultural background that allowed for that view? As I explore in this and subsequent chapters, astronomy's geometric understanding of the cosmos and Plato's emphasis on craft, divine and otherwise, can be linked in meaningful and spectacular ways. We have already seen that centuries later, Vitruvius defined cosmic craft in terms of the architectural unity of the late Republic. In search of the possible inspiration behind the geometry of the demiurgic construction of the cosmos and its eternal model, I will now consider buildings that may reflect the compass-and-ruler-based creations of the architects who designed them.

Geometric foundations of ichnography and astronomy The theme of geometry stands out in the question of ancient Greek ichnography. By clarifying what is meant by geometry in classical architecture, one can do that.

37 The zodiac as a construction of twenty-four parts. designer author. Distinguish between simple orthogonal relationships found in rectilinear temples such as the Parthenon or Artemision on Magnesia (Figure 23) and non-orthogonal shapes such as triangles, circles, and arches found on Temple A on Kos (Figure 31) or other buildings examined below. Another category could be designs based on irrational geometric proportions like 1:√2 or 1:√3. Although the proposed geometry is considered part of Hermogenes' design process, it does not stand up to rigorous mathematical analysis.27 Rather, this design approach may be limited to the Imperial period.28 Therefore, this chapter focuses on the principles of compass and the rule. and other related, instead of irrational and archetypal geometric forms

geometric relationships. Although explicit evidence of the process of his projects is lacking, there have been buildings since the fourth century whose conceptions are difficult to imagine without the art of iconography. A contemporary of Plato and Eudoxus in the early fourth century is the tholos on the Marmaria terrace of the sanctuary of Athena Pronaia at Delphi (Figure 38).29 According to Vitruvius (7.praef.12), Theodorus of Phocea wrote a volume of construction, then he was probably its architect. According to a recent metrological analysis, there are significant similarities with the modular system operating in the Parthenon,

38 Tholos on the Terrace of Marmaria, Sanctuary of Athena Pronaia, Delphi. Beginning of the 4th century BC Plant restored. Author of modified design from Ito 2004: Figure 4–2. "almost an indication that the tholos was originally intended as a reduced copy of the Parthenon." at least one possible influential role comes from Athens. A fundamental difference with the Parthenon is, of course, the geometry of the concentric circles in the tholos plane. As such, it appears to reflect engineering compass drawing practices. In addition, there is an arithmetical basis that Vitruvius, perhaps based on his reading of Theodore of Fokaia, recommends for peripteral tholoi: a 3:5 integer ratio between cella and stylobate diameters (De architectura 4.8.2). 32 Regardless of the relationship, until Vitruvius centuries later, building at Delphi was part of the world of fourth-century Greek circular buildings, which finds its richest and most complex expression in the tholos at the Asklepieion at Epidaurus, beginning around c. 360 (Figure 39).33

39 Tholos in the Asklepieion, Epidaurus. It began around 360 B.C. Cr. Plant restored. Author of the design, modified by P. Cavvadias, in Cavvadias 1891: Plate 4. Regarding the Epidaurus building, the simplicity of the Delphi tholos has a legacy in late republican Rome. Next to the Tiber is the famous round temple of Pentelic marble (Figure 40), probably related to the Temple of Hercules Olivarius at ca merit.35 His measurement technique reveals an interesting feature of its plan: the exact ratio of the total number of 3 :5 perimeters established in the cella wall and the stylobate,36 with reference to Vitruvio's recommendation for the relation of these characteristics in the peripteral tholoi.

However, Vitruvius's confirmation that such a ratio was intended does not seem to help a view that would like to see the round temple of Tiberside or its ancestors at Delphi as evidence of iconography. At best, Vitruvius articulates an arithmetic relationship between the edges of the curved masonry in a simple way that seems to avoid the need for geometric design when planning the final built form.37 In other words, syngraphically, how the specifications spoke or written can express such forms. in terms of simple proportions.38 The observation that shapes conform to commonly repeated proportions in


Rundtemple, Rome. Here. 100


Restored plant. He drew

The author modified from Rakob and Heilmeyer 1973: Plate 1. Rectilinear temples (Figures 15–18) should apply equally to what is found here on tholoi floor plans: that is to say, that such formulas are readily available, with no relationships they must be provided uncovered by scales -below drawings made with straightedge and compass.39 However, there are two additional considerations that do not support this view. First, as detailed in Chapter 4, Temple A on Kos of about 170 AD shows the same 3:5 diameter ratio at its geometric base centered on a Pythagorean triangle (Figure 31). It is the circular intersections with the compass and straightedge that allow for precise orthogonality when drawing straight lines that define the positions of the euthyntia, cella, and pronaos (Figure 32). Of course, as to the question of iconography at Delphi and Rome at the beginning of the 4th and end of the 2nd century, this example proves nothing. However, it suggests that the 3:5 formula for circles may be related to drawing practice, not just abstract formulas. Finally, in the case of Temple A, it is the design process that determines the location of the key points of the temple.

41 The Latin theater described by Vitruvius (De arch. 5.6.1-4). He drew

Author. important elements in the plan in a way that cannot be easily visualized without a graphical construction. Second, and more important, the buildings at Delphi and Rome (as well as other classical round buildings) exhibit a feature not associated with Temple A. In addition to the quality of the concentric circles, the surrounding ring of columns and their plate plates support indicate a radial arrangement. More than just central planning, it is this quality of shining from a center that reveals an origin in the use of the compass and straightedge. As seen in the Euclid diagram of the rotating geocentric cosmos (Figure 34), the circle with its centrifugal/centripetal lines emerges from the tools of technical drawing. For the moment, this generalization remains a layman's observation of typological similarities. However, an analysis of the literary testimonials below regarding these drawing qualities reveals something more fascinating about the work. In addition to small peripheral rotundas such as temples and heroines, Vitruvius describes the circular design of the potentially colossal Latin theater (De architectura 5.6.1-4).40 The project begins with a circumscribed set of four equilateral triangles (Fig. 41). This geometry determines the location of architectural elements such as the front of the scene and the radiating corridors of the cavea. Around the time of Augustus, then, we find a description—yes, a prescription—of ichnography using compass and straightedge.41 Working on the geometric basis of the design, the text explains that it is the same as “astrologers calculate the twelve Signs Celestials of the Musical Harmony of the Stars', quibus etiam in duodecim signorum caelestium astrologia ex musica convientia astorum ratiocinatur (5.6.1).42 The Fensterbusch edition of Vitruvius omits this part of the text and marks it as a later insertion. 43 In fact, the phrase lacks Book 9's more mechanistic emphasis on the zodiac as a belt of twelve signs of equal length revolving around the earth on a slope (9.1.3-5), in a manner more reminiscent of Eudoxus (Figure 41). However, if this comment really belongs to an interpolator, it could hardly be more appropriate.

To appreciate the importance of this well-grounded comparison between the common geometry underlying Vitruvius' Latin theater and the diagram of the twelve heavenly signs (Figure 35), an analysis of the straightedge and compass process that produces the form may be helpful. In his description of the training required to prepare for architectural practice, Vitruvius includes training in drawing and geometry to envision the proposed building and, using compass, ruler, and related tools, to carry out his vision in actual space on the site (1.1 4). Nowhere does Vitruvius explain the ins and outs of working with such tools, which is natural in a treatise on architectural theory, but obviously not intended to offer hands-on training in the practical skills a professional would need to acquire.44 The way in which how an ancient draughtsman would draw something like the circumscribed set of four equilateral triangles described by Vitruvius must therefore be based on scant archaeological evidence. Among the patterns Haselberger observed on the walls of the Didymaion Adyton is the repetitive shape of a six-petalled rosette (Fig. 42.1). totaling more than seven circles of equal radius.46 The graphical algorithm starts on a common theoretical baseline with two lateral circles centered on the outer arc of a central circle, followed by four more circles centered on the perimeter intersections. The most obvious value of this drawing is that it verifies the precision of the compass, while an instrument with a subtly curved neck reveals its defect with an imperfect rosette.47 This drawing is therefore the basis of the ancient technical drawing, not of the draughtsman. . ..anyone involved in architecture should not be as familiar with the process as a poet would be able to tune his own strings.48 Considering the operation of the compass in ancient drawing, its relationship to polygons such as the equilateral polygon of Vitruvian triangles makes it obvious. As already discussed in the case of the iconography of Temple A on Kos, the perimeter intersections create true orthogonality and precise angles, as in the temple walls and euthyntheria and the Pythagorean triangle that supports them (Figure 32). One Pair Lead

Compass in this sense is that, unlike a square, the drawing can be carried out on any surface, even on a flat wall or stone with a non-orthogonal contour. Also, drawing habits would have developed complex ways of working with compasses and rulers that may seem sophisticated to us, but were natural to those who worked with these tools in their daily lives. However, there is nothing complex about the circumscribed triangles that Vitruvius describes. Instead, the geometric base of the Latin Theater (Figure 41) is nothing more than the simple rosette of six petals, with the use of a ruler to connect their circumferential intersections with radial lines and chords (Figure 42.2). The simplicity and adaptability of this design is remarkable. The ease with which the algorithm lends itself to the balanced radial form may have influenced his assumption for the theory behind theatrical design in late republican Italy, whether or not that theory originated with Vitruvius himself. . The suitability of Vitruvius, or the later Interpolator, to relate to the Chart of the Twelve Signs derives from a familiarity with his geometry at the level of his compass and ruler design process; the same process creates the twelve equal 30 degree sides for the zodiac (Figure 35). Furthermore, as any ancient man with the slightest familiarity with design would have readily understood, the additional intersections of the chords would have fixed the positions of the radial lines of the aisles in the upper wedges of the Latin theater, and thus changed them in relation to each other. to the corridors of the lower wedges, as prescribed by Vitruvius (5.6.2). The result is then a construction of 24 pieces with angular divisions of 15 degrees. It is therefore adaptable to the diagram by the 4th century philosopher and musicologist Aristoxenos referred to by Vitruvius, based on the positions of the bronze vessels to be placed in two or four curved rows along the six equal radial divisions of a quadrant. and therefore 15 degrees) according to harmonic principles (Figure 43).49 In fact, Aristoxenus could have used the same six-petalled rosette to construct his diagram. Finally, one might even postulate that the importance of the sign centers in the Eudoxus Zodiac as intersections with the Tropic of Cancer and the Tropic of Cancer (Figures 36, 37) might have found similar graphic expression in a twenty-four of equal size . parts chart. Building. The similarities between the Latin theater and the zodiac result from a

The common geometric support observed by Vitruvius or his interpolator is relevant both for the construction and for the cosmic representation. Understood according to a geocentric model, the circle of the twelve signs of the zodiac rotates from east to west. In the opposite direction, the moon, the sun and the planets revolve in a circle through the twelve signs. In relation to the belt of signs, as Vitruvius predicts, these bodies “travel in a cycle of variable magnitude, as if they rotated at different points along an ascending ladder from west to east in the universe”, ut per graduum ascensionem percurrentes alius alia circuitionis magnitudeine ab occidenti ad orientem in mundo pervagantur (9.1.5). The implicit theatrical metaphor that allows Vitruvio and his readers to imagine something

42 The six-petal rosette: rosette (above) and connected with circumferential intersections with a rule (below). designer author.

43 Diagram of Aristoxenos (4th century BC) for the placement of sound vessels in the theater according to Vitruvius (De arch. 5.6.2-6). designer author. The mechanism of rotation of the cosmos could not be clearer. From the earth in a central position similar to that of the orchestra, the imaginary perspective includes a concentric construction in which the cavea and its numerous stairways are the planetary circuit. This circle, in turn, is related to the circle of the zodiac through the perspective of the terrestrial observer who radially locates the progress of planetary movements in longitudes of 30 degrees (Figure 44). It is not known if this "theatrical" representation of the cosmos is the work of Vitruvius himself or if it reflects an earlier source. whatever it is

In this case, the similarities observed so far raise the question of whether, for our purposes, there could be an understandable reason for using the same geometric support for both the construction of the theater and the representation of space. One might also wonder if the theater and the peripteral tholoi can be related as products of iconography from the 4th century onwards. Finally, it is worth asking which of them fostered the transition from a sculptural approach to an aesthetic based on constructions of space organized according to the concentric and radial principles derived from the compass and the ruler. The argument followed was that it was the theatre, as the architect's unique invention of a vessel for communal vision in the city, that first shaped the notion of order in space in the built world of the city, sanctuary, and cosmos. . At the center of this exploration is the role of models in the perception of the world, which are mutually reinforcing, for example, how theater can act as a model for seeing the universe and how vision itself becomes a model for theater (and vice versa). But the most intriguing question

44 cycles of revolutions of the moon, the sun and the planets through the zodiac, described by Vitruvius as an ascending ladder (De arch. 9.1.5). designer author. it is the original model that could have made any of these secondary models possible, a topic I address in Chapter 3. An interpretive analysis of the relevant evidence may suggest that this original model may have been a process in the art of building itself. .

The theater and the city.

The Theater of Pompey, which opened in the 1950s on the Campo de Mars south of Rome, is an example of a theater's potential to transform part of a city.50 In contrast to the Greek tradition of building seats in a On a natural hill, Pompey's Theater was a multi-story theatrical arrangement, the experience of which best approximates later surviving examples, such as Marcellus' Augustus Theater in the Circus Flaminius. The Pompey monument broke with republican traditions by becoming Rome's first permanent concrete and masonry theater, rather than a temporary wooden structure for specific performances. The excuse for this break with tradition was that the cavea were simply the steps leading up to Pompey's Temple of Venus Victrix51

45 Trajan's Market, Rome. Biberatic from the beginning of the 2nd century. Author of the photo.

to sue

view from the street

on a platform about 25 m wide in the central axis at the apex of the seating group, about 45 m above the surrounding level of the Campus Martius. Although it is no longer a visible monument,52 it is the mark of Pompey

The theater is preserved in the wide curve of Palazzo Pio Righetti, which incorporates the ancient remains into its foundations and still reflects the ancient architect's compass mark on its drawing board, as described by Vitruvius. In addition to the physical transformation of the southern Field of Mars, the shape of Pompey's monument created a local precedent for the monumental curvature of Rome's urban monuments, from the semicircles of the Forum of Augustus to Trajan's Markets (Figure 45) and beyond. As with the imperial forums, the practice of drawing on a reduced scale effectively united disparate parts into complexes and even complexes of complexes. The radial arrangement of the corridors of the cavea converged in the orchestra and joined along a single axis that extended from the Temple of Venus Victrix to Pompey's Curia at the opposite end of the Post-Scaenam Portico. and ca With a landscaped space of 135 by 180 m framed by the portico that stretched between the area now framed by Campo dei Fiori and Largo Argentina, neither the temple nor the curia were visible from each other. the dimensional shapes at different levels were designed accordingly

46 Theatre, Asklepieion, Epidaurus. Began around 300 Upper Eastern Koilon. Author of the photo.


seen from

to a flat design. In this way, iconography shaped the space south of the Field of Mars and set a precedent for transforming Rome into an urban aesthetic that broadly reflects the design principles of the compass and straightedge. This design approach, formulated so succinctly by Vitruvius in his description of the Latin theater, was central to the Hellenization of architecture in the middle and late periods, as was the introduction of Greek architects, building materials, and models of architectural advancement. . . Republican Rome. The Greek tradition on which Pompey's architect drew is perhaps most impressively represented in the well-preserved Asklepieion Theater at Epidaurus, which dates from around 1800. 300 (Figures 46, 47).55 If we follow the account of Pausanias (2.27.5), the connection between the concentric and radial designs of the theater and the nearby tholos (Figure 39) is perhaps more than accidental. According to him, an architect named Polykleitos was responsible for both buildings, a suggestion supported by the possibility that Pausanias misnamed the famous theater sculptor some six decades later.56 Regardless of these authorship issues, the Epidaurus monuments denounce the fourth In the 19th century, new approaches to space design were introduced in sanctuaries and urban settings. The culmination of this trend may be the Hellenistic Acropolis of Pergamon, where the radial lines of the third-century theatrical corridors (Figure 48) seem to organize and unify buildings and complexes above, according to a dynamic and centrifugal thrust of the orchestra. 57

47 Theatre, Asklepieion, Epidaurus. Design. Author's drawing modified by A.W. Pickard-Cambridge, in Pickard-Cambridge 1946: Figure 70.

48 Theatre, Acropolis, Pergamum. 3rd century BC BC View from the orchestra level. Author of the photo.

49 The Greek theater after Vitruvius (De arq. 5.7.1-2). designer author. Whether as a stand-alone or integrative conception, the flat qualities of his designs easily transfer to natural slopes, creating the koilon or seating arrangement as a 'void' that suggests the shape of the sphere. Subsequently, the orthographic projections of Roman theaters such as those of Pompey and Marcelo derive the cylindrical shape of the support of the cavea, creating monumental urban expressions in elevation. In contrast to the sculptural expressions of the temples, the experimental geometry of the theaters arises from the field of iconography. The main role of ichnography in Greek theater design finds support in Vitruvius (5.7.1-2). In contrast to the four triangles of Latin theaters, Greek theater planning begins with a series of three circumscribed squares defining the positions of the skene, proskenion, and side aisles, the latter again displaced in the upper rows of seats (Figure 49). Although the shapes are different, the radial and concentric design method stems from geometry.

the basis is the same.58 Vitruvius reserves us only one theory for the design of Greek theatres, which the Greek architects before him may not have actually followed in any formula. Nevertheless, the method is perceptible in the surviving works, ranging from creative variation to slavish dependence on the formula.59 In the lower theater of Cnidus from the mid-2nd century there is a striking coincidence with Vitruvius's description (fig. fifty). . 60 same can

50 Lower Theater of Cnidus, after the middle of the 2nd century B.C. State plan with the addition of geometric supports from post-Vitruvian Greek theaters. Author of the design, modified by I.C. Love, in love 1970: Figure 2.

the Delos theater of the end of the 4th century (Fig. 52.1). A contemporary of the Delian Theatre, the Priene Theater places the proskenion and skene according to the underlying geometry, but does not integrate all of the radiating corridors into the scheme (Figure 53).61 In fact, as analysis has shown, there are several examples of the 4th century that show variations on the basic circumscribed square scheme (Figures 51-52),62 although I know of no other examples than those of Delos and Cnidos, where the bishops are also adapted. However, the pattern suggests that Vitruvius's Greek theater was not the invention of a Roman architect. Whether Vitruvius learned of this design process from an earlier or later Hellenistic source has been questioned, the latter possibility being consistent with the building traditions of Asia Minor and its offshore islands, from which Vitruvius draws his description of the temples.63 Of course, the scarcity of surviving architectural writing makes this question difficult to answer, but it seems reasonable.

51 Diagrams of Greek Theaters with their Geometric Bases. Author's drawing, after H.P. Isler, in Isler 1989: Figs. 5-8 its direct source may have been a lost commentary from a later theater in Asia Minor, such as that at Cnidus (Fig. 50). A more relevant question about Vitruvius' relationship to his Greek sources for the present study concerns what his discussion of technical drawing in the theatrical design process may reveal. The geometry in the formula of the Latin theater lends itself to a

architectural composition of Roman theaters in relation to their Greek ancestors: a semicircular cavea and a deeper stage construction, the front edge of which coincides with the center of the theoretical circle of the orchestra.64 How Vitruvius arrives at changes in geometry that, at least At a theoretical level, does this other architectural type take into account?

52 Diagrams of Greek Theaters with their Geometric Bases. Author's drawing, after H.P. Isler, in Isler 1989: Figs. 9, 10

The new geometry is not as innovative as it seems. Remember how the theatrical Latin geometry of the four circumscribed equilateral triangles results simply from connecting the circumferential intersections of a six-petaled rosette with a ruler. A second observation that we still do not fully understand is that the geometric basis of three circumscribed squares used in the Greek theater is actually identical to that of the Latin theater. As Silvio Ferri has pointed out, Vitruvius' construction of the Latin theater is simply an extension of the Greek theatre, with the latter appearing at its center.65 So, in terms of the graphic algorithm that produces the Greek theatre, it also arises from the straight lines that they connect the intersections of the same rosette of six petals (Figure 42). In both cases, the same basic construction produces a protraction operation based on angular divisions of 15 and 30 degrees. The form of the zodiac (Figure 35) that the Vitruvian interpolator associates with the Latin theater also applies to the Greek theater. As we will see, the same way that shapes the sense of order in the universe works in a similar way in the city. The history of the origins of the concentric and radial forms of the theater and its relationship with the city begins with the Theater of Dionysus in Athens, built on the southern slope of the Acropolis (Figure 12). Construction of the limestone koilon seats, which can seat at least 15,000 spectators, appears to have begun around AD 370.66. C. and formed the basic model for the Greek theaters from that time. Prior to this permanent construction, the fifth-century theater of Euripides, Sophocles, and Aristophanes was made of wood, and its shape cannot be assumed to have anticipated the appearance of Menander's theater in the fourth century. It is more likely that his earlier orchestra was rectilinear rather than circular, with its rows of wooden tribunes rising in similar rectilinear or trapezoidal rows or even just straight lines nearly parallel to the front of the orchestra.67 Opposite the Theater of Dionysus, the stage main became more ritualistic Spectacle in Athens, in the archaic period, the agora as a multipurpose center of the city

it also seems to have fulfilled this function68. According to literary sources, the agora was the place of the orchestra69, a name given to a space dedicated to performances. Its name references the verb orkhesthai - "to dance" - in a way reminiscent of the Spartan use of the alternative term khoros, or "dance floor" for Sparta's own agora. facing the audience watching from the theatron, initially an informal theatrical or performance area71 and later probably provided with ikria or wooden steps. A natural setting for such performances would have been the skene, the tent or log cabin that also served as a dressing room for costumed performances. The other likely site for choral performances in the Archaic period was in front of the Temple of Dionysus, near the southern slope of the Acropolis.


Theater in Priene, late 4th century.


plant restored with

geometric support. Author of the drawing, modified after A. von Gerkan, in von Gerkan 1921: Table 29.3. hill.72 This place would have been the site of the Athenian festival of the city of Dionysia. In these early performances, the ikria would have seen the temple as a backdrop for the orchestra. At the beginning of the 5th century, Ikria collapsed. It is likely that this fact influenced the orchestra's movement north to the foot of the slope that served as support for the ascending stands. At this point, which would later be occupied by the colossal permanent theatre, beginning around 370 AD Athens hosted performances by famous classical dramatists for both Athenian and foreign audiences. More generally, performances of the City of Dionysus resulted in shared viewing experiences (ωρ ν) between the Athenian theaters or spectators and the theoroi or spectators sent abroad by their respective poleis.73 More specifically, the Theater of Dionysus was the seat of theoria, the ritualized and institutionalized witnessing of sacred spectacles at the religious festivals of a foreign city, which was the central experience of theoria by theoros.74 This Greek cultural activity involved the dispatch of theoroi as ambassadors, who they traveled abroad to see such spectacles, and then returned there to explain to their respective hometowns what they saw.75 The relationship between such ritualized vision, philosophy, and architecture would have far-reaching consequences for the course of productive culture. This established practice was the model adopted by Plato in his description of the theory in books 5 to 7 of The Republic.76 The activity provided Plato with a way to describe the philosopher's journey into the intelligible realm, to establish the truth in ideas. transcendental, see and then he returns to narrate his experience in the manner of the escaped prisoner in the Allegory of the cave (República 514-517). As I argue in the next section, the cultural practice of theoria in Athens that Plato used took place within the architectural framework of the theatre, which shaped the experience of "seeing theoretically" in much the same way that Plato did in his description to see and see I could take the vision for granted. TRUE. By way of related background, Plato's idea of ​​the ideal predates a reduced architectural practice of drawing, using compass and straightedge, which shaped the shape of space and saw itself in terms of the same methods of technical drawing that built a sense of order in the cosmos. EITHER

The metaphor of craft in describing the patterns in the mechanisms of the revolving universe already had fertile potential before Plato exploited it. In this way, the theater as a place of dramatic representation preceded telling the truth and seeing in the "philosophical drama" of Plato's own dialogues. from here. 370 ff., reflects the general form of his immediate predecessor. I am not opposed to rebuilding a rectangular orchestra with straight rows of seats in the early stages of the theater. However, it has been suggested that the theater may have been rebuilt sometime in 420-410, although the possible layout of this layout has not been studied.78 The evidence I will discuss for the design of this layout has important implications for the future. . Edition of Icnography and Linear Perspective in Athens of the fifth century.

Theater as City The comedy The Birds was produced in the city of Dionysia in 414.79 This play survives as one of the masterpieces of Aristophanes, the comic playwright of Plato's symposium, although it ranked only second.80 It contains the importance of the work in the Athenian drama. his commentary on contemporary life in Athens is a cautious reflection on the arrangement of architectural space in the last quarter of the fifth century. The verses in question are 992-1020, in which a character named the astronomer Meto appears as a meticulous aspirant to be a designer of a city for the birds.81 Aristophanes is clear in the right direction in his descriptions of the procedures and tools of technical drawing. After Meton enters, the play's protagonist, Peisetairos, asks him, "What is your design idea?" (τ δ α β λ ματ .) Here Aristophanes uses the idea some three decades before Plato's metaphysically charged use of the term in his intervening dialogues, and it would be incorrect to read any comparable meaning in its occurrence in the Metonian context. drawing Rather, Aristophanes' use of the idea in prose is common.82 In fact, the gist of Peisetairos's question might simply be: "What kind of project do you have in mind?"83

However, using the idea along the lines of Peisetairos implies some significant observations that have not yet been recognized. Given the context, there is a fairly clear association here with the process of making in a way consistent with Plato's later observation that ideas are common in the craft. Again, in the words of Socrates: “And don't we usually say that the craftsman . (Republic 596b). By adopting this metaphor for his understandable archetypes, Plato would give them a philosophical connotation that, even in relation to the architectural theory of Vitruvian's writings, was probably as important to the ancient reader as it is to us. More importantly, using the idea to describe Meton's action that follows demonstrates its connection to architectural design practice. Whatever connotations a writer or reader attaches to the term at any given time, Aristophanes' birds show a precursor to Vitruvius' use of the Greek term in the fifth century to describe iconography, linear perspective, and orthography (De architecture 1.2.1- two). . The dialogue that follows is fascinating. In response to Peisetairos, Meton notes: “I want to geometrize the air for you and divide it into sections” (γ ωμ τρ σαι β λ μαι τ ν ρα μ ν δι λ ν τ κατ γ α). in your hands for this task, says Meton, Ruler of Air (καν ν ρ). First, all the air is mainly in the form (δ αν) of a pot lid (κατ πνιγ α). From above I place this rule that is curved (καμπ λν), I place a compass... we have with a star - which is circular in itself - the rays will radiate in a straight line (999-1009). After this speech, Peisetairos accuses Meton of being a charlatan, beats him, and expels him with the final insult that he must go compete elsewhere. Several points in the lines of Aristophanes deserve comment. Instead of translating πν γ as the type of pressure-actuated hydraulic reservoir described

much later, from Hero of Alexandria (Pneumatica 1.42),85 I follow Dunbar in imagining a traditional hemispherical cover for a terracotta baking dish.86 While both are technically possible, for comic reasons only the latter that sounds familiar could witness. Advertising. enough to resonate. In taking this position, I argue that Aristophanes' humor depends on a correspondence with reality, the larger picture of which his audience could grasp, though not in detail. To understand these lines it is important that we decipher the instruments described by Aristophanes and their uses. In Wycherly's reading, Aristophanes refers to a straightedge, a compass, and a square.87 The first two are obvious, but the last requires explanation. If I understand his reasoning, he uses τ ν καν… τ ν καμπ λ ν to indicate a “curved” rule and not a “curved” rule, which would be linguistically defensible. On the other hand, the square has no convincing drawing-board application to the process described by Meton, and Wycherly must posit that the compass is centered on the interior angle of the square to draw a quarter circle, followed by removal of the square to complete the full circle According to this idea, the initial arc connectors would establish the positions in which the straight edge snaps to extend straight lines through the center, allowing the circle to be divided into quarters.88 Although this can Not being the most elegant method for the task, it's an A. The more fundamental problem is that this explanation doesn't provide a clear means of discerning the lines emanating from the surrounding center: the streets emanating from the Agora. Even more difficult is the question of how this proceeding could have been presented in a meaningful way for the audience. According to Wycherly, the actor would have traced the character on the ground (Proskenion?), which by conveying the short lines of him would have been impossible to see and extremely difficult to execute. In Dunbar's reading, Aristophanes is referring to a curved ruler, which he reasonably imagines as a semicircular disc or protractor. the air in the section. He holds this curved ruler in the air and then uses compass and ruler to draw the circle of the agora and the streets orthogonally and radiantly in the air itself, while he gestures with three instruments. Apart from the ambiguity that such gestures would give, it can be doubted that this act is only

possible with only two hands. The resulting form that Meton describes, according to Dunbar, is a city semicircular in section beyond the semidisc of his curved ruler, containing within itself the circle of the Agora, from which the streets radiate to the heavens and beyond. the country around. My own reconstruction offers a different interpretation of the instrument in question (καν ν καμπ λ). What Aristophanes evokes is a curved ruler (rather than a curved ruler), but contrary to Dunbar's suggestion, his function in these lines resembles his function in the real world. Attaching a protractor should not be a template for the shape of a semicircle, which can most easily be made to any size with a compass and ruler, which Meton also brings with him. Instead, when bending a ruler, consider the relevance of your measurements.

54 Hypothetical Greek protractor or "curved ruler" showing angular divisions of 15°. designer author. it moves from the outer edge toward the center along its straight base (Figure 54). In other words, these measurements along the curve are associated with angles, and by the principle of radial protraction, the measure of a given angle remains constant regardless of the radius of the instrument.90 In combination with the ruler, the protractor establishes locations accurate for radials. lines drawn by a project a central point along a plane. Meton's use of these tools implies the same action as he

In its construction, it describes a circular agora from which the streets emanate as rays that radiate directly from a circular star, both radial and orthogonal. Considering that Meton is describing the plan of a city, the protraction function in his design is obviously an extension of scale, a flat projection from small to large that can expand into a real space of movement and vision. Aristophanes, in Athens in 414, describes a reduced drawing based on geometry made possible by the tools of technical drawing and presents it as a ridiculous subject. Just as important as the instruments and their uses is the form that Meton describes. The question of form is not pedantic here, divorced from the comic intention of Aristophanes' dialogue. Rather, that's why it's funny. Speculations based on the Aristophanes joke range from Meton's recklessness in studying the mechanisms of celestial phenomena,91 to accusations that Meton had feigned insanity to avoid his military service obligations,92 to claims that Meton actually represented the famous schemer Hippodamus, as if Aristophanes were persecuting someone by replacing him entirely with someone else.93 Aristophanes is clearly making fun of something, and there is no reason to doubt that the focus of his mocking includes meton. However, if one carefully considers how the joke works, one might pay more attention to the action performed than to the character performing it. This action is the production of a form whose properties are specified in the dialogue, though the audience's perception of these details required more visual aid than the props and gestures Meton provided in his swift delivery of lines. One possibility that should be seriously considered is that Meton is describing skenographia, referring directly to what was painted in accordance with that technique on the skene immediately behind him. His description of his tools and the construction of lines emanating from a central point are certainly consistent with Vitruvius' characterization of skenographia as radial lines converging at the center of a circle drawn by a compass. Invented by the painter Agatharkos in the first half of the fifth century, this method of illusionistic extension of the audience's visual rays into the scene would be familiar enough to connect the joke with the audience. So, in this interpretation, Meton would use this theoretical technique, which sounds like a sophistry in painting, to design a city, creating an absurd and excessively intellectual imagination that is the basis of humor.

In addition to this first interpretation, I propose and defend a second. This second proposal does not replace the first, but expands and completes it. Although unlikely, the larger arguments of the present study do not depend on it, for reasons that will become clear in Chapter 3. The cornerstone of the following interpretation is thus the proposed chronology, because it points to an earlier, rather than earlier, scenographic development. The attraction of Meton's geometric construction to its intended audience is the fact that it accurately depicts the theater in which he stands while reciting these lines. The description of it as a concentric shape with converging lines emanating from the center corresponds both to the appearance of Greek theaters and to the way Vitruvius describes Greek theater as a geometric construction with ruler and compass (5.7.1-2 ). It is true that the Meton lines were delivered in the year 414, and we can see what the Theater of Dionysus looked like before its enlargement and renovation into a stone construction around the year 370. On the other hand, there is no good reason to suppose that latter form is indistinguishable from its immediate predecessor built of wood on the lower southern slope of the Acropolis hill. Had the new design during this period introduced the new circular arrangement into a traditionally rectilinear shaped institution, it would have been in place for some four decades before being set in stone. In this scenario, the proposed circular wooden version might have been ripe for a replacement and, more importantly, would have mitigated the radical boldness embodied in our current model that the new form in durable stone of the second quarter of the fourth century seems without precedents. Moreover, it must seem strange that in a play performed in this place, Aristophanes so accurately describes only the form of the later theater with which neither he nor his present audience have any connection. In fact, Aristophanes is obviously making fun of something, and to imagine that his actor's words and gestures failed to hint at something the audience could recognize would deprive this scene of its purpose and miss the joke entirely. As we found it difficult to agree on the basis of humor in Meton's verse, at the risk of suppressing all the comic power of it, I will detail a

New explanation for the joke. The agora of Athens was a gathering place for sacred, political, commercial, and social activities and people. Traditionally, it was even a performance venue, as evidenced by the inclusion of an area called the Athens Orchestra. Birds in the sky in the center, a position humorously reminiscent of the audience's position on the ascending koilon between the city's plain and its sanctuary on the Acropolis. Referring to the idea of ​​geometric construction to create converging streets towards the agora of this paradisiacal city, Meton evokes –and almost certainly alludes to– the paths of the theater corridors that lead to the central orchestra on which it stands, they converge. Meton's further statement that his scheme is like a circular star whose rays radiate directly in all directions equates the city he describes with the shape of the theater in which he presents those lines. The fact that Aristophanes expected his audience to laugh at Meton's expense might indicate that the idea of ​​a space so designed was strange and novel. This possibility may indicate that in the year 414, when this comedy was first performed, the form of the theater - the form one would expect of a theater today - was a very recent innovation, perhaps even a completely new reconfiguration for the Dionysian of the time. City . . . .

The city and the cosmos If, as I propose here, Aristophanes' Meto does not serve as an indirect reference to the Hippodamo of Miletus, the comic role of an astronomer shaping architectural space deserves an explanation. Interestingly, Vitruvius defines architecture not only in terms of architecture, but also in terms of clocks and machines. Book 9 is largely devoted to astronomy, with the universe being characterized as a cosmic mechanism created by an architect, just as the machines themselves imitate the rotation of the cosmos. In Athens, Meton himself was a maker of sundials,95 an activity that Vitruvius later identified as one of the three faculties of architecture. These coincidences do not go so far as to show some kind of continuous tradition stretching from Athens in the fifth century to Rome in the first century. However, our loss of classical and Hellenistic architectural writing

The comments make this possibility hard to rule out. Furthermore, the parallels between Plato's divine craftsman and Vitruvian's world architect suggest a kind of discourse on construction and the cosmos discernible in lines 992-1020 of Aristophanes' The Birds. Furthermore, Anaximander's geocentric cosmic sphere supposedly represented the Earth much earlier in the form of a columnar drum.96 Beyond this question of continuity and its translation, these coincidences suggest that our own strict separation between astronomy and construction is not necessarily natural, in terms of performance borrowed by emphasizing the incorporation of the design and operation of the universe into the first definition of architecture. We should therefore have little difficulty in considering how an Athenian public in the classical period could have identified with the idea of ​​an astronomer and sundial maker in the role of an architect. As for his namesake in Birds, Meton's known real-world activities leave us with no hint of any design achievement beyond sundials. In 432, he and Euktemon observed the summer solstice to more accurately measure the length of a year.97 He was also the discoverer of the lunar Metonic cycles that bear his name, corresponding to a nineteen-year interval between lunar reappearances. at a certain point in the sky and in an identical phase.98 There is, however, a parallelism between the type of technical drawing that Meto would have produced and the geometry represented by his fictional counterpart. Along with his observation of the solstices, and along with Euktemon and Democritos, he used parapegmata, astronomical calendars that allowed him to define precise durations for the seasons and the year. Parapegmas divide the year into twelve equal parts, a division that arises from the zodiac as a circular construction with twelve signs based on equal angular divisions of 30 degrees (Figure 35), first appearing in Greek astronomy in the late 19th century. fifth century. along with the parapegmas of Meto, Euctemon, and Democritus.99 One may recall how Vitruvius or his interpolator observed how the same algorithm of circumscribed triangles creates both the Latin theater and the zodiac (Figures 35, 41), an observation with a greater reach. transcendence. . . As already mentioned, this procedure is identical in the Greek theater, where the circumscribed squares determine the shape of the building by the principle of

Protraction, resulting in twenty-four equal divisions of 15 degrees (Figure 49). Of course, the circumscribed square divides the circle in the manner suggested by Aristophanes' Meto, "place a straight ruler, and lengthen it to form a quarter circle, with an agora in the center, and just as we do with a star— since it is itself circular — the rays will radiate directly forward.” The focus of Meto's lines and Vitruvian's descriptions of theaters is not on the construction of squares but on the squares that arise naturally from an identical graphical algorithm used in the formation of an ideal city or theater.Greek Theater Design , and the "curved ruler" instrument (Figure 54) that facilitates it, are products of the same application of the compass and ruler that make up the zodiac, an observation made clear by the fact that it is a more interesting is Astronomer , whose urban landscape resembles not a city but the theater it is located in. Such is the affinity between the circular and radial forms of the theater and the zodiac that Vitruvius (9.1.5) later used the former as a metaphor for the second to describe the spinning mechanisms of the cosmos (Fig. 44).Meton's city of birds is an idea no other city imitates, but it stands at the beginning of a venerable tradition.While it may have been impractical Building the circular and radial utopias dreamed of and sometimes built for early modern cities like Palmanova, the Place de l'Etoile in Paris, and the Prati region of Rome, the idea itself would make even the Time classics reappear. in the USA Overtime. In the Laws of Him (778c), Plato describes the shape of a city equally idealized as circular in plan, a shape that in Critias (115c) also characterizes Atlantis as a concentric idea with interconnected linear canals and bridges over belts of water. and land. which may reflect a reduced graphic conception of the built space built with ruler and compass. Once again, the order given to the diagram seems to evoke the cycles that describe the orbits of bodies that revolve around a central Earth, recalling what Plato's idea of ​​the city could have been as an imitation of the cosmos.100 In the modern city from Athens, the Agora's traditional multipurpose character as a gathering place of all sorts began to unravel not only with the decline of its orchestra in favor of the Temple of Dionysus at the southern end of the Acropolis, but also with the establishment of the Agora, the largest open space on Pnyx Hill as the site of their Ekklesia or General Assemblies. From the beginning of the fifth century, these assemblies included the

unprecedented gathering of 5,000 or more male citizens to perform the functions of Athens' new democratic political system. Pnyx visible today. First, Meton built a sundial in the 430s, the foundations of which are recognised.102 Second, in the late fifth century, after the Theater of Dionysus had been rebuilt before 414, as proposed here, a retaining wall defined a new semicircular shape for the pnyx, where all lines of sight were on the speaker's bema or platform, which was exactly on the central axis defined by the position of Meton's sundial directly behind it (Figures 55, 56 ). 103 The semicircular shape and focus of the center The visual Pnyx of the late fifth century recalls the basic appearance of the Theater of Dionysus of around 370, which during the fourth century replaced the Pnyx as a place of political meetings in Athens. In the form of Meton's sundial and Aristophanes' representation of it in Birds, the actual meeting of the Athenian astronomer and the fictional headquarters.

55 Pnyx, Athens, phase III, end of the 5th century against Bema. Author of the photo.


View of Koilon

The presence in both places may be accidental, but still appropriate. On the Pnyx, Meton's sundial forms the center of the audience's line of sight. In the Theater of Dionysus, Meton articulates how the central focus is like a star, its rays radiating outwards and thus radiating towards the audience. A common principle of Greek optical theory in the traditions before and after Aristophanes' birds is the emission of light from the eye, its fusion with the external light surrounding the observed object, and its return to the eye.104 Like Euclid's cone Seeing that it refers to this schema, the theater captures precisely that centripetal and centrifugal act of seeing that characterizes both Aristophanes' description of the city through Meto and the description of the single-pointed linear perspective used for the theater in Athens. invented in the 5th century its streets, agora and town halls in this schematic way, the perspective itself was political, an act of positioning subjects and linking them in the construction of thea, the idea of ​​seeing and being seen in relation to the whole and being Center . As we commonly recognize, the theatron was a place for thea or seeing, but in this etymology it must be recognized that in large urban concentrations such as the theater or the pnyx, seeing necessarily goes hand in hand with being seen.105 This quality of gaze it is emphasized in accounts of the literary effects of the attention generated by certain spectators in the theater or the way of voting in the Pnyx, which openly displayed tribal and individual voices to the entire assembled assembly.106 Explaining matters such as

56 Pnyx, Athens, Phase III. simplified plan. designer author. Objectification inscribed them in normative roles as citizens and invited foreign viewers to participate in specific and institutionalized practices of viewing. There are interesting parallels between this visualization and the Greek descriptions of the drawing. Also in Plato's account of vision, an emission of light rays from the eye combines with the light of the world and forms a physical connection between the subjective and external light and the object seen. In Meton's Lines, the rays emanate from the center as a radiant star, suggesting an independent projection origin corresponding to the object of focus for the audience's lines of sight at the Koilon, merging Theatai and Theoroi into a unified performance experience. and collective in what

The performance and its perception express a concrete form. This form - Aristophanes' conception of meton - radiates from a circle traced by a compass as the center or 'agora' and the active centrality of this space, as the Vitruvian Theater orchestra (and possibly its Greek sources) becomes model to see the revolutions of the cosmos. According to this model, the perspective is that of the center looking out to see the totality in the manner of Jeremy Benthem's panopticon, in this case that of the earth. In Euclid's proof of the geocentric cosmos and the accompanying diagram (Figure 34), it is also the terrestrial observer whose eye directs his visual rays towards the stars, which in turn are arranged according to their signs as an even radial division into twelve parts, that reminds of that Greek theater of twelve or twenty-four parts, describing Vitruvius. Alongside each variation of these zodiacal and theatrical models, there is an important geometric constant: the construction of a circle whose radial lines converge at a central point. That Plato's visionary account and its correlative institution of theoria as activity centered in the theater of Dionysus also lend themselves to this construction need not have been conscious or intentional. Rather, he would say that this form was the model available as a locus of theory and modeling of cosmic order that could be grasped by the eye in diagrammatic form, a model that Aristophanes so aptly ascribes to an astronomer creating urban space. From Meto to Eudoxus, Euclid and beyond, the common practices of technical drawing in astronomy and optics resemble the graphic art of building spaces for collective visualization. Of particular interest is the further similarity between this circular and radial design for the theater and the linear perspective in painting described by Vitruvius. His identification of Agatharcus as the inventor of scenery in the first half of the fifth century would place its existence before the geometric form described by Aristophanes Meton.107 An art historical critique of this early date for the invention of one-point linear perspective is that of no reflection on its application in painting before a much later date,108 though it is not clear why the paintings on the small, convex surfaces of the vases should have imitated a technique intended to create realistic backgrounds for dramatic performances. 109 Furthermore, any perceived limitations in the correct theoretical understanding of a single vanishing point in the surviving murals in Campania and

Rome should not prevent its correct application in its original context in Greece during the classical period. speculate about the possible influence of the first on the second. If that were the case, both linear perspective and drawing practices would have theorized thea in a way that shaped theatron specifically as a place to see. In the sense that both linear perspective in Skene and its analogous graphic construction for Orkhestra and Koilon are geometric foundations or rationalizations and not the experience of seeing itself, they can be understood as ideal in that they allow one to see ( δ ν ) Thea through of them allow theoretical inner workings. The painted compositions for the backgrounds and the structure of the seats and corridors built in the ascending cave of the hill, therefore, represent the ideas, drawn on a reduced scale, to which the craftsman, as a painter or architect, directs his gaze towards the realization . of these works. in real space, as described by Plato in his metaphorical discussion of the Ideas (Republic 596b). Theory. Just as the theater, in its iconographic idea, presents self-contemplation as constructed, for Vitruvio it becomes a model to visualize the orbits of the planets along the circuits of a spiral staircase that runs through the signs of the zodiac, itself graphically built with the same means as the theater. For Plato (Republic 529c-e) we should treat the mechanisms of the revolving cosmos as paradeigmata or models of intelligible reality rather than eternal truth itself, just as we would treat the beautiful geometric diagrams of Daedalus or any other skilled craftsman or painter. In a way that may become clearer after considering this chapter on technical drawing for theater and astronomy, Plato's allusion to a craftsman's diagrams of cosmic mechanisms is not a departure from astronomical representation. Rather, the reference to drawing in the craft fits within the context of his discussion of the motions of the stars commonly understood through cosmic diagrams, although Plato's use of the general term 'craftsman' instead of 'architect' still does not is clear through detailed considerations of drawing practices in the next chapter. second the

the adequacy of his inclusion of the painters' geometric diagrams in this context is also evident, since the geometry on the circular and radial basis of Skenographia finds its application in a similar way to that of cosmic diagrams. In considering these connections, it is not necessary to postulate that Plato would have found formal similarities in technical drawing in crafts, painting, and astronomy. Rather, he would have in mind simply forms of graphic construction using compasses and rulers, related to Daedalus, crafts, and painting, to emphasize the beauty of such drawings and thus be able to distinguish between beauty and absolute truth, personified by actual speed. Movement on an understandable level. For our purposes, the importance of associating the hand drawing with the rotations of the stars is that the resemblance was obvious enough to lend itself naturally to an astronomical reference, as Aristophanes would send Meto on the stage to design a city. Similarly, Vitruvius in his later discussion of sundials - an acquaintance of Meto's - would describe the analemma (Figure 57) as a graphical figure that reveals the movements of the sun in the universe with the aid of a compass and some kind of calculus, which is "architectural" (9.1.1), just as nature itself as architect (9.1.2) shaped the upheavals of the cosmos. In both Aristophanes and Plato we see reflections on the centrality of drawing in activities related to crafts, astronomy and mechanics, which would later be collectively called architecture. Despite our difficulty in reliably discerning the iconography at work in fifth-century and earlier temples, the relevant lines from Aristophanes' birds leave no doubt as to their application in Athens around 414. In the city Aristophanes' ideal and, I submit, The design of the Theater of Dionysus to which this imaginary form referred predated its apparent application in fourth-century concentric and radial tholoi such as those at Delphi and Epidaurus. As discussed at the end of Chapter 1, the question of where and when iconography was first drawn is perhaps less interesting than the question of when iconography became architectural. In other words, whether the Archaic or High Classic temple architects designed the iconography or not, there may be a difference between them.

these earlier examples and later practices informed by a rigorous application of the theory. This theory is based, according to Vitruvius, on a set of Greek terms (taxis, diathesis, eurythmy, symmetry, oikonomia) that describe the principles that make up architecture and find their application in ideas: ichnography, linear perspective and orthography (1.2 .1 –9). Furthermore, architecture is defined by three parts: the art of building, clock making (including the art of astronomy-based sundials), and machinery (1.3.1). As Vitruvio explains, the last two of these divisions reflect or make visible the sense of order in the mechanisms of nature. In the next two chapters, he examines how the art of building, as the first of these subdivisions, can shape and visualize this sense of order. As the first order-generating activity in the Greek world, architecture provided the model for order in the cosmos by establishing a correspondence between construction and nature through design principles and techniques. In fact, this agreement was strong enough for Vitruvius to appear to be the opposite: that it is the building that reflects the ideal nature, and not the other way around, as in the temple designed on the principles of the ideal human body (3.1). .2) . . . . The ideal, however, is the product of the idea, the device of iconography, linear perspective, orthography and, as I will argue later, the working practices of 1:1 scale drawing, which are the ancestors of drawing. reduced. drawing to scale in construction are .Greeks. . As I explain in Chapter 3, the transition from 1:1 drawing to reduced-scale drawing was a function of vision, or more specifically, vision display, in which traditional scale drawing tools and techniques are seen. augmented by protraction, framing and magnification. they are of spatial order in the way described by Meto of Aristophanes. As indicated in the chronology of innovations in the Theater of Dionysus, iconography was born from linear perspective and thus reflects this theory of vision. However, like the order of space in the viewer's experience, linear perspective itself followed a pattern of order already present in the construction, as did the cosmic diagrams that represented the final reduction in scale in the contraction of the universe in a sufficiently small. build with ruler and compass.

57 Graphic form of the analemma as described by Vitruvius (from Arch. 9.1.1). designer author.

The Craft, Painting, and Diagrams of Plato's Daedalus Up to this point in this study, Plato has served as a source for addressing architecture as seen through a Vitruvian lens, a view appropriate both to Plato's time and to for the wicked of them. philosophical purposes. In this last section of the chapter I briefly consider some of the implications of the material examined here for interpreting the influence of craft on Plato's intention of expression. As discussed in particular in Chapter 1, the value of the craft metaphor is evident in the Timaeus, where the patterns and products of the divine craftsman, and the role of sight in his intuition, form an integral part of Plato's philosophy. Through the analysis of Chapter 2, the Republic can be approached again as an incipient expression of Plato's thought about the trade of his own time that served him in a positive way.

Looking at the Republic in the Timaeus, Plato metaphorically characterizes its earlier volume as a painting (Timaeus 19b-c). Education would be his recently discovered ability to open the eyes of his soul to the idea of ​​good that should be his paradigm (Republic 540a). Earlier in the same text, he compares philosophers to painters, similarly noting that the goal of philosophical rulers is to trace the shape of the city as painters drawing on a divine paradigm (484c, 500e-501c). . Furthermore, he compares his ideal city with a painter's paradigm of human beauty (472d) and, with reference to painting, suggests that the shape of the ideal city, metaphorically speaking, follows a different paradigm from the shape of any real city. . The paradigms of painting to which the Republic refers are ideals, or ideals in the manner of the Idea of ​​the Good, a point explained in 540a. Plato, in turn, portrays the idea of ​​the good as that which illuminates the intelligible realm (508e), as well as the source of the luminous power of the sun and of truth and beauty in the phenomenal realm (517b-c). "High vision" as an active emanation of rays from the eye of the soul and the complementary penetration of such rays into the soul - the way of seeing the beautiful through geometry (527b) or astronomy (529b) - leads to the birth of intelligence and truth and with it knowledge (490b). In a later elaboration on the Timaeus, Plato distinguishes between two types of paradeigmata: the eternal models of the divine craftsman and the models produced from becoming that imitate the eternals (Timaios 27d-28a, 28c-29a, 48e-49a). Paradigms of the second type are those of the "ordinary" (rather than divine) craftsman or painter, as in the astronomical discussion in the Republic, where the diagrams of Daedalus or other craftsmen or painters are "more beautiful" geometric designs, though they cannot transmit the truth for themselves (Republic 529e-530a). As his earlier discussion of the 'divided line' passage points out, acknowledging the limitations of the artisan's or painter's geometric paradigm is not a condemnation. Rather, in the ordinary, everyday world, geometric design provides the understanding that drives one to grasp truth in the intelligible realm of ideas (509d-511e). Why would Plato mention a painter along with a craftsman in a discussion?

geometric design are easy to explain. Already in the fifth century, the paradigm of the monumental painter included the graphic technique of radial protraction, which had been developed in other trades. In addition to the designers of temples and sundials, it would be obvious to include painting in relation to geometric design in the crafts. Unlike traditional designers, however, this use of radial protraction served a purpose explicitly related to vision, which was a major issue in Plato's adoption of the theoria metaphor. If we can direct our attention to the rituals behind this and other metaphors that would be more familiar to Plato's audience, a new meaning emerges. As Simon Goldhill acknowledges, classical theater dialogue is replete with sight references.113 This language is integral to two of the central purposes of performances in the Theater of Dionysus: the training of Athenians as theatai in the new age. of democracy and, more relevant to Plato, the rituals of theoria are the visual encounter with truth and the account of that experience.114 Like the dramas on which such representations are based, Plato writes plays in which various characters they dialogue.115 Furthermore, Per Proposal for Action Plato calls his republic a painting and evokes painting and its paradigms in his descriptions of the goals of his newly invented philosophical institution. In doing so, he presents the Republic as a work that, like a drama, explicitly calls for observation while offering a new point of view, explained by reference to the geometry that draws theoroi into the representation of its incomprehensible case. Realm of ideas through his own experiences. Calling his readers out of their everyday existence as citizens of the city Socrates executed, his Athenian readers become theoroi to whom he offers the possibility of transformation by beholding truths that shine like the sun, which is blinding at first. , but able to penetrate them. in one's soul in the generation of intelligence and beauty that can make one a philosopher fit to rule in his ideal city. It is worth considering the similarities between Plato and Aristophanes. Illuminated by the idea of ​​the good that the philosophical ruler opens the eyes of the soul as the paradigm on which the painter bases his composition, the ideal city thus outlined will be different from any existing city. At the same time, decades before, Aristophanes brings Meto on stage, whose idea is also the painter's paradigm: a construction with the

Radial protraction tools and methods that radiate like a star in a straight line around you. Like Plato's ideal city, Meton's form for the City of Birds is unlike any existing city, created from a graphic device for on-the-spot vision intended for theory. In our own comparison of these accounts side by side, it would be foolish to posit Aristophanes' influence on Plato. More importantly, the careers of these two very different writers intersected as products of the same medium of cultural production in classical Athens. Their respective expressions were therefore based on the same institutions and other factors from which their references and metaphors could be drawn to describe the shape of a city different from any real city, which stands as an alternative and even rival to Athens. In the hands of Aristophanes, the expression is ridiculous and fleeting. For Plato it is serious and a subject to be exposed in volumes of dialogues. In this sense, the parallels observable in Aristophanes and Plato do not come close to bridging the gap between them. Rather, the similarities are limited to relying on the same metaphors of craft, ritual, and exploration of the fabric of the universe that define their shared time and place.

3. The genesis of scale drawing and linear perspective As explored in the previous two chapters, the analysis of texts and buildings can be useful in interpreting the origins of linear perspective and iconography. Ultimately, however, these analyzes must also integrate what can be learned from the surviving drawings and how these drawings might have functioned in the process of designing buildings and their functions. This chapter discusses existing and hypothetical drawings and their respective roles in design, arguing that linear perspective and iconography arose from tools and techniques first explored in graphic methods of discrete element construction and refinements. In the context of philosophy, optics and astronomy discussed so far in this study, the contributions of these tools and techniques to the construction of the current concept of order both in nature and in the observer's perception of it are considered. .

Uniaxial protraction Direct evidence for ancient Greek architectural drawings is limited by the transience of graphic representation. While whitewashed planks of wood, papyrus, or parchment were suitable, albeit expensive, for drawing, our downside is that these materials did not hold up.1 We are fortunate, therefore, that Greek masons and architects also worked their forms on the place. Masonry blocks. By covering these surfaces with red pigment, the use of an engraver with ruler and compass produced designs whose white linear incisions stood out clearly against the surrounding color.2 Masons later attempted to polish these blocks after construction was complete. However, projects like the colossal Hellenistic Temple of Apollo at Didyma (Figures 58, 59) were never completed, and here is the site

58 Hellenistic Didimaion. Summary Northeast. Author of the photo.

Hellenistic 59 Didimaion. Bottom view of the pillars. Author of the photo. Haselberger made his now famous discovery of Greek plants. Carved drawings made over about half a millennium, beginning in the 3rd century, cover some 200 square meters of the walls of Didymaion's Adyton.3 Most of these projects, classified as "working drawings", demonstrate large-scale elaboration of the architectural details. Among these drawings at Didyma, however, there are two important exceptions that may provide useful insight into a broader theory of how small-scale drawing was practiced in Greek construction. In this chapter, therefore, an analysis of these planes opens new insights into the role of number, geometry, and the principle of protraction in the invention of linear perspective and ichnography. On the north wall of Didymaion's Adyton, to the right of the north tunnel on the way down (Figures 8-10) are drawn two related plans for the construction of the colossal column shafts of the temple, which stood 20 m above of the stylobate (Figure 33), both of which would be

completed in the mid-3rd century.4 As noted by their discoverer, Haselberger, these drawings include, on the left, the radial construction for the grooved drum and, on the right, a sectional drawing of a column that preserves the joining process. . Entasis, which roughly means 'tension', refers to the subtle curvature of a column's profile so that, as Vitruvius recommends, the curve reaches its maximum height near the center of the shaft (De architectura 3.5.14).5 Common in found in temple columns since archaic times6, the degree of curvature varies considerably from one monument to another. This refinement gives the spine a unified, organic quality, replacing the potentially cold inertia of a straight pole and a drop with the effect of muscle expansion in response to weight bearing.7 As Vitruvius explains, the rate is also a response to whose longing it is a habit to seek beauty (3.3.13). Without a doubt, Haselberger's recognition and explanation of the method found in entasis design (Figure 60) represents one of the most far-reaching contributions to modern research on the design and construction processes of Greek architecture. Prior to this discovery at Didyma, the method of calculating the ecstasy remained a total mystery, and innumerable attempts to reconstruct it date back to the early sixteenth century8. None of the solutions offered restored the simplicity and ingenuity of the Hellenistic method explained by Haselberger, designed by an ancient architect on the walls of the Adyton, um to design the majestic colossal shafts of the temple. At full size, the curvature would have been impossible to construct with available engineering drawing tools, as it would require a radius of nearly 900m. In section, therefore, the architect designed the thick axis from the central axis (i) to the outer curved profile (g) at a scale of 1:1, a measure of approximately 1.01 m for the outer profile before carving (f ). However, its height is compressed to one-sixteenth the height of the actual columns to be erected. The reasoning

Hellenistic 60 Didymaion. Plant restored for entasis (detail of figure 33). Author of the drawing, modified by L. Haselberger, in Haselberger 1980: Figure 1. for this scale 1:16 is the ratio of dactyls to feet in ancient Greek metrology, where one foot equals sixteen dactyls (or “digits”). In the case of the Didyma drawing, the foot measurement used is an Attic (or Cycladic) foot of 0.296 m, with each dactyl measuring 0.0185 m.9 The diagonal chord (h) flanks the arc (g) in the drawing turning the page to the left Provides a theoretical path connecting the outer radii of the lower and upper shafts when the column profile is straight rather than curved. To describe the curvature of the axis contour, an arc with a maximum height of 0.0465 m above the chord h (called Sagitta in mathematics) with a radius of about 3.2 at the center is created at the center of the axis. of the axis by a rotation of a pair of divisors m. Finally, the shaded horizontal lines in the drawing are separated by a dactyl distance (d1-d65) and

correspond to distances of one foot in height from the actual column of 18 m. Since the drawing maintains full scale in the horizontal direction, a pair of dividers can find the actual change in radius of the axis at any given foot of elevation. Based on the measurements obtained, a second axis was drawn in width and height in its lateral section at full scale on the Adyton wall, which in turn only shows the radius of the column from the central axis to the slightly curved exterior. profile. The resulting stasis is therefore the product of a protraction along a single vertical axis, transforming the arc of a circle into an arc of an ellipse that describes the curved profile of the rod in real dimensions, which can take a long time. . it predates its use there, possibly going back to the same uniaxial method of protraction in the design of columns in classical buildings such as the Parthenon.11

Haselberger's graphical basis of horizontal curvature theorizes precedents for Didyma's construction not only in the context of Entasis, but also of the curvature design process, which commonly began at the temple platform and then moved horizontally through all the layers. construction features. Along with entasis, this horizontal curvature had its beginnings in the Archaic period.12 Like entasis, Vitruvius characterizes horizontal curvature as a response to the needs of vision, using magnification to create convexity intended to overcome the tendency of correct eye to make large horizontal features appear. hollow” (3.4.5).13 The main evidence for the Didyma-related method of constructing the curvature was identified in the late fifth-century unfinished temple of Segesta, whose design reflects influences from temple architecture in Athens. 14 Here Dieter Mertens discovered a regular succession of cruciform markings cut into the vertical planes of Euthyntia, all theoretically level and equally spaced. he identified the Vitruvian without further details as the element providing the incremental curvature by leveling the stylobate (3.4.5, 5.9.4).16 Mertens proposes that the unpaired scamilli are the ordinates of the

Tip of Euthynteria or Stylobate, following a curved pattern, with its highest elevation in the center, unequal to the succession of cross-mark planes below. According to Mertens, to create these unequal ordinates, the architect would have hung a cable from end to end along the Eutinteria, whose curvature resulted in an almost parabolic catenary.17 Thanks to the good state of conservation of the north flank, Mertens was able to demonstrate the accuracy of this method to demonstrate high accuracy in recreating the hypothetical chord line.18 Thus, the distance of each cross to the plane of the chord would give a distance equal to the ordinate marked above, giving the incremental curvature of the Euthyntia measured from point to point. After leveling the upper surface of the euthynteria according to these marked ordinates, the curvature was fixed for all subsequent strata in the superstructure. While this string method is convincing for near-parabolic curvature, the discovery of the Entasis layout at Didyma provides a more likely hypothesis.

61 Temples of Segesta. Representation of the graphic method for the curvature of the platform. Author's drawing, adapted from L. Haselberger, in Haselberger and Seybold 1991: Figure 3.

Solution by means of a graphical construction for the curvature. As shown mathematically, the ordinates corresponding to the edge of the euthynterian line on the cross marks along the long, well-preserved northern flank more accurately describe an ellipse than a parabola, a solution that also applies to curvature analysis. in the northern stylobate. of the Parthenon.19 Along with the mathematician Hans Seybold, Haselberger proposes instead that the crosses in a hypothetical working drawing similar to the one found at Didyma (Figure 61) correspond to subdivisions of a chord within an arc of a circle.20 the spaces between the crosses are lengthened along the chord as the Baseline in the drawing, while the Euthyteria curvature ordinates simply transfer the drawing measurements between the chord and the arc at a 1:1 scale. This uniaxial protraction therefore maintains an identical maximum elevation (sagitta) in design and euntery (0.086m) while extending the design circle to a theoretical ellipse describing the horizontal curvature of the temple. The dimensions of the lost working drawing were calculated on the basis of the ordinates: circle radius approximately 1.49 m, baseline (wire) approximately 1 m (Figure 61).21 If we, together with Haselberger and others, can present If we hypothesize that the architect of Segesta borrowed this method from the Parthenon and other Athenian temples, then we can glimpse the possibility that reduced-scale architectural drawings are at play. in temples as early as the fifth century, at least in the uniaxial variant.22

A Reanalysis of Working Drawings Given the difficulty in Chapter 1 in finding a philological or design justification for working with ichnography in classical temples, the possibility of uniaxial protraction as a common technique has important implications for the Greek principles underlying the working drawings. the construction of large-dimensional graphics. . Haselberger's study of the Didyma plant and its further relevance to curvature is comprehensive and impressive. However, along with the new avenues this research opens up for questions of technical drawing and the architectural design process, much remains to be learned about the drawings themselves, including the surviving drawing at Didyma and the hypothesized drawing of curvature at Gets pregnant. Analysis of the present study in Appendix A, based on Didyma's construction and Seybold's calculations, reveals potentially surprising features that have never occurred before.

observed in these drawings, which may be important for understanding the graphic foundations of Greek construction. As Appendices A-B and the additional considerations in this chapter show, the planning process for curvature in columns (entasis) and in the horizontal planes of Greek temples may have involved more than simple addition or subtraction based on simple intuition. Rather, the analyzes here suggest that graphical techniques for visual refinement may have been based on the equal application of integer and comparable modular features to the design of individual elements and major dimensions in elevation and plan. In particular, my analysis shows that the Entasis design at Didyma is constructed according to a geometric basis of a 3:4:5 Pythagorean triangle ABC, with a modulus formed by maximally increasing curvature, and whole number significant fractions. that appear in the total. drawing (Figure 62). Second, I show that the theoretical working design construction for the Segesta north face is a chord-to-radius integral ratio of 2:3. Finally, I show how this procedure at Segesta might reflect an earlier application of the same procedure made for the curvature of the flanks of the Parthenon, whose calculations decades earlier appear to have yielded the same 2:3 chord-ray ratio (Figure 64). By designing monumental forms through uniaxial protraction in this way, the Greek art of engineering drawing seems to project whole numbers onto buildings through a geometric transformation of conic sections (circle to ellipse). In the manifestation of number in its constructed forms, the construction process to be described here takes it beyond immediate perception. Constructed in this way, number and geometry do not visibly exist in the world, but from a Platonic point of view they can only be measured. The process is like that of the divine craftsman of Timaeus building numbers in the world through the circular movements of the celestial bodies that create

62 Hellenistic Didimaion. Restored design for Entasis with suggested geometric base. Author of the design, modified by L. Haselberger, in Haselberger 1980: Figure 1. The dimensions that configure a sense of order in space. ) the forms or ideas could be fully grasped if one had the opportunity to observe them directly ( δν, βλ π ιν, π βλ π ιν, κατιδ ν). Penetrating us through a duly directed "ascending" look (Republic 490b, 527b, 529b), in which it is the perspective of "soul vision" (519b) that sees the ideas, even if incomplete. For this point of view, arithmetic (525c) and geometry (526e) prepare more adequately to see things, just as for Vitruvius arithmetic and geometry (along with optics) prepare the architect to build them properly, mainly through the proper use of tools in technical drawing. and construction (De architecture 1.1.4). I like

As indicated in Didyma and Segesta's discussions in this chapter, design and construction with the aid of optical refinements does not just trick the eye with addition and subtraction. What is more, they retain the true character of number and geometry in a rationally enlarged way. When reading Plato, it may make more sense to focus on the role of measurement in the construction process rather than the outside observer's perspective of the completed work. In this sense, it is interesting that Plato, in his criticism of losing sight of "the true adequacy of beautiful forms" by not adhering to "the adequacy of the model", resorts to figurative sculpture rather than architecture (Sophist 235d- me). .25 Among the arts, on the other hand, Plato singles out the craft of construction as particularly commendable because its tools (compass, ruler, square, plumb line, stake, and rope) allow such “scientific” precision (τ χνιχωτ ραν ) in their measurements. (Philbus 56b-c). Given the nature of the working plans discussed here, one can consider exactly what kind of measurement guided the builders in using such precise instruments. As Plato himself surely knew, they were guided by views on relations to integers, approximation, and "beautiful" geometry. These guiding visions would have taken the form of a model (anagrapheus), a model (paradeigma), a 1:1 drawing (all three with individual elements planned to scale), and a reduced-scale drawing.26 We have seen Plato's use of metaphor of the paradigms taken from the arts and crafts. Furthermore, the description of small-scale drawing in Aristophanes' Birds reflects the existence of this drawing technique in Athens in the year 414, and establishes such an idea (to use the Greek term for Vitruvius) as a metaphor available to Plato in Athens. While the philosophical use of these terms may be artisan in origin, they do not necessarily indicate a great interest in construction on Plato's part, despite his great prestige over the other arts, certain design and construction processes somehow led to the ideas conveyed in their dialogues became. Rather, we can limit our consideration to the qualities implicitly inherent in such items, which could easily have occurred to Plato as an observant Athenian of the classical period, who admired construction tools and precision of measurement enough to mention such items. things, but whose widely varied goals were those of an architect writing about his craft.

In light of the analysis of the evidence for entasis and curvature designs in this chapter, the role of number in shaping deserves emphasis as a plausible explanation of Plato's interest in the precision of measurement made possible by drawing tools. and builders construction. The focus on integer proportions in these examples (Figures 62, 64) is obviously reminiscent of Pythagorean thought, but their design and construction process exhibits an application of numbers that deviates somewhat from the Pythagorean spirit of numbers as "unit atoms." "concrete. 28 Rather, numbers exist beyond material form at the same time that the architect builds them into them, remaining quantitatively constant while qualitatively transformable in space through altered forms and scales. Particularly in uniaxial protraction, the fit is maintained in a strictly abstract, concrete, and conspicuously lost way by stretching several proportional units along one dimension. The notion of the immutability of numbers would then be reduced to their abstract ontological characterization as disembodied ideas distinct from constructed forms, though of course it is highly doubtful that any Greek architect ever thought of them in this way. But like the respective measures of interval and time in music and astronomy, which must ultimately refer to transcendent numbers and standards of beauty and goodness (Republic 530d–531c),29 craftsmen on the construction site misdirect the look and the tools of a platonic point. view numbers defined in a model. This model, in turn, represents the idea of ​​the work itself in a graphic form that exists beyond the concrete and visible qualities of the work that define it. However, as discussed in Chapter 1, Plato complicates the metaphor by confusing craft with the creation of cosmic order (Daedalus or some other Republic 529e craftsman or painter, and later Timaeus's divine craftsman) and by introducing two types of paradeigmata. : the secondary models of becoming and the eternal models of being that generate these secondary models (Timaeus 27d–28a, 48e–49a). The status of Daedalus' "most beautiful" geometric designs is thus reduced to "admirable" rather than true in the absolute or autonomous sense. With this move, Plato subverts the metaphor of craft on which his discourse is based and allows his readers to redirect their attention to a higher truth and beauty, just as a "real" observer of geometry or astronomy can redirect their vision.

"up" as the soul should see it. Thus, the metaphors of vision and craft come together through a reflection on the role of models in creating order.

Building Entasis on Didyma None of these claims regarding Plato can be sustained without first demonstrating the existence of integral reason and geometric form in the drawings themselves. As Appendix A shows, the ecstasy pattern at Didyma is based on a 3:4:5 Pythagorean triangle ABC, enclosed by a 2:3 rectangle (Figure 62). In addition to this geometric support, the theoretical Pythagorean triangle is based on a modular conception, where the maximum elevation of the arc (g) over the chord (h) forms the module that forms triangle ABC in a ratio of 18:24:30 Relevance of the maximum increase in curvature as an unequivocal measure is reflected in Vitruvius, who prescribes that this aiektio should determine the amplitude of the curves in the fluting of the column. in terms of geometric shape, integral proportions and modular alignment. The effort required to process all of these correspondences into a monumental final product in which those relationships are visually lost makes it all the more interesting. This procedure might suggest Pythagorean motivations for design, as explored in Chapter 1 and its supporting digression, but there is at least part of it a more practical explanation. The considerations underlying the design process probably began with the architect's goal of creating column shafts 60 3/4 ft tall and with a 9:1 ratio for their bottom diameters (= approx. 18 and 2 m). . Given that magnitude, he settled on about two and a half dactyls as a reasonable maximum ecstasy increase. To create a 1:1 scale plan in width, he would need to build and center a pair of colossal calipers of the correct size specifically for the task (as in Figure 64). For the layout at Didyma, how could you have predicted the correct giant radius of 3.2 m (!) and the location of its center without undue trial and error? A likely solution is for the design itself to have been created at a lower cost.

Scale. In this way, the construction of the secondary level according to integral proportions could be easily transferred to the wall surface of the adyton. On a small scale, the architect could manipulate full-size instruments and trace his way through the different versions necessary to obtain the desired relationships between the parts.31 So he was able to start building the Pythagorean triangle ABC. The purpose of this form would not be mystical, but the control of orthogonal relationships throughout the drawing, ensured by the integer numerical measure of the hypotenuse; In a Pythagorean triangle, the integer ratios between the sides and the hypotenuse form a perfect right triangle and therefore perpendicularity. Experiment with a compass would find the center of a ray capable of making an arc of maximum height equal to part of either side of triangle ABC on a chord drawn at B. Based on these measurements, all these details could be mathematically converted into the blocks patron both of the large compass made especially for the occasion and of the project whose curvature he is building. If the plausibility of this conjecture is accepted, then the practices of 1) single-axis protraction represented by the plane and 2) full protraction indicated by plane generation from the previous hypothetical plane can be considered to have coexisted in the medium. of the third century.

Segesta and the Parthenon There is another observation dating from the fifth century about Haselberger and Seybold's hypothetical working design for the horizontal curvature at Segesta (Figure 61). As shown in Appendix B of this book, the chord in this drawing shares a 2:3 integral ratio with the radius of the arc. Rather than request a reduced version of the design in the manner suggested here for Didyma, the architect appears to have simply started with a ratio of 2:3 and constructed this ratio as a chord and circle of length and radius eighteen and twenty seven modules. , respectively.

63 Parthenon, Athens. Chord and arch restored according to Seybold's calculations from construction to the curvature of the platform on the north flank. designer author. Despite this difference, the hypothetical construction of the Segesta curve reveals a clear relationship with the Didyma plant characteristics revealed in the present study. In both examples, integers applied to the design with a compass and straightedge drive the design process for features that need to be understood visually rather than through numerical or geometric considerations. In the case of Segesta's hypothetical design, the 2:3 ratio and the eighteen to twenty-seven module ratio also contemplate a large-scale application of dimensions based on ratios divisible by two and three across the length of the view (Figure 17), as shown in the 2nd:3 ratio between the widths of the triglyph and the metope and the axis of the columns and the height of the entablature and the ratio 9:4 in the main rectangle and the spacing of the columns and the height of the steps . In the plant there is also another ratio of 9:4 in the relationship between the length and width of the stylobate. Drawing to scale is driven by a schematic approach similar to that found in relationships between discrete features and broad dimensions. Perhaps most notable is the fact that evidence of the same process can be seen on the Parthenon itself. As shown in the analysis in Appendix C, the long, relatively well-preserved northern flank of the stylobate makes for an interesting and mathematically sound discovery in terms of the graphical method.

for the construction of the bend of the Parthenon. As noted for the proposed theoretical working design for the curvature of the flanks at Segesta (Figure 61), in the theoretical design the chord required to produce the curvature of the Parthenon's flanks has an integral ratio of 2:3 to the radius of the arch (Figures 63, 64). Whatever similarities are found in the theoretical plans of Segesta and the Parthenon, it is important to emphasize that the analysis proves nothing here. Rather, it simply combines Seybold's calculations with data drawn from a sample of field measurements and other archaeological considerations from an identical context (flank curvature) at the Temple of Segesta and the Parthenon. The identical ratios of 2:3 for the same theoretical construct in both cases may be completely coincidental and, barring additional future evidence, it would be best to remain cautious about this isolated consistency of Segesta and the Parthenon. It should also be emphasized that the result found here for the Parthenon depends on the conscious reading of the different levels, which does not necessarily have to be the case. On the other hand, the identical result returned for both cases is arguably interesting, since it establishes a possible plausibility of the 2:3 relationship in either case. The suggestion of a pattern may also support Haselberger's suggestion that Didyma's construction could have been used for Entasis at Segesta, the Parthenon, and perhaps other temples. Finally, while one can more positively view the present analysis's reliance on the Parthenon's notion of "hyper-refinement" as a weakness, the result of this approach can in turn be seen as support for increases as by design. In short, reading Seybold's geometric calculations and analyzes today can offer inconclusive new insights into our ongoing (and perhaps endless) discussion of how ancient Greek architects might have designed curvature. Thus, when put to a simple mathematical proof, the Parthenon evidence can support Haselberger's "Didyma conjecture" in the process of designing the curvature at Segesta. Since the latter's other features reflect Attic influences,33 it would make sense that his method of determining curvature was derived from practices already established in an Athenian precursor such as the Parthenon. The preliminary proposal of this

The analysis that the Parthenon may have used the same method, and even the same integer ratio, of the Temple of Segesta makes the theory of intentional "refinements of refinements" (rather than errors in leveling) in the Parthenon be even more convincing. Most importantly for the present study, the calculations in these two temples for which data are available provide some support for the proposed practice of uniaxial protraction for curvature. On the north flanks, both at Segesta and the Parthenon, a drawing to scale may exist by the architect's application of the numbers two and three to a chord and a radius and the extension of the division of the chord into corresponding segments to the actual dimensions of the room. correspond.

Uniaxial Protraction Reconsidered Regardless of when and where uniaxial-scale design was invented, the means by which architects conveyed a sense of order appear to continue traditional design practices. As an example, Gruben shows that the archaic precursor of Hellenism is in the capitals.

64 Proposals for graphic constructions for the curvature of the platform on the north flanks of the Temple of Segesta and the Parthenon. designer author. Didymaion, a Pythagorean triangle 3:4:5 ABC fixed both the width of the volutes and the diameter of the axis of the upper column according to an integer ratio of 4:5 with the diameter of the cusp (Figure 65).34 In construction of Entasis by uniaxial protraction in the Hellenistic Didymaion, the same geometric base returns. In the following century, the use of the Pythagorean triangle as an ordering principle in the art of painting can be found in Temple A of the Asklepieion on Kos.

Iconography (Fig. 86).35 This continuity may suggest that the origins of the ideal, in terms of small-scale drawings that shape spatial relationships, may be closely linked to ancient methods of order-building in individual masses. However, despite the survival of such a tradition, the transition from a geometric base that shapes tangible and plastic features to an invisible linear network that aerially views relationships through gaps represents a significant intellectual shift that deserves explanation. more detailed in this chapter. First, the relationship between number and shape can be emphasized, built through the application and manipulation of geometric shapes. In Chapter 1 and

65 Archaic Didymeon, 6th century BC Restored capital by G. Gruben represented following the model of the Pythagorean triangle ABC. Author of the drawing, modified after G. Gruben, in Gruben 1963: 126. Author of the drawing. In his supporting digression, he notes that Polykleitos' canon, as a text with Pythagorean overtones and possibly reflecting architectural theory, appears to have combined beauty with adequacy,36 and that integers produce a "good" through what seem to be intuitive adjustments. of these numbers.37 In this context, the possibility arises

that optical refinements, such as deviations from "true" numbers and straightness, are an essential part of the beauty and quality of buildings. In this context, the digression also mentions Aristotle's emphasis on chance in architecture (Nicomachean Ethics 6.4). Although it is not clear if this value is applicable to optical refinements in monumental temples, a possible reading of Aristotle's statement seems consistent with the link between intuitive judgment and good results. On the other hand, the role of intuition and chance, especially in construction, can simply be related to the effectiveness of pre-planned adjustments that can only be truly appreciated in the dimensions of the finished form.

Radial protraction Adjacent and partly intersecting, Didymaion's design for the Entasis is a large semicircle with radial divisions forming two wedge-shaped sections, each corresponding to one twelfth of the semicircle (Figure 66).38 The purpose The obvious feature of this design is to have equal divisions to make the circumference of the column axis for the twenty-four flutes and crests of the Ionic order, although the details of how this procedure works require explanation. In general, however, the plan shows how a Greek architect might have conceived the fluting of the columns as a construction radiating from the center of a circle.

66 Hellenistic Didimaion. Restored design for column channels (see Figure 33). Author of the drawing, modified by L. Haselberger, in Haselberger 1980: Figure 1. The drawing at Didyma is compared with other known material. An Ionic capital from Pergamon in the Bergama Museum preserves the radial lines that positioned its edges,39 and there is a Doric capital that shows the same method in action.40 The drums of the Hellenistic Stoa in the Agora of Kos, in turn, they preserve the Radial construction for the flute of their Ionic columns (Figure 67), showing in this case the graphic arches of the flutes before carving. Restoration of drums based on surviving fragments.42 The method relies on the flat surface of the drum or neck of the capital to produce fluting, which differs from the method apparently applied to the unfinished Roman columns on the western face of the capital. Artemision was applied in Sardis, for example, where flute playing was started but never finished (Figure 68). This is one of two full-length columns erected in the 2nd century AD. It ends with the extension of its flutings above the base of the capital (certainly a technique devised to avoid damaging the delicate arseille during placement on the vertical column), suggesting that the divisions in the curved surface of the neck profile.43 Indeed, as current temple researcher Fikret Yegül showed me at the site, finely incised vertical lines along the length of the staves, possibly plumb lines cast from above, defining the groove at the apex as well as its intended continuation towards the base. . An unfinished column in the Didymaion portico also bears similar incised lines around the perimeter of its lower shaft, in this case clearly marking the edges. However, the use of such plumb bobs would not prevent radial construction in the flat plane of the upper drum that may exist.

67 Stoa, Agora, Cos. Unfinished ion column drum retaining the radial construction to groove the ion columns. Author of the photo. determines the suspension points in a manner that will be described later. But what distinguishes Didyma's design from each of these examples is its function as a model for columns yet to be designed, rather than as a guiding method for working on the columns themselves.44 In general, the relationship between segments along of a circular perimeter and radial lines converging at a central point were undoubtedly obvious and quite old, observable in everyday activities such as cutting round slices of bread. Specifically in architecture, the surface patterns carved and painted around concentric circles in works such as the monumental disk-shaped terracotta acroteria of Heraion at Olympia from around AD 600 indicate that interest in such patterns was quite old and they were used as columns in timber construction (and tree trunks left behind), preserved vascular rays emanating from a natural center (the core), possibly suggesting a similar shape for the

The tops of the columns, as well as the naturally vertical stripes on the curved surface, may have suggested the idea of ​​channels running along an axis. As seen on half-timbered houses or modern telephone poles, these vertical stripes are in fact the same vascular rays that appear radially when viewed on the surface from above and below, and it is conceivable that the beginnings of the columnar undulation have something to do with doing it by imitating and regularizing this natural linearity

68 Artemision, Sardis. column detail Author of the photo. Matchstick on a wooden background. Regardless of this question of origin, however, a regulated precision characterizes the undulation in the surviving columns as that of Didyma. Without the precision of a 15 degree angle measurement for each of the 24 divisions of a drum specified in the design, the pillars would look flawed no matter how carefully they were made. It is unknown how this precision was achieved. Vitruvius, who clarifies that Ionic axes require twenty-four equal flutes (De architectura 3.5.

as well as how the method is intended to be performed.46 One hypothesis emphasizes that the method need not be based on theory and that the task may depend on some degree of "falsification" with a pair of divisors gradually adjusted through trial and error. 47 As a second possibility, it is considered here that the architects in the classical era were masters in handling the instruments and methods of technical drawing. From this perspective, the notion that these architects faked their way through graphic constructions into something as mundane as the flute by mere trial and error confuses their knowledge with our own unfamiliarity with their tools and processes, or unduly discredits the breadth of the flute. of experience gained on the job. with such tools since the earliest days of Hellenic construction. At least hypothetically, the fluting on the Didyma colossal columns (Figures 69, 70) can be understood as the product of a deliberate construction process, aided by the pattern of grooves preserved on the Adyton Wall (Figures 66, 73). Which was designed with a radius greater than that of the necks

69 Hellenistic Didimaion. Detail of the permanent columns of the northeast flank. Author of the photo.

of columns ensured that it could fit necks of slightly different widths due to the different heights of the column drums, a concern that is perhaps also reflected in the larger circumference drawn around the edge markings on the Kos column (Figure 67). Using compasses, the mason can transfer the entire design to his block of marble, including its radial lines connecting the perimeter to the center (Figure 71.1). This guide structure could be placed at the top or bottom of the drum. In the latter case, the mason can then trace within his radius the smallest radius of his columnar drum, whose intersections with the radial line can, with a pair of dividers, determine the width of the ridges that will be repeated on its circumference ( Figure 71.2). By centering your dividers at each marked point, small even arcs form the ridges and crests (Figure 71.3). After having chiseled the column drum on the curved surface formed by the smaller radius, the groove can be chiseled from the bottom of the drum towards its lip (Figure 70), which will serve as a guide to mark the grooves along their entire length. . the axis (Figure 59). This explanation still does not explain how the architect created the 15 degree radial divisions in the plan that serve this process. One likely method would be to follow the same perimeter pruning algorithm found in the six-petal rosette (Figures 42). To do this, the architect would first quadruple the circle containing the intersection of two arcs at the top of his drawing.

Hellenistic 70 Didymaion. Detail of the permanent pillar on the southeast flank. Author of the photo. formed by a compass centered at each end of the baseline (Figure 72). You would then mark a segment that is one sixth of the semicircle from the top of the arc and then divide it with a pair of dividers (Figure 72). Alternatively, the architect may have used a tool after dividing the circle into quarters.

similar to the “curved ruler” (Figure 74) described by Aristophanes, which would have allowed him to simply place a ruler over the guide rays of the curved ruler and then, to set the ruler to plane level, remove the curved ruler, before cut the rays of the plane from the perimeter to the center (ray lines in the drawings continue beyond the centers - see Figure 73). The ease of using the rosette or curved rule method raises the question of why masons couldn't just whistle without the aid of an architect's blueprint. Indeed, one wonders if such skilled craftsmen ever bothered to follow the pattern provided. Pure

71 Proposed order for flutes and drums in the Hellenistic Didymaion based on project analysis. designer author. The didactic motivations of the plan by the architect should not be ruled out. As anyone who has mastered certain tools knows, art does not have to depend on schematic processes. Similarly, one might question the practical versus theoretical value of the previously discussed neighboring design for entahsis, a possibility that should in no way limit its value to our knowledge of Hellenistic architects' understanding of the design process. In the case of the Doric order, an architect or mason divides the circumference of his drums into twenty 18-degree segments, rather than the twenty-four 15-degree segments required for Ionic flutes.48 Again, Vitruvius does not specify how this construction is can come. Be a proposed procedure

72 "Rosette-based" method to determine the undulation of a plant like Didyma. designer author. What is overlooked is the determination of the twenty equal segments as half the diagonal distance from the vertex of a circle to an arc whose diameter is equal to the radius of the circle (Figure 75.1).49 Simply, a geometric analysis of this method shows a tolerance for the required precision of .50 grooved

Hellenistic 73 Didymaion. Hole in the surface of the north wall of the Didymaion adyton, marking the point of convergence of the radial lines and the center point of the great semicircular arch of the design for the fluting of the column. Author of the photo.

Hellenistic 74 Didymaion. Restored plan of fluted columns at Didyma, showing the hypothetical location of the proposed transporter to construct the radial lines for the twenty-four divisions of the circumference. Design author, modified by L. Haselberger, in Haselberger 1980: Figure 1.

75 Hypothetical methods to produce twenty equal circumferential divisions for Doric tides proposed by P. Gros (top) and J. Ito (bottom). designer author.

A more plausible solution is to subdivide the circumference into segments, each equal to five-sixteenths of the radius, resulting in a demonstrable degree of precision (Figure 75.2).51 Perhaps the only serious drawback of this second proposed method is its complexity. Given the inevitable small variations in the radii of the flat surfaces of the individual drums, it would be difficult to compute five-sixteenths of a radius at once with a pair of dividers. Each ray would have to be quartered, and two of those quartered sections would have to be quartered again to find five rooms. I am not aware of any finding of markings on drum surfaces resembling this construction, but there is reason to believe that a method at least related to this technique was used. As already mentioned, the Ionic columns of the Stoics in the Agora of Kos (fig. 67) preserve an incised radial construction similar to the design at Didyma, and the lower part of a Doric capital at Pergamum demonstrates the conception of the flute. Doric as a centrifugal arrangement, dated to radiate from the center of a circle.52 Regardless of whether the construction in question is of twenty-four or twenty segments, these drawings evidently represent a radial extension of equal angular divisions, ready to be applied to circumferences of different sizes. Equally obvious, the instrument that would facilitate this radial protraction is the curved rule mentioned by Aristophanes. Unlike the rosette-based method of cutting equal perimeters, which could easily construct the radial divisions of the curved rule for use in the Ionic order, an architect could use the find Method to construct five-sixteenths of the radius of this semicircle and connect the resulting divisions in the circumference of the tool to its center.53 As products of the compass and straightedge, these straightedges would have been extensions of these generative tools and thus part of a standard apparatus for designing columns according to the principle of protraction. radial. The method proposed here, based on Didyma's design, would describe only one of many possible possibilities, such as Greek and

Masons would have flute drums. To be sure, various means have been employed in the many construction projects in the Greek world over the centuries. The paucity of evidence of the poorly preserved type at Didyma, Pergamon, and Kos prevents us from even remotely suggesting a commonly used method of corrugating columns in antiquity. On the other hand, it would be unwise to equate limited explicit evidence with anything like the frequency with which the proposed technique would have been applied. First, the happy survival of the plants at Didyma, given the unfinished state of the colossal sanctuary, certainly suggests the existence of similar graphic models at the site that have not survived. Haselberger's 'Didyma conjecture' discussed above suggests precisely this possibility, using the same construction for Entasis as early as the 5th century. Furthermore, the repeated radius ratio of 2:3 in hypothetical working drawings for curvature in these temples observed here provides further support for the similarity of such designs, and it stands to reason that the same degree of similarity proposed for uniaxial protraction could also be extended to designs for radial protraction. Secondly, in addition to the problems of models such as the grooved plan from Didyma, the reference to radial protraction on the shafts from Kos and the capital from Pergamum suggests the existence of a direct application of the technique without dependence on a model. In other words, even when the architect provides a model to obtain the dimensions of flutes for drums of different diameters, as in the case of Didyma, the traces left on these other elements may show that the artisans in some cases would simply apply their own protractor. . In such cases, the hassle of cutting the radial divisions emanating from the curved ruler would just be one way, perhaps too tedious, to use this tool. Arguably a better method than cutting along a straightedge of the curved rule would be to use a plumb bob in conjunction with the curved rule, which would allow the craftsman to alternately set the marks for grooving on the top, edge, or edge. curved outer surface of the barrel (Figure 76) or capital. Possibly this method could have been applied to the surviving unfinished drums of the Archaic Parthenon, which have received the initial fluting ready to continue to the necks of the capitals (Figure 25). how long seen

blunt lines running through the aforementioned columns at Sardis, the plumb bob in combination with a protractor can even provide additional control for the length of the flutes that run through the waves. The plumb would interfere with the adherence of the line to the surface of the shaft, but this problem could easily be solved by applying manual pressure to the line so that its true verticality is not compromised. In most cases, however, the use of the straightedge, plumb bob, and compass should have left no trace of breakage other than the flute itself. Therefore, there are several ways to use the well-known curved rule of Aristophanes in combination with compasses, rulers, and plumb bobs. It should also not be ignored the extent to which various tools and procedures would have been used together to ensure a number of checks for the sake of accuracy and conformance, including direct application of the curved rule, even when dealing with an architect's design as in Didyma. In fact, it is the full range of tools available that allow construction to reach its high precision that seems to have impressed Plato as the highest of technai (Philebus 56b-c). Before concluding this brief introduction to radial protraction instruments and methods in columnar flute design, a preliminary and unlikely conjecture about their relationship to uniaxial protraction may be of value. Despite the clear evidence of uniaxial protraction provided by the third-century Didyma design (Figure 66), the entablature and platform curvature in its earliest Archaic manifestations may have arisen from the catenary and other possible methods.54 Despite With a similar result, Seybold's calculations and, to a lesser extent, the observations of integer correspondences discussed in this chapter, support the plausibility that uniaxial protraction was one of the methods used by scientists. architects since the early 5th century. However, when considering something like hanging a rope in the catenary method, the technique of extending metric adjustment along a single direction is so abstract that one wonders how anyone could have such a concept. One possibility worth considering is that the method may have been inspired by the habits of working with graphical constructions for tides. In addition to the protractor-based method, the related rosette-based method of cutting circles is applied directly to the perimeter of a design.

or the ion drum surface produced a multifaceted polygon. With or without a protractor, an architect's observation that the same technique of crossing the perimeter produces an equal number of segments, regardless of the size of the drum, would have suggested the very concept of small-scale drawing: the process of drawing to a scale. relatively small. smaller anticipates an identical shape on a larger scale. Again with or without a protractor, the principle that unites the smallest and largest forms is the principle of equal angular divisions in a polyaxial arrangement converging from the center of a circle, which describes the very principle of radial protraction. On the basis of these radial axes a polygon of twenty-four chords results, the presence of these chords being perhaps more pronounced when intertwined, as in the related construction of the Zodiac (Fig. 77). The Entasis design and related hypothetical designs for platform curvature are simply constructions of these same basic elements of axis, chord, and circle or arc, except that protraction is generated abstractly along a single axis in place of all axes. To understand this principle of protraction, it would help to first look at it in radial protraction, where it is actually visible and not just understandable. By building 1:1 scale flutes for drums of different sizes, experience in handling and developing tools and techniques would allow architects to see the relationship between the resulting product of fluted rods and the universally applicable geometric form that governs all these bars. based. despite individual differences between them. Since the underlying form exists separately as a concept in the architect's mind or on his canvas, he can abstractly transform it through measurement and imagination. this way everyone

76 Hypothetical methods of fluted columns using a protractor. designer author. Numbers that define the perimeter according to the convergent radial divisions

at a midpoint they are offset by integers that define radius, chord, and other dimensions by linear rather than angular measurements. But perhaps it was the integral adjustments of the curved perimeter, born of angular relationships and visually defined as concrete units of fillet and fillet, that were among the first modules of classical architecture. 61) and, as we shall see, through space in accordance with the full potential of radial protraction, the module as an anchor for the principle of commensuration could have emerged along with the 1 : 1 scale drawing tools and techniques for columnar. stretch marks

Linear perspective and the birth of architecture As discussed in Chapter 2, Meton's geometric form in Birds does not describe a city that exists outside of Aristophanes' fictional dialogue, and makes more sense as an allusion to circular and radial form. of the theater itself. at the Meton deliver your work. lines. Once again, theaters were traditionally non-circular and radiating, the earliest example without wood being the Theater of Dionysus, the rebuilding of which in stone began around 1900. 370. Either Aristophanes' verses of 414 anticipate the later form, or, more plausibly , the theatrical stone form gave permanent expression to the experimental circular and radial composition of his earlier phase. As such, the theater to which Aristophanes refers in order to relate it to the experience of his audience was influential in reshaping the pnyx in the late fifth century according to a circular arrangement for a city of birds in Aristophanes' Ridiculous Dialogue: From here I place this curved ruler, I insert a couple of compasses... and I put a straight ruler and extend it to form a square circle with an agora in the center, and like a star, which is itself circular, the rays will emanate straight around it. (999-1009) In addition to the question of the formal appearance, the metons are declared tools (curves

ruler, compass, hairline) and procedure (quarter circle, radial lines) apply to flow construction in Didyma as well as theater planning. Even as a general observation, Vitruvian's method of building theaters in plan may suggest the technique of arranging twenty-four equal flutes on an Ionic column. Drawing on the verses of Aristophanes, the notion that ancient column percussion practices lent themselves to the redesign of monumental theater through scale drawing offers a seemingly straightforward explanation. Still, in the case of the Pythagorean triangle as a geometric support, there is a hint of a progression

77 drawings with circular and radial correspondences indicate: the zodiac as a circular construction with twelve equal sectors for the signs (above); That

Greek theater (below) according to Vitruvius (From arch. 5.7.1-2). designer author. from individual Ionic capitals to the Entasis design and the scale plan of a building such as Temple A on Kos (Figures 62, 65). Still, there is a big difference between this type of design used in the case of Temple A and the Theater of Dionysus. A second-century product, Temple A may follow a rectilinear, reduced temple design pattern that dates back to Hermogenes in the third century and to Pytheos before his work (Fig. 81). As a related tradition, there are also fourth-century radial buildings, such as those at Epidaurus and Delphi (Figures 38, 39). According to Vitruvius (7.praef.12), Theodore of Fokaia wrote a manual for this tholos at Delphi. As discussed in Chapter 2, the 3:5 ratio of the diameters of the cella and stylobate of the Delphi building is repeated in Vitruvius's writings (De architectura 4.8.2) and also appears in the Round Temple of the Late Republic on the Tiber in Rome. Furthermore, this is exactly the same ratio of integers in the diameters of the circular massif on Kos (Figure 31). In addition to oral traditions, written works on the building trade were available to guide architects in the design of their buildings. As a result, by the time of Temple A, iconography in temples was probably a matter of course. However, as discussed in Chapter 1, the same conclusion cannot be drawn from the fifth century. If the Pnyx and Theater of Dionysus designs are exceptions to this conclusion, there are two possibilities. Either iconography was common in fifth-century temples, despite its apparent lack of integration (or necessity) with the designs it produced, or the invention of iconography took place in the specific context of spaces designed for large gatherings of people, who focused on individualities. . actions and speakers. Whichever of these two possibilities may have been the case, the available evidence suggests that the remodeling of entire buildings, specifically according to the tools, techniques and principles previously applied to the unique character of the columnar drums, was first attempted on a large scale. . place at joint observation sites. . By addressing the particular circumstance that such display spaces represent, it can be explained why they have undergone the transformation described. As in the temples, the traditional form of theaters

it was simple, a fact that seems less likely to cause the theater to take the form of a column drum than that of a temple. Rather, there might be something intrinsic to the functions of temples and theaters that invites the transformation of the latter rather than the former. In Greek temples, the focal point of the communal gathering was the altar as a place of worship in front of the building of worship. During offerings, the cell doors were opened to reveal the cult statue of the deity framed by the door. In this state, the statue now stood (or sat) in front of the participants, bringing the god into visible presence as the recipient of the ritual offering. In addition to offerings, other notable rituals may have taken place in front of a temple. During the Archaic period, the choral performances of the City of Dionysus appear to have taken place in front of the Temple of Dionysus, near the southern slope of the Acropolis hill.57 Wooden tribunes were erected here to meet the performances with the temple as a backdrop. . In the early fifth century, when seating was moved north to take advantage of the safer rise of the Acropolis hill, the temple stage was lost and replaced by a skene, the orchestra-style dressing room tent. in the Agora as the other great performance venue in the city. This visual separation of the temple from the rituals of the show would have allowed new considerations in the design of the sets to give spatial meaning to the representations of tragedy and comedy. In this context, the invention of skenographia arose, which consisted of painting on the scene using an illusionist device to create scenarios that offered a realistic setting appropriate for specific actions and dialogues. According to Vitruvius, scenography was first applied in the tragic productions of Aiskhylus (7.praef.11), whose death in 456 suggests a terminus ante quem for this technique, which Vitruvius says was the invention of a painter named Agatharcus. Care must be taken in considering what exactly might have characterized Agatharcus's works, although certain conclusions can be drawn about the overall formal qualities and chronology of the set design. Vitruvius is clear in his description of skenographia as radial lines to and from circini centrum, the center of a circle drawn by a compass as the vanishing point (1.2.2). However, it is not known whether this precise definition corresponds to Agatharcus's practice as opposed to that of later painters. Aristotle's testimony is

agrees with Vitruvius's claim that skenographia was a fifth-century invention (Poetics 1449a.18-19), but his location of its introduction in Sophocles' tragedies (which initially coincided with Aiskhylos but flourished after his death ) can point to a point. inconsistency in the respective sources of Vitruvius and Artitoteles. Perhaps Agatharcus invented skenographia for Sophocles' tragedies instead of Aiskhylus. Alternatively, Aristotle's sources may not have recognized Agatharcus' painted landscape as suitable set design, the qualities of which were developed in Agatharcus's work with innovations by somewhat later painters in Sofokles' theatre. It is conceivable that the first scenography of the first half of the fifth century does not resemble a painting by Masaccio or Alberti's theory in which radial lines converge at a central point. Rather, it may have been more intuitive and less systematic, as in Trecento Italian paintings where axial or parallel lines converge roughly along a central axis. In other words, the new desire for spatial illusionism as a means of evoking a realistic sense of drama's location may have stimulated an experimental and empirical approach to linear perspective rather than one based on theory. As Vitruvius tells us (7.praef.11), Agatharcus invented and wrote about scenery, but his account in turn informed the studies of Anaxagoras (c. 500–428) and Democritus (c. 460–c. 370) who as Cosmologists and astronomers would probably have something new to add to the subject. Regardless of who first theorized the set as a circular construction with radial lines converging at a central point, there can be little doubt that this shape, and the tools and techniques necessary to produce it, were at the time the fictional figure. . the astronomer Meton described it in the theater in 414. It is unlikely that Greek painters developed their own independent practices of composing geometric bases using ruler and compass before the invention of linear perspective. As early as the 9th century, vase painters created horizontal registers, which are circular due to the shape of the vase, as well as other motifs such as meanders, guilloches, and diaper patterns. These elements of compositional organization and decoration are obviously of a different nature than the use of the ruler and compass to guide plane relationships. Instead, fifth-century painters would have learned the trade.

technical drawing of those who have practiced it for a long time. Among these connoisseurs were astronomers, whose methods for studying the relative motions, distances, and sizes of rotating bodies in the cosmos and representing orders used the graphic medium of technical diagrams. Diagrams like the zodiac and other designs based on them were prominent in this tradition. In drawings like these, the circular and radial construction was natural and capable of representing order itself. As discussed in Chapter 2, Euclid's Phenomena shows the central position of the Earth in the universe by means of a diagram (Figure 34) with the visual rays of a terrestrial observer radiating outward, like the visual cone theorized in the Euclid optics. These rays extend towards the eastern and western constellations, having equal lengths from convergence to circumference, thus demonstrating a geocentric structure. What allows this cosmic diagram to "prove" the centrality of the earth is nothing other than the initial assumption that the universe is spherical and surrounded by a circular belt of constellations divided into twelve equal segments. Furthermore, as a radial construction showing the full profile of the sign belt, the drawing theorizes the visual experience of the eastern and western visions of the terrestrial observer as an abstract entity imagined from outside his perspective, a representation of the vision itself. . unanswerable question to ask, where does this representation of order come from as a circular and radial graphic construction applied both to the world and to the way of seeing the world? A possible negative answer here is that the origin of this sense of order can be identified with a single circumstance. As discussed in the following digression, in archaic times, Khersiphron, the architect of the Artemision in Ephesus, devised a mechanism to transport columns by attaching them as axes to a wooden frame with fulcrums that allowed the wheels to turn. In Anaximander's model of the cosmos from the same period, the earth is a drum with columns at the central axis around which the heavenly bodies revolve, suggesting how craftsmanship may have influenced the way in which shape and form were conceived. mechanism of the universe in the 5th century. used the same construction as an ionic column to divide the revolving belt of signs around a central ground. A potentially intriguing conclusion would point to the ribbing of the pillar as the origin of classical cosmology, with the graphic method of construction of the first

transferred to the zodiac, which in turn was transferred to the theater. However, one doesn't really have to worry about the evidence gaps one would have to fill in for such an interpretation. Although architecture could have had such a direct impact on Anaximander's model of the universe, it need not have. In an alternative hypothetical scenario, Anaximander's pillar-based model may have been the invention of later sources, who noted a similarity between the construction of the pillars and the zodiac, just as a later interpolator may have inserted Vitruvius' comment on the identical construction for the Latin theater and the zodiac.59 However Anaximander may actually have conceived of the cosmos, another interpretation of the connection between the pillar and the cosmic diagrams is more plausible, if unlikely. As with the innovation of uniaxial protraction as a graphical method of generating platform enthasis and curvature, Archean period columnar undulation may not have occurred in the manner described here, based on evidence at Didyma and elsewhere and Aristophanes dialogue. However, whenever such techniques were put into practice, they would have created, through repetition, habits of working with compasses and rulers, along with the development of the protractor as a product of these tools. In time, these work habits would have developed the radial division into twenty-four parts and the methods of making them as the standard construction for engineering drawing. In this context, the ancient Greeks' observation that twelve constellations of stars rise, cross the sky, and set repeatedly would have led to specific ways of visualizing the character of this process. First, familiarity with the mechanics of the wheel turning around a fulcrum would have suggested a circular pattern of rotation in the progression of such bodies, although it may be difficult to convincingly demonstrate such a mechanistic view of nature before the Hellenistic period. 60 More relevant to the geometric interests of Plato and his students, this turn would resemble the experiment of tracing a path around a central point with a compass. In addition, the rosette method of perimeter intersections and the related radial protraction method would have satisfied graphical needs for both creation and theorization.

Whether craft influences theorizing or vice versa, the difficult distinction between these two types of cultural production lacks authority even before a relatively late date. Figures like Ptolemy in the Roman imperial period and Euclid and Plato's student Eudoxus before him are clearly in the theoretical mode, exercising the skills of technical drawing to discover and explain the universe, vision, and geometry in characteristically abstract and inwardly coherent ways. . However, before Plato adopted theoria as a metaphor, it is not always easy to strictly separate empirical action as doing and reporting from doing (as in written works like those of Khersiphron and Metagenes or the Polycletus canon). . and accounts of nature on the other hand. Long after Anaximander built his sundial and Cosmos Sphere, Meton continued to build sundials even as he refined annual measurements and discovered lunar cycles. Similarly, in the Republic, Plato might invoke the name of Daedalus in a discussion of the truth of speed in cosmic revolution, just as he might present the sense of order in the universe as the product of a divine craftsman in the Timaeus. . Even a later writer like Vitruvius accepts or perceives the intersection of construction, mechanics, and timekeeping well enough to classify them as separate departments under the architecture of a single institution. So it might be a bit of a stretch to conclude that construction and astronomy use the same technical drawing tools and methods, let alone that one borrowed those tools and techniques from the other. More specifically, one can imagine how construction and astronomy were shared by a range of craft techniques as a range of activities related to the existence of an order in the world, be it that order in the visible objects that are next to each other. within arm's reach, or in the larger totality of cosmology that requires visualization through theorizing by oral, written, or graphic means. As noted at the end of chapter 2, Plato himself characterized his dialogue as a form of craftsmanship. Understood in this way, one need not imagine a philosopher, an astronomer, or anyone else looking at the groove of a pillar as a model of cosmic order. With the repetition of the radial division of a circle in technical drawing for various purposes, the shape itself would have acquired an association with order over time. A similar development is likely to occur when refining Skenographia. Whether or not there were intuitive initial attempts at a linear method

To create the spatial illusion, the painting would have been based on existing methods of technical drawing in structural engineering or astronomy, as the arts were based on such methods. In the hands of those who habitually built graphic forms according to converging radial lines in the center of a circle traced with a compass, a systematic and artificial concept would have been determined to understand how vision works according to the same properties. In a design-driven visuality, vision then becomes an extension of radial rays converging at the center of a circle, providing a model for Euclid in the later theory of optics. Finally, the new form of the Theater of Dionysus, which is so influential to this day, adopts the same circular and radial shape as a repetition of the same method of graphic construction. Rather than simply imitating fluted column construction, the theater's floor plan preceded the practice of linear perspective used in its scene. Skenographia as such used a device that made the theatron a place for shared viewing, merging the optic rays of theoroi (foreign spectators) and theatai (Athenian spectators) into a shared experience of ritual spectacle. Through the principle of radial protraction, such a drawing can extend from its plane into the void at any scale, drawing the audience's gaze from all directions towards a focal point. Far from being merely decorative and incidental to the theoria that theaters served, the question of seeing or thea was a salient intention of theoros and theates experience. As Goldhill asserts, the theater is the very place where one learns to be a theater, and the language of tragedy is replete with repeated and assertive references to the act of seeing and the importance of observing the actions of its characters.61 Although The First discovery Radial protraction may have occurred in crack corrugation practice, so the 1:1 evolution towards reduced drawing in architecture involved another important development. The reorganization of the entire theater into a circular and radial building was not just a transfer of the design process of the column drums to that of the entire monumental building through reduced drawings. Most convincingly, it was a transfer of geometric support from the vertical surface of the skene that shaped the visual experience of theoroi and theatai now applied to the hollow slope of the curved koilon. The mode of this transfer was flat, retracted

reduced into an abstract surface from an aerial perspective to represent the theoretical projection of rays from a perspective outside of the viewing experience of the audience. In doing so, he anticipated the unnatural view given in Euclid's cosmic diagram (Figure 34) that describes Thea's experience of the outside terrestrial observer. By designing a building in this way in accordance with the theoretical understanding of the process of seeing, the theater became a complete expression of a place of seeing that reified the understanding of seeing itself as a radial convergence of rays in space. According to this interpretation, linear perspective, applied for the first time in the first half of the fifth century in the Theater of Dionysus, preceded and guided the use of iconography. A concept elaborated through scale drawing, this iconography was, in the words of Vitruvius and also Aristophanes, one of the first examples of what would later be called an idea. Although it is not known whether the new design of the Theater of Dionysus reflects the earliest example of ichnography in Hellenic construction, from the perspective of later theory it is at least perhaps the earliest recognized architectural application of the practice. Along with the mechanical and astronomical qualities of architecture, Vitruvius defines this institution as the most obvious category of architecture. Traditional for this art, the graphic elaboration of the drawing in the horizontal plane of the column drum establishes the organization of specific features (of the flutes).

78 Artemision and now Magnesia-on-the-Maeander. Restored floor plan with a geometric base proposed by W. Hoepfner. He drew

Author, modified after W. Hoepfner, in Hermogenes: Figure 1. Integral part of the visual experience of the building. By contrast, when archaic and classical temples used ichnography, they did so in a way that cannot be readily appreciated in a way that combines the three-dimensional experience with the instruments and technical drawing methods that produced it. In the Greek theater (Figure 77), the radial construction with ruler and compass establishes the ascending forms of the koilon and its courses. The invention of this new form of theater introduced an equally new way of designing all buildings in accordance with the craft of technical design through iconography, a derivative that transcended theater as an isolated type. The round building at Delphi (Figure 38), with its circular arrangement of twenty columns, represents an extension of the same radial arrangement of undulations of its Doric columns. The circular temple of the Tiber is less internally coherent, repeating the 3:5 diameters of the temple. Delphic building and its arrangement of twenty columns,62 although the columns of this Roman building now show the twenty-four divisions of the Corinthian order. In addition to circular buildings in particular, the use of ichnography to guide general building design was also extended to traditional rectilinear temples (Figures 23, 81). Furthermore, the radial and axial approach in theater design can even be extended to the design of relationships across voids within and between complexes, as in the connection of the Sanctuary of Artemis Leukophryne and the neighboring agora at Magnesia-on-the-Maeander ( Figure 78). 63 Interestingly, then, the graphic media of spatial design began as a way to articulate the sculptural surfaces of columns in traditional buildings that existed as sculptural expressions in their own right. With the help of Vitruvius and the Greek sources reflected in his writing, the following chapter examines the principles that drove such design processes in individual temple buildings and ultimately their surroundings.

Four architectural visions One of the main purposes of Vitruvio's treatise was to convey that architecture is more than a practical activity. In the words of Andrew Wallace-Hadrill, on the other hand, it is "an expression of deep rational structures, of ordinatio and dispositio, of eurythmy and symmetry, which can give logic and order to the built environment, supported by the logic and order of nature.'1 There is no reason to doubt that Vitruvius himself really believed in this vision of architecture and in the ordering power of the procedures and principles of Greek origin (Ordinatio, Dispositio, Eurythmy and Symmetria) that make up architecture. However, Vitruvius would probably have been surprised if the present study indicated that the structures and mechanisms of nature reflected in architecture arose from a particular way of seeing, which arose mainly through repeated drawing habits in architecture. This final chapter continues this theme by focusing on Vitruvius's writings on the Greek methods and criteria of good design, the ideas of architecture (echnography, elevation drawing, and linear perspective), and the observable presence of these qualities in the physical products of the architecture. techniques that produced them. Finally, the configuration of space in Hellenistic and Roman buildings and complexes as a result of a particular type of vision in pre-Vitruvian and post-Vitruvian architecture is briefly considered.

Nature and architectural vision In addition to what Polykleitos's canon and its emphasis on symmetry may have had due to architectural theory, the influence could also have gone in the opposite direction. Vitruvius explains the need for adequacy in the design of the temples through the human body showing integral relationships between the parts and the whole, as in the proportions 6:1, 8:1 and 10:1 between the total height of the body and the Foot, head or face length (De architectura 3.1.1-4). There's also

there should be additional alignments between the members, and Vitruvius credits the famous painters and sculptors of antiquity with using such alignment based on proportion ( ) in their works. On the other hand, Vitruv Polykleitos is one of the most famous Greek sculptors (1.1.13, 3.praef.2). Therefore, it is likely that he had Polykleitos in mind directly in his own writings, along with the general influences that reflect the Roman architect. Thus, the "many numbers" that the architects of the Vitruvian age worked arithmetically on the basis of desirable proportions seem to have something in common with the working methods of sculpture. For Vitruvio, however, these correspondences between body and temple acquire a decidedly architectural character: in the same way, the elements of sacred temples must have dimensions for each individual part that correspond to the total size of the work. For example, the navel is also the center and center of the human body. Because if a man were to lie on his back with his arms and feet extended in a circle centered on his belly button, his fingers and toes would trace the circumference of that circle as they move. But just as there is a circular outline on the body, a square design is also evident. Because if we measure from the soles of the feet to the top of the head, and compare this measurement with that of the outstretched hands, we find that this width is equal to the height, just as with the areas squared by the quadratic theorem ( 3.1.3) 2 This is the description of the "Vitruvian man" (Figure 79) so convincingly illustrated by Leonardo during the Renaissance, albeit with his own deviations from the ancient formula.3 The passage draws the analogy of the temple with the most beyond arithmetic. considerations of underlying proportions, to figurative sculpture or a classical historical building like the Parthenon, moving design into the realm of geometry. In doing so, he proposes the idea of ​​the compass, a fundamental tool of technical drawing, centered on the tip of the navel and forming a perimeter touched by the fingers and toes of the rotating members. What Vitrúvio evokes here is iconography, a geometric plane drawn with a ruler and compass.

describes the interrelationship of temple forms through the analogy of a man lying face up on the ground plane.4 So, in addition to Vitruvius's acknowledgment of the existence of this practice in his time (1.2.2), we have an explicit explanation, and quite colorful of it. In a way, describing a man and a temple in terms of numbers and geometry corresponds to a certain mathematical way of seeing the world. Again, one can quote Plato, but it is also instructive to look at descriptions of actual objects. A passage from Strabo preserves the description of a particular tree according to Attalus I of Pergamum: Its circumference ( ) is twenty-four feet; and its trunk rises to a height of sixty-seven feet from the root, and then divides into three equidistant parts, and then contracts again into a head, reaching a total height of two plethras and fifteen cubits will . (Strab 13.1.44)5 Attalus's use of mathematical language to describe a natural form in terms of the integral dimensions of circumference, height, and isometric intervals between parts shows a level of abstraction similar to Vitruvius's description of a body. human. Neither captures the variation and irregularity of shapes in the real world, but instead conveys the elements of number and spatial composition. Despite the strangeness of this tree that Attalos describes, it is not the physical details that inform the account of it, but the mathematical considerations of quantity and form that define the primary nature of the tree, the idea of ​​it. One way to explain this point of view would be to point to the philosophical interests of the Attalids. Before and after Attalus I, the rulers of Pergamum generously supported the Academy of Athens. Four different philosophers from the Pergamum area became the leaders of the Academy over time.6 In Platonic idealism, sense perception is not valued for its own sake. Rather, the value lies in what the experience of seeing can teach about eternal and transcendent reality. Thus understood, the random irregularities of physical characteristics may be less privileged, less eternal, and less "real" than the metaphysical ground from which they imperfectly arise. In addition to a conscious intention to geometrize objects in verbal or graphic representations, the mathematical qualities of

Objects can already be formed at the level of intuition. Cultural trends would no doubt have determined the way objects were viewed by literate subjects in the Hellenistic world. In other words, visuality, or seeing practices that depend on the cultural and social context that conditions seeing, may have determined representation from the start.7 Idealism as such need not have reflected chosen beliefs. Rather, it may have been to some degree a display habit, which influenced the way a monarch or architect trained during the Hellenistic period represented bodies in space. Architectural drawings were conceived in the best sense of the word as graphic descriptions of buildings. In addition to this idealistic quality, there is a second, more mundane explanation that could account for these descriptions of Attalus and Vitruvius. Rather than simply alluding to the existence of a transcendent realm or universal numbers and geometry, or reflecting perceptions of particular themes, these passages can be understood as deliberately imparting a sense of order to the objects they represent.

79 Human form defined by pattern modules, proportions and geometry as described by Vitruvius (De arch. 3.1.2-3). Here the modules are shown with their respective relation to the total height/width. designer author. Describe removing the distraction of details. In the case of the tree, the geometry and integers effectively provide the reader with the general shape and scale information needed to accurately visualize the appearance.

experience of that object in the mind's eye. In the Vitruvian man, integral proportions and geometry allow for a standardized composition of body form, illustrating the need for temples to show a "similar correspondence between the measurement of individual elements and the appearance of the work as a whole." a whole". Philosophical and practical interpretations are not mutually exclusive, and it may be remarkable that the idea of ​​order is conceived and transmitted for both purposes through the idealizing means of number and geometry. Whatever the actual motivations behind these ancient passages, an adequate description of how these passages work to convey an aesthetic of order does not depend on the nature of their relationship to Platonic idealism. I will briefly go into this theoretically described formal specification element, which is intended for practical implementation in architecture. What distinguishes the descriptions of Attalus and Vitruvius, despite their conceptual similarities, is the latter's association with design theory. Rather than simply articulate a series of observations, the Vitruvian Man exemplifies the qualities of architecture, a point emphasized in a separate discussion of adequacy appearing in the specific context of Greek architectural design: "As in the human body , there is a harmonious quality of form expressed in the form of the ulna, foot, palm, fingers and other small units, so it is in the realization of works of architecture” (De architectura 1.2.4).9 The expression of this form or eurythmy is of a process toward three different types of ideals, including iconography, elevation drawing, and linear perspective or scenery (1.2.1-4).Vitruvius defines iconography as “the skilful and true-to-scale use of compass and the rule, by which project design is accomplished on site” (1.2.2).10 Vitruvius is equally prosaic in his characterization of the primary purpose (among others) of geometry in the training of an architect, co How to learn to use the compass and ruler in the execution of building plans (1.1.4). This execution follows a convenient two-part procedure (1.1.2). The first part, called taxis (Latin ordinatio) in Greek, is the process of establishing quantitas (Gr. ), whose meaning in the Vitruvian architectural sense goes beyond the purely arithmetic meaning of quantity as number.11 Rather, it is creation of modules taken from parts of the building, as well as a successful composition of the set that expresses these modules. As described by Vitruvius, this Quantitas is the base of

Taxis, in which an integral and universal alignment, called symmetria in Greek, is created through proportional interrelationships between the individual modules and the building as a whole, indicating a system based on whole numbers rather than irrational numbers.12 Architecturally, then, the taxis is the creation of a building layout, in which the modules are proportional to the general scheme. Nowhere does Vitruvius strictly say that this construction process must be geometric. Neither does his text suggest that irrational numbers derived from measures such as the diagonal of a square play a role in the development of composition, which would indeed undermine the reliance on taxi symmetry. Rather, as a graphic construction defined by clearly measurable elements and the intervals that separate them, Taxis is the execution of the form according to arithmetic principles. Of course, however, the overall composition would appear geometric in the aesthetic sense of archetypal polygons or circles, but characterized by integral proportions. In any case, this taxi is not the complete architectural design, but one of the two essential parts in its execution. The other part of the Greek process is diathesis (lat. dispositio). It is "the correct placement of things and the elegant effect obtained by arranging them according to the nature of the work". . , and vice versa. The analogy with the human form, which nature provides as a model for good design, illustrates how this process works at the level of a drawing as iconography. In the Vitruvian man, a module like the foot with all the parts together forms an integral ratio of 1:6. All these parts are in turn proportional to the square that has the height and width of the figure. These and similar proportions are also implied by the circle that describes the outer extent of the rotated elements (Figure 79). However, in view of the other correspondences that the Vitruvian Man shares with the descriptions of taxis and diathesis, this last feature creates an ambiguous note: there is no explicit integral alignment between the diameter of the circle and the width of the square. Modular support for inclined elements can still extend the sense of scale to this diameter, but this requires some design flexibility.

Spirit and imagination to do it. One possible explanation for this divergence is that it shows us the human element in design and that expectations of a strict correspondence between theory and practice should be avoided. Another possibility is that the theory itself addresses precisely this human element. Vitruvius introduces the three types of architectural design (ichnography, orthography, and perspective) in his discussion of diathesis and writes: These types are generated by analysis (cogitatio) and invention (inventio). The analysis is dedicated to concern and vigilant attention for a pleasant execution, cura studii plena et industriae vigilantiaeque effectus propositi cum voluptate. Invention below is the resolution of obscure problems, the achievement of a new set of principles through energetic flexibility, vigore mobili. Those are the terms for design, dispositio.14 (1.2.2) Significantly, in Vitruvius's discussion of the diathesis (= dispositio) this dedication to a good result and the "energy flexibility" required to meet design challenges belong and they do not belong more than for Taxis. This context makes it clear that the diathesis does not have to be a mechanical placement of architectural elements according to the composition worked at the level of the taxis. Rather, realizing the modular basis of the design, the geometry of the design emerges through analytical and creative approaches aimed at creating an attractive form through principles independent from those established by the cabins. Vitruvius offers explanations of two additional Greek terms to support architectural design procedures (1.2.3-4). He defines symmetry as a relationship both of the parts among themselves and of the figure as a whole (1.2.4) and thus clarifies its compositional role in taxis as a quantity expressed by modules ( ), which serve as a measure for the composition drawn in its entirety (1.2.2).15 The other Greek term is eurythmy, a word with an obvious connection to music theory, which Vitruvius explains as the pleasing, coherent appearance of a pattern that occurs when all parts of the work point in unison. all the senses. the directions (height to width, length to width) are proportionally unified with the whole.16 These two definitions sound pretty similar, and they are. However, they are not

Synonymous. By comparison, Greek poetry has its meter ( ) and rhythm 17 ( ). These terms are also almost identical in their definitions. While meter establishes quantity by using long and short syllables through the feet, rhythm joins meter by inserting phonetic values ​​into the order of the chosen words. The meter and the symmetry give measure to the composition, but neither does the composition. Rather, the art of the poem or drawing only emerges through the unit of measure and rhythm or eurythmy, whereby a harmony emerges that is unmistakable to the trained ear or eye. Both verbal and pictorial art achieve orderly expression through restraint and good form that stands out from everyday language and visual experience. Vitruvius relates his discussion of the ideal explicitly to the human body (1.2.4), and the Vitruvian man in particular offers an analogy with iconography. In this famous passage you can see the Greek qualities of design as defined by Vitruvius. This coincidence is not intentional, but is due to Vitruvius's habits of mind as an architect who came of age towards the end of the Hellenistic period. Of course, his discussion of the design of the temple through drawings composed with compasses and rulers reflects his explanations of qualities of Greek architectural design that he evidently knew well enough to describe elsewhere in his text. . The Vitruvian man, then, has cabins in the variety of parts of him - foot, palm, head, etc. - that serve as modules that express symmetry through integral proportions with the body as a whole. Through analysis and invention, the hands are positioned (diatheses) so that the leg serves as an axis running orthogonal to the length of the body from head to toe. So this diathesis establishes a 1:1 relationship between the x and y dimensions, an overall relationship that results in the eurythmy of the square. The square, in turn, articulates the modules that compose it, all taken together as Quantitas, thus expressing the symmetry of the parts with each other and the whole, and therefore also its taxis. Later analysis and invention rotate the limbs to bring the hands and feet into positions that express eurythmy through the circular shape. Following a process that aims for both adequacy and "good form" in composition, the architect uses the qualities inherent in the natural configuration of the body as a means to shape order in space. Thus, at the level of iconography, the representation or idea of ​​a temple acquires arithmetic and geometric principles that

Define the relationships of its parts to the whole. In one possible reading, the geometry of the Vitruvian Man seems to represent a conceptual difference in terms of geometry that a true iconography would aid in the design process. In this drawing, the geometry would actually create the composition through taxis and diathesis. In the Vitruvian man, however, the body is already given as an idealized model of nature, and it is the body itself that produces the geometry. Therefore, the passage cannot be understood as a guide for architectural design.18 Other considerations may broaden the implications of this reading for the classical design process. Although the human body actually already exists, Vitruvius makes it clear who is responsible for its design: it is nature itself that composed it (3.1.2). While such a poetic vision can hardly be equated with a "manual" for temple architects, its intended didactic value in the design process is unquestionable. Concluding his description of the circumscribed body, Vitruvius says: And so, if nature has composed the human body, Ergo si ita natura composuit corpus hominis, so that the separate individual elements correspond in their proportions to the general form, then Antiquity, Antiqui (that is, the early Greeks) seem to have had reason to decide that the realization of their creations also required a correspondence between the measure of the individual elements and the appearance of the work as a whole.19 (3.1.4) The passage does not prescribe that. However, he offers a theoretical justification for the design principles he advocates, symmetry and eurythmy, and the geometric form that results from them. More importantly, the Vitruvian Man helps spread and develop a concept that Vitruvius draws from his Greek sources and with which some of his Latin-speaking readers may be relatively less familiar: the relationship between geometry and nature. If it is accepted that the text describes the body as arising from nature and not from the geometric tools and processes of an architect,20 a new question arises: geometry is supposed to be inherent

in natural human form. The distinction between circle and square in the spatial order of the body presupposes practices of abstract vision that are anything but natural and universal. Only in a culture somewhat focused on graphic forms made with a compass and ruler would it be claimed that such a composition exists in nature, as in Attalus I's description of the tree in terms of circumference and equidistant tripartition. However, it would be too easy to completely equate Attalus's account with Vitruvian man. Besides the important contextual difference emphasized above (mere description vs. design theory), one can separate Attalus and Vitruvius based on their respective subcultures. A patron of science concerned with the intellectual pitfalls of the monarchy, Attalus I was probably quite familiar with the philosophical and mathematical traditions of Plato's academy, which would have influenced the idealistic depiction of him. Vitruvius also knew Plato, although it is not the relative superficiality of his knowledge that distinguishes him from the Hellenistic basileus. already with the arrival of the Greek Hermodoro from Salamis in the 2nd century,22 as Vitruvius writes. Whatever the level of familiarity with the philosophy, his architectural training was defined by a devotion to design consistent with the principles he outlined. Given his experience, he should not be surprised that he conceived of the objects and spaces he defined precisely in terms of integer proportions, modular adequacy, and the circular, crystalline form of the idea constructed with straightedge and compass. Regardless of his awareness of philosophical idealism, this repeated experience would have strengthened his visual perception enough to claim that we find geometry in the products of nature. Vitruvius' additional comments underscore this lack of agreement with philosophy. Haselberger fully documents Vitruvius' understanding of the refinements.23 In explaining the motivation behind the curvature of the platform, Vitruvius emphasizes the need for this "addition" of mass to the center to correct the visual impression of concavity that arises when viewing lines horizontal (3.4 5 ). He goes into this problem of optics (6.2.2) and claims that seeing does not produce true impressions. On the contrary, the mind is often confused by visual judgments. Rough comparison of various passages in

Vitruvius, Philon Mechanikos (On Artillery 50-51), and other Greek writings leave no doubt that this approach to refinement through addition and subtraction was a feature of architectural theory before the end of the third century. These clear and specific textual equivalents have been fully and eloquently elaborated elsewhere and will not be repeated here.24 Their importance shows that Hellenistic architectural theory, as reflected in Vitruvius, tends to invert Plato's hierarchy. Rather than the role of vision as God's precious gift of aiding understanding that can lead to higher insight into embodied truth in the realm of ideas, it is the eye itself that is served by the design process. This clear correspondence between Vitruvius's commentary on refinements and that of the Greek writers raises the question of whether the Roman author's account of iconography finds similar support in a Greek context. An inscription from Priene bears witness to the connection between iconography and temples in the 2nd century. He identifies a Hermogenes as "the hipographer () of the temple, whom he also executed". ,26 But the term hippograph suggests the idea of ​​a design that has at least something to do with the idea of ​​what is below or below, and thus may be consistent with the idea of ​​being viewed from above.27 Hippograph is generally refers to a clear sketch of a detailed image,28 and an inscription from a separate architectural context uses the term in reference to designating the details of elements, not the design of entire buildings.29 Another complication arising from the Priene inscription is its commemoration of a Dedication, suggesting that the function of this particular hipographer was more than part of a planning process as discussed by Vitruvius and other Romans. sources.30 Given this only available evidence, we are left with a term whose meaning is unclear and which does not provide textual confirmation of the role of iconography in the design process of Greek prismatic buildings such as temples. Therefore, we are completely dependent on Vitruvius for the theoretical basis of the iconographies. His text makes it clear that the issue of refinements serving as visual corrections is part of a larger concern. In a discussion about

Proportion and Optics (6.1.1) writes that the most important thing for an architect is to establish a system of symmetry. After determining this and relating its proportions to the actual dimensions to be built, a good architect will consider the appearance, location, and intended use of the buildings and, based on these considerations, "make adjustments... subtract or add from proportions "a system so that it appears to be correctly designed without anything missing in its appearance."31 This emphasis on correct appearance by addition or subtraction is found repeatedly throughout Vitruvius's text.32 Polykleitos of Philo: That “it good" comes from small deviations from the many shapes achieved by the designer. Creating symmetry is invaluable, but modifying it through analysis, invention, and eurythmy is essential to good architecture. These are also the procedures and principles of the idea , which are elaborated through taxis and diathesis Given all these considerations, it seems that idealism in architecture has similarities with Pythagorean thought. rich and platonic, but also significant differences. The idea is processed through the design process, and in fact it is the design. As in the Meno, Socrates, or a geometer, will draw to discover and demonstrate certainty through two-dimensional spatial properties and measured relationships. An architect uses the same tools as technical drawing with the aim of forming proportional and modular spatial relationships that look or feel good, especially to an architect with sufficient knowledge. Through small deviations from true proportions, the architectural design process transcends the interests of mathematics and philosophy. Before turning to actual Greek buildings, a brief summary of the theoretical considerations discussed so far may be helpful. In his description of architectural design and its Greek terminology in the late Hellenistic period, Vitruvius writes as if iconography were a given in the design process. His recipe for designing temples uses the analogy of the human form, described as a plane drawn by a compass, illustrating how taxis, diathesis, symmetry, and eurythmy define spatial spaces.

Query. As an idea described by number and geometry, the "Vitruvian man" evokes a philosophical idealism that probably also shapes the world view of many educated people. However, classical iconography is not to be understood simply as a precise parallel to, or an expression of, the Platonic or Pythagorean traditions. As part of architectural design, it was instead a product created by professionals who generally drew with compass and straightedge in the creation of columns and theaters and refinements through uniaxial protraction, a repeated practice that seems to have influenced the way in which architects would have made the objects. seen in nature in relation to a regular geometric shape. Furthermore, the practice of architecture and sculpture had traditions of working with symmetry going back centuries, as in the proportions observable in the Parthenon and mentioned in Polykleitos' canon, at least to the extent that later commentaries on symmetry are intended to represent Polykleitos. points of view. As can be seen from the refinements of classical buildings and Philo Mechanikos' possible reference to the paramicron as small deviations from the numbers, architects and sculptors were primarily concerned with creating pleasing forms for sensory experiences. Regardless of the nature of individual Greek architects' beliefs, impenetrable without direct testimony, this practical consideration distinguishes ideals in architecture from ideals in philosophy. It could be said that reference to philosophy itself, in particular Plato's exaltation of the ideal, would be an unsatisfactory justification for the use of the ideal in the design process of a Greek building. After the transformation of the theater as a container of the communal vision expressed through skenography and the planar conception of ichnography, the practice of geometric planning of buildings on a reduced scale explicitly entered the architect's design process. Before and after this transformation, the design process of the one-column fluted drum suggested the principle of spatial protraction and an ordering model given by both the square of a quadrant and the modular approximation of the fluted perimeter. In addition to the radial configurations of round buildings, such as those at Delphi and Epidaurus, the application of often-recurring axial, circular, and square shapes, together with the principles of protraction and symmetry, prepared each building to be viewed from a different angle. advantageous position. point .summary. Aerial view from directly above, as abstract as the visualization of the universe itself in the form of a twelve-part zodiac or a reclining man made up of different and comparable parts. Although the fluted column

In fact, he set the original model for this view in cosmic diagrams, linear perspectives, and buildings, it was certainly the repetition of the tools and techniques of such constructions that determined both the perception and the modeling of the environment. Born out of linear perspective, as argued in Chapter 3, through this iteration, ichnography became a peculiarly architectural vision over time.

Iconography in the Ionian tradition of Pytheos and Hermogenes The tradition of iconography on rectilinear buildings probably goes back at least to the Temple of Athena Polias of Pytheos, built in the Late Classic period around c. . design that can still be found more than a century later in the work of Hermogenes (Figure 23) and, indeed, in numerous temples throughout the Roman period.34 This grid is based on center distances of columns twice as wide. that the bases In other words, the bases serve as a module that establishes proportionality with the axial distances (two modules) and the dimensions of the naos along the axes of the walls and antae (six by sixteen modules), the axes of the peripteron. (ten by twenty modules), the stylobate (eleven by twenty-one modules) and the general plan in the crepis (twelve by twenty-two modules). relatively recent discovery. An almost complete incised drawing of an entablature and pediment appears on a stone block erected in the Temple of Athena Polias at Priene (Figure 80), which is believed to be related to the temple pediment itself.36 As in According to the drawings of work discovered in the Hellenistic Didymaion, the example of Priene shows how the Greek masons and architects elaborated their projects in ashlars. By covering these areas with red chalk, using an engraver with ruler and compass, designs were obtained whose white linear incisions stood out clearly against the surrounding colour.37 Monumental pediment designs are found elsewhere, such as in the design used for the Design by Didymaion Naiskos. carved into the western wall of the Adyton were used

and the working drawing for the façade of the Pantheon, engraved in the marble pavement in front of the Mausoleum of Augustus in Rome.38 However, the extant width of Priene's drawing is less than 48 cm. If this drawing does indeed relate to the design of the temple, this would indicate that Pytheos drew it on a reduced scale, suggesting that the architect may also have been working on its plan. Whether or not Pytheos's scheme exerted a great influence on the practice of iconography in his own time,39 the relevance of it to Hermogenes in

80 Temple of Athena Polias, Priene. Restored design of cornice and pediment incised in a block embedded in the temple. Width: about 47 cm. Author of the design, modified by J. Misiakievicz, in Koenigs 1983: Figure 1. The next century is coming

Discourse for Ionic Temple Design, which Hermogenes read and contributed to his own publications on the temples of Artemis Leukophryne at Magnesia-on-the-Maeander and of Dionysus at Teos (Figures 81, 83).41 In addition to the application of the latticework, the latter is practically a copy of the temple of Pytheos at Priene (Figure 81).42 In this context, the Priene inscription should be remembered, which identifies Hermogenes as the performer and initiation artist of the hipographer of the temple of Athena. polys. If this inscription really refers to the builder of the Temple of Teos, then Hermogenes may have dedicated an iconography as his own monument, demonstrating the system he learned from the writings of his ancestors,43 perhaps in the form of working drawings carved in stone by the discovered at Priene (Figure 80). Regardless of this possibility, Hermogenes generally did not slavishly copy the forms of Pytheos or the system that determined their location. Instead, his iconography displays a creative flexibility in shaping spatial order. Along the middle of the plan of his Artimesion (figs. 23, 81) he increased the spacing of the columns by one third.44 In addition, the layout of the temple is octastyle rather than hexatile, and the axial locations of the outer columns coincide with the second instead of adjacent axes

81 The Temple of Athena Polias at Priene began around 340 BC. 220 B.C. C. by Pytheos (left) and Temple of Artemis Leukophryne at Magnesia-on-the-Maeander (right). by Hermogenes. Comparison of grid-based floor plans. Author's drawing modified by J.J. Coulton, in Coulton 1977: Figure 23. next to the walls of the naos. Although the "empty" axial intersections of the lattice could accommodate an additional inner row of columns in the form of dipteran arrays, Hermogenes' scheme creates an expanded interior space on all four sides of the peripteron. The result is a pseudodipterous temple that, according to Vitruvius, was the invention of Hermogenes (De

Architecture 3.3.8). Hermogenes' Artemision is not the earliest example of the pseudodipteran type, dating back to the Archaic Kerkyra Artemision and other examples,45 but Vitruvius's claim about its inventive role is probably still correct. Finally, it is unlikely that Hermogenes knew of precursors created in the traditions of mainland Greece and southern Italy, distant in time and space from his own experience. As a student of the Ionian tradition of Pytheos, he may not have discovered the arrangement through knowledge of widely separated earlier examples of Ptera, but rather through the design process that Vitruvius describes in terms of diathesis. In addition to the taxis, where in this case the temple grid is created by modules from the dimensions of the bases, the diathesis becomes new through “care and vigilant attention for a pleasant execution” and “dissolving dark problems, arriving, through principles of energetic flexibility." Previous work. In addition to this resemblance, ichnography creates pseudodipterans as a positive expression of spatial order, and not just as a temporary absence of mass.47 This "analysis" and "invention" through "energy flexibility" in diathesis not only leads to new explorations, but formally also in subtle departures from the taxis installed in the temples of Priene and Magnesia, except for slight variations in the measurements of the elements and dimensions of the temple of Pytheos , neither the entrance wall to the cella nor the wall that separates the cella from the opisthodomo are as aligned with the theoretical axes of the grid as the other elements (Figure 81). ).48 In the Temple of Hermogenes, the two rows of three columns within the cella also do not align with its grid, which is separated longitudinally by center-to-center distances of 3.60 m, rather than the 3.94 m spacing that defines the length of all axial divisions along the temporal lattice.49 Such minor deviations create exceptions to the integral proportional relationships defined by the lattice and articulate a design method that appears to be in the spirit of Polycleus's statement on "the well" that arises from the small deviations ( ) of the numbers (Philo Mechanikos On Artillery 50.6.).

As discussed in Chapter 1, such deviations in the Parthenon find their most prominent expression in the third dimension, with refinements such as curvature, tilt, and adjusted levels (Figures 20, 21). A similar platform curvature is also observed at Priene (Figure 82),50 but what distinguishes the design of the Parthenon from the temple of Pytheos is the latter's relative independence from changes in plan and elevation features. In the Parthenon, the deviations from the standard ratio of 4:9 found in the relationship between the diameters of the columns and their distances between centers are contractions in the corners and façades, which respond to deviations in the location of the triglyphs in the frieze. That said, traditional Doric design considerations in height required changes to the plan. By contrast, the off-axis location of the opisthodomos wall at Priene allowed the option of a more spacious ambulance around the axially placed pedestal for the cult statue, and the reduced distances separating the cella columns at Magnesia allowed for three rooms. plus. . fixed. - Table of measurements for

82 Temple of Athena Polias, Priene. Western flank seen from the south with curvature. Author of the photo.

the base of his statue (Figure 81). Whereas the design of the Parthenon is conceived primarily in a sculptural sense, reflecting subtle changes in plan, the floor plans of Priene and Magnesia show slight deviations from nothing more than the geometry that dictates the location of most temples. Resources. Such exceptions underscore both the primacy of iconographies in the Ionic design process and their existence as actual entities in the classical world, rather than our own modern assumptions about how a building should be composed. A geometric support to which architectural features conform to or slightly deviate, the grid is a separate graphic component from material forms, guiding their placement according to well-established principles and good aesthetic judgment. Faced with these Ionic iconographies, one can appreciate their strangeness in relation to our own architectural traditions. The ancient practices of iconography seem to have been completely lost during the Middle Ages and had to be reinvented during the Gothic period. . In the Renaissance, drawing a building in plan involved the free use of a compass and straightedge to create circular and polygonal outlines, followed by overlaying a grid to establish scale.52 In contrast, in the examples here, the grid defines the Geometry of the building through the practice of diathesis. Consequently, the placement of elements at the intersections of the axes controls the symmetry quantitatively through the integral modular relations of the parts with each other and with the general outline of the stylobate or crepe, as in the Pytheos plinth proportions of 1:2 with the separations of the axes. , 1:10 and 1:20 with the respective axial width and length of the peripteron and 1:12 and 1:22 with the respective width and length of the crepis. Simultaneously, the grid performs eurythmy by establishing integer width-to-length ratios, as in peripteron 1:2, stylobate 11:21, and crepis 6:11, as well as common ratios between different dimensions, such as this 1:2 ratio. of the widths of naos and crepis, and ratio 4:5 of the lengths of naos and peripteron. In this way, moderation and harmony give order and a pleasant appearance to the layout of the building.

This brief review of Ionian architecture in the Late Classical and Hellenistic periods suggests the possibility that Greek iconography was synonymous with truss-based approaches to design, and thus restricted to the Ionic order. In Doric temples such as the Parthenon, the architects' insistence on placing triglyphs at the corners of the friezes required variations in the spaces between them, which led to adjustments in the placement of the columns below, which were aligned axially with the triglyphs. .53 While most Ionic temple layouts can be “planar oriented” by a grid, the Doric temple layout depends on height elements and is therefore incompatible with a regularly spaced grid.54 Interestingly, Vitruvius states that this is precisely the problem that led Hermogenes to abandon the Doric design. order, and that Pytheos also rejected the Doric order "because the system of proportion was inevitably faulty and inharmonious". Ionic architects.56 As demonstrated for Temple A in the Asklepieion on Kos (Figure 86), a Hellenistic temple of the Doric Order could employ ichnography in its design process and respond to the challenge of axial contraction with innovative geometry, different and yet as simple... as the grid that supports the layout of Ionic temples such as those of Pytheus and Hermogenes.57 In fact, the temples of the Ionic tradition arguably cannot stand alone as evidence of the Greek iconography and its principles as described by Vitruvius. It should not be forgotten that the question of iconography requires a skillful interpretation of extremely limited evidence: no examples of actual drawings survive, and although Vitruvius directly and analogously attests to the existence and qualities of the practice, he nowhere tells us who it is. responsible for its creation and where it was used. In connection with the limited physical evidence cited to support the application of the reduced-scale design to Ionic material, the small sketch of the pediment discovered on the block within the Temple of Athena Polias must be considered.

83 Temple of Dionysus in Theos, Roman restoration of the work of Hermogenes from the 3rd century BC. designer author. (Figure 80) with deep reserves. A working drawing cannot be assumed to be necessarily related to the structure on which it was built, instead retaining an unrelated drawing of a reused block. Especially problematic in this case are the size of the composition (about 47 cm) and the lines that set a vertical accent in slightly different places in the corners of the pediment. Rather than a scale sketch for the temple façade, the dimensions and features of this design suggest a simple funerary stele with its figurative composition framed by columns, examples of which abound in the Greek world. Furthermore, Vitruvius does not explicitly state that the iconography involved the drawing of latticework. What Vitruvius describes is the Eustyle symmetry system of Hermogenes, determined by the diameters and axial distances of the columns, along with four other classifications (Pycnostyle, Sistylus, Diastyle, and Araeostyle) that express different magnitudes of separation that are equal in modules given the diameter of a column. .58 One might be very skeptical that even if the resulting schematic corresponds to a square grid overlay on the plan, a grid-based scale plan would not be necessary to create such a simple building. As such, the temples of Pittheus and Hermogenes would not meet the same need criteria assessed for the Parthenon in Chapter 1 of this book. On the contrary, it can be argued that iconography is more necessary in more varied montages.59 The reason is simple: although the grids are obviously geometric in shape, they are arithmetic in their modular and proportional relationships based on integers. Rather than drawings, they would therefore be conceivable and easily transmitted through traditional written descriptions of dimensions (syngraphai) combined with models of individual elements (paradeigmata) such as bases and paving slabs.60 Finally, theoretical ichnographies based on grids of Pytheos and Hermogenes does not correspond exactly to the general unifying geometry of something like a circle and a square found in the Vitruvian iconography analogy through the human form (Figure 79). How Greek iconography may have been related to royal construction

In fact, I do not dispute that ichnography replaced written descriptions and plastic models, with the sudden appearance of architects and masons on the site, referring to floor plans, as well as working drawings for Entasis and fluted columns at Didyma. Clearly, the architect of projects like Didyma's at least envisioned his designs to accommodate larger forms, details, and refinements that required unified execution by many individual masons. However, given the demonstrated utility of verbal descriptions in establishing the flat location of such features, there is no reason to believe that icnographers were always available to workers. It is just as likely that the iconographies in many cases only served the architects who drew them when it came to developing spatial relationships with a compass and straightedge. In fact, at the time they were first introduced, these geometric concepts probably would not have been familiar to many workers if they had known how to use them. This is not to say that Freemasons of all ages are in no way limited to confronting abstract ideas. The iconography itself would have been limited compared to the concrete provision of actual measurements and scale models and drawings. On the one hand, a graphic idea such as a grid or other geometry underlying the positioning of the building forms has questionable relevance at the start of construction. Furthermore, it cannot be assumed that Greek iconography always had a unified and comprehensive scale relationship, and that it was large and detailed enough to accommodate written indications of individual measurements. The constant need to relate abstract aerial representations to pieces, or even worse, calculate their measurements by reason, means unfathomable steps for a construction culture that already had established ways of working. Rather, the architects who designed ichnographs probably converted them from graphic descriptions to written descriptions whose metric specifications were proportional to the sizes of the design. In fact, this transformation can be preserved in the same passage from the Vitruvian Man, which describes textually, rather than graphically, the modular dimensions and proportions of the human form. It is not surprising, then, that such ideas did not survive the construction of the buildings whose spatial arrangement they determined.

Therefore, the assumption that ichnography drove temple design in the Ionian tradition of Pittheus and Hermogenes must be based on other factors. First, circular temple- and theater-like buildings with radiating constructions, which more clearly reflect the tools and procedures depicted in Aristophanes' birds, were well established in the Late Classic and provided contemporary comparators expressing the principles of iconography found more late in Vitruvius. The explicit presence of such practices thus supports the notion of projects based on similar principles observed in the works of Pytheos and Hermogenes. Second, there is the important question of configuration, a consideration that goes beyond the observation that both the temples of Pytheos and Hermogenes lie within the "Hippodamian" orthogonal planes of Priene and Magnesia-on-the -Maeander. Constructed in the century after Aristophanes outlined the plan of a city of birds in the form of scale drawings, these city maps may reflect graphic ideas. Furthermore, at least in the case of the Temple of Hermogenes, there is the possible suggestion of an even more pronounced graphic design at the junction of several buildings The temple stands at an oblique angle determined by the orientation of the archaic temple that the Hermogenes building replaced . A single axis that crosses the center of the temple, the altar and the altar.

84 Asklepieion, Cos. Restored aerial view. Drawing by the author, after P. Schazmann, in Schazmann 1932: Plate 1. Propylon meets the center of the open space of the Agora, and the dial of the southern half of the Agora defines the location of the Temple of Zeus.62 The Sense of Order The spatial dependence depends on it from a rather simple axial arrangement, suggesting a possible influential role as a precursor to the type of planning approach that would later shape the urban architecture of Rome.63

Beyond Hermogenes: From Kos to Rome The difficulty of applying the Hellenistic and Late Classical tradition of lattice-based Ionian iconography to Doric temples has been accompanied by a lack of opportunity to do so. Although the Doric order continued to thrive on the Stoics during the Hellenistic period, from the fourth century the Ionic order dominated temple building. A rare Hellenistic exception of a Doric religious temple in a large Panhellenic sanctuary is Temple A on Kos, built around 170 (Figures 84–86).

Three terraces on the island's famous Asklepieion, Temple A dominates the medicinal sanctuary with its axial position at the apex of the grand upper stair rise. Since it was a Doric temple without the readily available potential of the Ionic order for a lattice-like arrangement in the manner described above, a different approach was required for taxis and diathesis. Therefore, the architect drew a plan of proportions of six by eleven, within which a Pythagorean triangle 3:4:5 ABC determined the locations of cella and pronaos in the same proportion of 3:5.

85 Upper Terrace with Temple A, Asklepieion, Kos. He started about 170 author designs.


86 Temple A, Asklepieion, Cos. It began around 170 B.C. BC Restored floor plan showing the geometric support of the Pythagorean triangle ABC. designer author.

87 Shrine of Juno, Gabii, around 160 B.C. BC Aerial view restored. Author of the drawing, modified by M. Almagro-Gorbea, in Gabii: Figure 133. of the rays that govern the cella and stylobato in the tholoi of Delphi (Figure 38) and later in Rome (Figure 40).65 In addition to these Base geometric, a remarkable element of this building is its modular base. The six by eleven temple and the 3:5 ratio of its circular booths represent an integral approach based on a module expressed by a selected part of the whole in the manner described by Vitruvius. In Temple A this module is expressed by the length of the paving slab supported by columns.66 Thus, the total dimensions of the plan, six by eleven, correspond to twelve by twenty-two modules, corresponding to the Temple of Pytheos in Priene in its crepis.67 In addition, the 3:5- radii of their equal basic diameters are six and ten.68 Since the maximum elevation of the ecstasy determines the modulus for the design of the ecstasy on Didyma, the plan of Kos results from a modular 3: 4:5 Triangle of Pythagoras.69 In both cases we are faced with a form whose geometric and modular foundations may not be obvious. On the other hand, both reflect customs of making forms projected from drawing ideas as whole reasons, such as the fact that the capital can arise from the dimensions of a Pythagorean triangle (Fig. 65) or the fluting of its column from a circumference measure. of twenty four slots placed in the ridge (Figure 57), or the design for the curvature of the deck from a chord to radius ratio of 2:3 (Figure 64).

Another feature of Kos heralds a development that would be of great importance to architectural history. Similar to the work of Hermogenes at Magnesia-on-the-Maeander (Figures 23, 78), the iconography of Temple A extends to the entire surrounding area, shaping the upper terrace as a complex dominated by a central guiding axis that anchored the temple. . under his molded Stoa (Figures 84, 85). Apart from the trend of irregular and twisted relationships between autonomous buildings like those of the Athenian Acropolis, the graphic conception of iconography now establishes compositions of integrated buildings.

88 Temple of Juno, Gabii, around 160 B.C. Restored floor plan showing the use of the Pythagorean triangle in generating its design. Original drawing, modified by M. Almagro-Gorbea, in Gabii: Figure 2.

Coinciding with this complex on Kos was the sanctuary of Juno at Gabii, which was inaugurated ca. . to the upper terrace complex of Kos (Figure 84).71 Interestingly, excavators of the sanctuary revealed that a Pythagorean triangle of 3:4:5 supports the Corinthian order temple design (Figure 88) with the ten equal divisions of the hypotenuse

89 Temple of Juno, Gabii. Restored unified plan and view design concept illustration. Author of the drawing modified by M. Almagro-

Gorbea, in Gabii: Figure 4. Orientation on the placement of the lateral columns in the form of taxis and diathesis. Although this discovery predates the recent discovery of the 3:4:5 triangle at the Koan Temple (Figure 86), the Gabii excavators recognized that the design of this sanctuary reflected the conception of a Greek architect and even identified it as Hermodorus. of Salamis,72 the first known Greek architect in Rome. Whoever was the architect of it, the practice of ichnography

90 Sanctuary of Aphrodite (with Temples of Aphrodite Pandemos and Pontia), Kos. Late 3rd or early 2nd century B.C. Restored plant. The author's design, modified by V. Brighenti, in Morricone 1950: Figure 17. from Greek traditions, shaped both the cult building and its surroundings in a clearly Hellenistic manner. according to their excavators

After the restoration of the Temple of Juno, the design practices that guided its formation were so systematic that they unified its iconography with its elevation (Figure 89) and created a complete expression of plan-oriented design. The character of the upper terrace complex of the Asklepieion on Kos had a local precedent. Next to the agora, next to the port, are the remains of the sanctuary of Aphrodite from the end of the 3rd or beginning of the 2nd century (Figure 90). In an arrangement unique to the Greek world, two temples (dedicated to the cults of Aphrodite Pandemos and Aphrodite Pontia) are aligned within a portico with square altars.73 As found in correspondences between the Asklepieion on Kos and the sanctuary of Juno in Gabii a complex in Rome again follows a precursor of the koan. Based on excavations and fragments of the Severan marble plan (Figure 91), the 140s Porticus Metelli is being restored as a closed portico complex for two axially aligned temples with square monumental altars (Figure 92).74 These temples they include the temples of Juno Regina and Jupiter Stator, the latter of which was the oldest marble temple in Rome.

91 Fragments of the marble plan of Severanus showing the Porticus Octaviae in Rome (Porticus Metelli, renamed and rebuilt under Augustus), enclosing his Temples of Juno Regina and Jupiter Stator and flanking the south side of the Augustan-era Porticus Philippi, with partial restoration. designer author. (Velleius Paterculus 1.11.4–5), built by Hermodoros of Salamis (Vitruvius 3.2.5), the first known Greek architect to work in Rome. It is important to emphasize that apart from these two complexes at Kos and Rome (Figures 90, 92), I am not aware of other examples of this particular arrangement anywhere in the classical world. The two connections shown here point to an important legacy of ancient Greek iconography: the graphic modeling of the architectural structure of Rome as a product of its Hellenization, in which symmetrical porticoes enclosed axially arranged temples. The ultimate expression of this typological combination, united by a drawing board mentality, is the

Trajan's Forum, which completed the series of imperial forums that dominated central Rome (Figure 93).75 Here is a modeling of the environment made possible through continuous practice in an abstract and disembodied way of viewing from above and from Pushing the boundaries of the natural See where technical drawing tools and methods can shape huge room floor plans through flat ideas.

92 Porticus Metelli (later Porticus Octaviae), Rome. After 146 B.C. Plan restored from fragments of the Severan Marble Plant and excavations. designer author.

Vision, Design and Construction The parallel between the development of ancient design in the presentation offered here and that of the Renaissance deserves recognition. Architects in the Early Middle Ages were often master craftsmen of masonry and carpentry. 77 Although perspective drawings were useful to architects in practice, Alberti's On Building framed a distinction between the painter's and the architect's drawings in a remarkably humanistic aesthetic logic that would have seemed alien to traditional craft concerns: the difference between the drawings is that of the painter and that of the architect this: the first deals with emphasizing the relief of the objects in the paintings through shading and the reduction of lines and angles; the architect rejects shading, but takes its projections from the plan and, without altering the lines and preserving the angles, leaves open the size and shape of each view and side - it is he who does not want his work to be judged as deceptive appearances , but according to certain calculated standards. (De re aedifictoria 2.1)78 While the painter deceives through the modeling of values ​​and the composition of inherent lines and angles according to the vision in perspective (and, therefore, in linear perspective), the true lines and angles of the Architects' ichnographies and elevations are quite misleading according to given judgment principles and forms subject to mathematical verification rather than embodied experience.79 This notion is analogous to Ficino's contemporary Neoplatonic assertion, discussed in the introduction at the beginning of this book, in which the building imitates "the disembodied idea of ​​the craftsman". and that "(the building) must be judged more by a certain disembodied order than by its material 'forms' in sculpture as opposed to the 'spirits' of sculptors who alter proportions for the sake of appearance (Sophist 235d-236e ) They are also in the spirit of Plato

Celebrating architecture for its design and construction tools that ensure a precise sense of order, verifiable by measurement (Philebus 56b-c). Finally, Ficino and Alberti's emphasis on "calculated and incorporeal patterns" is reminiscent of the Vitruvian man, where the body is represented as an ideal form by analogy with the temple through alignment and the orthogonal and circular lines of the compass and the ruler. Here, the architect replaces the natural perspective experience of a concrete human form with a flattened graphic projection, in which even the protruding fingers share the same two-dimensional plane as a compass circle: a perfect geometry circumscribing a theoretically centered frontal image. of the body lying down on his back from an abstract aerial perspective directly overhead. In theoretical writing, this difference and sometimes the tension between ontological and experiential concerns with representation can be almost tantamount to a rejection of painting. Plato ridicules painters who claim their illusionistic effects as intrinsic virtues of their work (Republic 598b-c) and compares their imitations to someone who can simply hold up a mirror to the things of the world (596d-e).81 This mirror analogy anticipates Brunelleschi's notably more sophisticated Demonstration of his illusionary system of one-point linear perspective as used in his Florentine Baptistery painting, which we know from the Life of Brunelleschi, written by his successor Antonio Manetti.82 On the panel of this painting he drilled a peephole at the vanishing point

93 Trajan's Forum, Rome. TO SHOW. early 2nd century. Restored plant. Author of the drawing, modified by S. Rizzo, in Rizzo 2000: plate 62.

through which the viewer must look again at the royal baptistery from the perspective from which the scene was painted. Between the baptistery and the painting, the viewer held a mirror that reflected the painting at some distance to verify the accuracy of the painter's rendering, and thus the success of his system of perspective by moving the mirror back and forth. In this way it can be said that Brunelleschi unintentionally responded to the old criticism of Plato by penetrating the instrumental rather than the intrinsic value of pictorial illusionism through geometric principles.83 Alberti was one of several when he used these geometric principles in his Über painting dedicated to Brunelleschi are theoretical theorists (such as Piero della Francesca, Leonardo and Drer) who elaborated on the contribution of the first Quattrocento painter, just as Anaxagoras and Democritus elaborated on the ancient Greek invention of linear perspective by Agatharkhos (Vitruvius 7.praef .11). However, in the passage quoted above from Alberti's subsequent On Construction, he abstracts the elements of line and angle that underlie Brunelleschi's invention and elevates it to a level of predictable veracity that transcends concerns about deceptive appearances. In the orthographic projections of ichnography, it is the graphic vision of the pure idea and not the pictorial arrogance for the visual experience of the architectural space that should guide the built form. This humanistic sentiment, based on literary rather than craft traditions, reflects a growing disconnection of the Renaissance architect as an intellectual from craft traditions. Intricately, however, this distancing from the craft was shared by painters and thus a point of comparison, not contrast, with figurative artists.84 In fact, the intellectual underpinnings were applied to their own architectural projects. by artists from Brunelleschi to Leonardo, Michelangelo, and many others. The development of linear perspective in painting thus found a suitable vehicle to enter the architectural design process, complementing the imitation of the ancient authority of Vitruvius, who wrote that architecture is made up of the ideas of linear perspective, ichnography, and drawing of elevation. In the Greek theater of the classical period, as I have already noted, the invention of linear perspective in Greek painting also helped to produce iconography in accordance with a strong architectural vision based on a more than experienced ontological form. Although written commentaries on Greek architecture preceded it

Vitruvius, there can be little doubt as to the influence writers/practitioners since Pytheos must have had on the intellectualized conception of design reflected in the Roman writer's description of architecture. In both antiquity and the Renaissance, therefore, developments in painting, along with theoretical discourses, probably contributed to the architect seeing and shaping the world through the abstract form of iconography. Alongside this rise of iconography in Roman and Renaissance architecture, there is another important legacy of sign habits originating in the Greek world. The circular approach, hidden in the design process of Kos (Figure 86) and evident in the Greek theater and other radial buildings, would find its full expression in Roman buildings made of concrete, a material capable of dividing the interior space around and above. in accordance with O to shape

94 Octagon of Nero's Golden House on the Esquiline Hill in Rome. AD 64-68 C. Original project. Author of the drawing, according to B.M. Boyle, D. Scutt, R. Larason Guthrie, and D. Thorbeck, in MacDonald 1982: Plate 103. Circular and polygonal forms of the drawing board. In Nero's time, after the middle of the first century AD. C., a building as remarkable as the octagon of his Golden House had a radial plan, with a centrifugal arrangement of rooms that radiated from the center, which in turn was arched (Fig. 94). This central room may be the emperor's dining room described by Suetonius (Nero 31), covered by a circular vault that rotated like the sky. Even more famous was Hadrian's Pantheon (Figures 1, 95), surmounted by a hinged hemispherical dome with a radial pattern of concentric chests. Here, the beacon of Oculus's only light source slowly moves through the interior as the sun streaks across the sky, bringing the revolutions of the cosmos to the viewing experience. Like Plato's Diadalos diagrams, the visualization of the cosmos through geometric designs for the Golden House and the Pantheon was an expression of craftsmanship rather than astronomy. However, in the eras after Vitruvius, his interest in the innate structure and mechanism of what can be seen in the universe was able to merge under the single unity of

95 Pantheon, Rome. View from the bottom of the dome. Author of the photo. architecture. To convey this sense of order that characterizes the entirety of space in the cosmos, the architect of the Pantheon designed what is surely one of the oldest known graphic expressions in architecture: the circular and radial shape built for the ribbing of a single columnar drum. .

Excursus Plato and Vitruvius's conception of the cosmic mechanism An excursus follows Plato, Vitruvius, and earlier traditions of thought and craft going back to Anaximander and archaic architects. By addressing possible alternative justifications for the existence of iconography before the Late Classic, the analysis here complements the exploration of buildings in Chapter 1. Leaving buildings aside for philosophical texts and architectural theory, it allows one to engage fully with the current premise. : that interest in design in architects trained as intellectuals may have arisen from a literary training in abstract thinking rather than just the practical demands of planning. Along with a later return to visual material in Chapter 2, this overview will offer a differentiated view of the connections between craft, intellectual traditions, and knowledge production in the Classic period. As noted in the main chapters of the text, the rise of iconography, linear perspective, and the distinctive Greek understanding of order in nature seems to owe much to the design process of Greek architects in the construction sector, particularly with regarding the role of design in construction. the creation of individual features on a 1:1 scale, which preceded the scale drawing. Furthermore, a careful examination of the texts changes the nature of the questions that are asked about the material evidence, as one finds additional concerns expressed in the intellectual traditions. Like the ideas that embody the principles that make up architecture for Vitruvius, unexpectedly for Plato they are combined with the vision and graphic role of nature associated with it through representations of cosmic mechanisms. A closer affinity with Vitruvian's definition of architecture, encompassing construction, chronometry, and machinery, leads in Chapters 2 and 3 to an examination of the role of vision in the development of linear perspective and ichnography. Furthermore, it only provides a useful model for Plato's discussion of transcendent truth, ideals such as architectural designs could be understood as carriers of truth and spiritual value even before Plato. In this context, one can cite the use of numbers and geometry to support the elevation and plan of the Archaic Temple of Athena in Paestum with its Pythagorean architecture.

triangles (Figure 29). In accordance with Aristotle's scrupulous critique of Pythagorean thought (Metaphysics 985b23–986b8, 1090a21–1090a14), the Pythagoreans postulated numbers as the essence of all things, whether physical bodies or abstract concepts. At the center of this all-important function of numbers are harmonies expressed by whole ratios, like in music, where an octave occupies intervals between notes expressed as 2:1, 3:2, 4:3, etc. Borrowing from Aristotle (Metaphysics 1080b16), it has been convincingly suggested that numbers for the Pythagoreans represent not only arithmetic values, but also concrete "unit atoms" in space.1 Apparently, in expression of this idea, in the 18th century V, a Pythagorean named Eurytos used Pebbles to compose schematic illustrations of people, horses, and other phenomena in which numbers defined the true essence of the object depicted.2 This nexus of spatial representation, measure, beauty, and truth in The Demonstration of Ideas is not it's easy to understand. accessible senses is indeed consistent with the notion of a theoretical justification for iconographies created for fifth-century buildings. As discussed in Chapter 1, for example, buildings like the Parthenon, the full proportions of the entire temple plan elude perception. visual. . In addition to the interesting possibilities for parallels between Plato's ideas and architecture presented so far, Plato directly addresses drawing in the Republic. At one point (529e-530a) he refers to the beautiful geometry of the diagrams of Daedalus, the mythological builder of the labyrinth, in a discussion of truth and models, duplications, and other approximations that ultimately do not convey the truth. itself,4 which is not surprising given that Plato associates absolute truth with the intelligible rather than the phenomenal realm. Even before this discussion, he offers the passage from The Republic on the Divided Line (509d-511e), in which he proposes a more nuanced relationship between the visible and the intelligible. Here he analyzes geometric diagrams as visible images that the geometer can draw in search of truth to be grasped by the mind rather than the eye. In this way, geometric design is equated with understanding (διάν ια), which ranks second in the hierarchy of knowledge after the rational part of the soul, itself the means of access to truth in the intelligible realm of the ideas. This point is further clarified in the Timaeus (47a-b), where Plato explains the great value of seeing as a gift from God, that when it is just

directed, in fact it leads us to philosophy itself. In this series of passages, then, Plato seems to invite the reader into his text to explore the existence and meaning of drawings like those of Daedalus. This invitation presents difficulties, but by following it one is better prepared to recognize the beginnings of the graphic construction of architectural space, which I believe first occurs in fifth-century Athens. A possible theoretical value of iconography as truth in plane geometry and approximation may be consistent with Greek architectural thought in the fifth century, while our loss of Greek architectural treatises during this and all periods may to some extent justify our only philosophical writing, but one can at least think of ancient testimonies directly about him that address what Greek practitioners of the visual arts had to say on related topics other than architecture. The testimonies to the fifth-century thought of Polykleitos in his lost Canon, the famous treatise on sculpture whose title (ν ν) was the term used for the type of measuring stick used by architects, may be particularly helpful in this regard.5 As a prose work focused on monumental figurative art and a unique work (presumably the Doryphoros), the canon seems unprecedented6. On the other hand, the tradition of architectural treatises dates back to the first half of the 16th century. Century, when, according to Vitruvius, Theodoros and Rhoikos wrote their commentaries on the Temple of Hera on Samos and Khersiphron and Metagenes on their work on the Temple of Artemis in Ephesus (De architectura 7.praef.12-17). Similar comments on individual works continue into the Classical period, with a work by Iktinos and a specific period by Karpion (a misinterpretation or corruption of Callicrates?). Recalling that Greek architects, since Theodore and Rhoikos, were also sculptors in general, the possibility that adequacy was a concern long shared by architects and sculptors raises the compelling possibility that the concepts attributed by Polykleitos are also applicable to contemporary architects,10 and may therefore be relevant to the present question of the possible value of the ideal in the sense of architectural drawings.

Through this possible connection between architectural writing and Polykleitos, additional connections between architecture and Plato can begin to be seen. At first it must be emphasized that the evidence for what Polykleitos actually wrote is fragmentary and belated, and the interpretations offered here are tenuous. Citing the canon as the authority for him, the second century AD physician Galen. justified the belief of all philosophers and physicians that "beauty lies in the fitness of the parts of the body" (κ λλ τ σ ματ ν τ τ ν μ ρ ων σ μμ τρ, On the Teachings of Hippocrates and Plato 5.48) . If this statement accurately reflects Polykleitos's beliefs, then it seems to anticipate Plato's privilege of the "true approximation (σ μμ τρ α) of beautiful forms" (Plato Sophocles 235e). To rest here, however, would be to ignore some very strong recent interpretations of an important related statement that seems to shed light on how Polykleitos' adequacy produced beauty. According to a proverb attributed directly to Polykleitos by Philo Mechanikos, "for Mikron good grows out of many numbers" (τ γ ρ παρ μικρ ν δι π λλ ν ρι μ ν γ γν σ αι, Philon Mechanikos On Artillery 50.6). 11 Although various interpretations of the meaning of paramicron are possible,12 it seems quite likely to convey the idea of ​​small exceptions to the rule, such as small deviations through corrections that painstakingly add or subtract precise arithmetic relationships according to the experience of the sculptor. as a craftsman.13 Understood in this way, the strict resemblance to Plato's idealism begins to break down: truth cannot be confined to a transcendental realm, accessible only through a mimesis that strictly adheres to the proportions of the perfect idea. If one does accept microns in this sense of adaptation to numbers, then the connection of Philo's quote to number mysticism in Pythagorean thought - a quality susceptible to the idealistic views found later in Plato - might be something. more problematic. . than what appears to the naked eye.14 Finally, it is the numbers themselves that are corrected in the process of creation, and it seems that this point of view represents a departure from the Pythagorean notion of number as the main element of the universe, just as than these same settings. affirm the value of embodied experience against an abstract ideal.15 In other words, the

The integral proportions of the idea are not "the good" in themselves, but a means in a process of beauty that is not achieved until the sculptor makes small adjustments to them. Therefore, the parallel with idealism is far from clear. If parallels with later philosophy are needed, the spirit of Polykleitos' statement could even be interpreted as anticipating not only Plato's, but also Aristotle's description of architecture (κ δ μικ) as an art (τ χνη) that , like all arts, produces objects by chance (τ χη): “Art loves chance, and chance loves art” (τ χνη τ χην στ ρξ κα τ χη τ χνην, Nicomachean Ethics 6.4.5). Of course, this assumption of randomness in the design process is consistent with Polykleitos's sculpture, which follows an arithmetic plan “within a bit” (for microns) when skillful or intuitive adjustment of the ruler produces a more visually satisfying form. .16 By de These reflections do not detract in any way from the value that the canon should have given to complete adaptation in the design process. Nor should they seriously imply a proto-Aristotelian understanding of Polykleitos. They suggest that despite the legitimate question of how fifth-century Greek art and its related theory might relate to contemporary and later philosophy, the differences in possible interpretations leave one on shaky ground in actually trying to prove such a connection. However, for reasons I will examine later, Polykleitos's departure from pure number may not be a reason for outright dismissing his association with Pythagorean thought. For Plato, the difference between what astronomers see and measure and the underlying truth of such optical capture and calculation is captured by metaphors. Consequently, we must approach astral bodies as models (παραδ γματα) of transcendent reality in the same way that we would approach the geometric diagrams (διαγράμμασιν) of Daedalus or any other craftsman (δημι ργ) or painter (γραφ). cuerpo Bodies, Diagrams The artisan's geometric forms are models, but as such they are not simply models to be imitated in the built work. Finally, this imitation is a problem for the production of things, as shown elsewhere in Plato's classification of the Creator in the realm of appearances with the possibly pejorative term "imitator" (μιμητ, Republic 597e).18 Rather , the positive value of Models in it in their almost synaptic character as objects that move away from the truth and lead to the truth through thinking and thinking

Reason (Republic 529d). On the one hand, from Plato's point of view, his clear separation of ideas in the intelligible realm may suggest that they should not deserve to be described as an ideal in Vitruvius (De architectura 1.2.1-4) in the sense of ichnography, drawing. elevation or similar spelling and drawing in perspective. On the other hand, as models, they are like the movements of the celestial bodies because they invite us to understand the truth. With the precise measurement tools in the construction industry (Plato Philebus 56b-c), one could even read the indication that the privileged position of this trade results from its scientific processes, which connect it with the truth through the geometric surfaces as their models. . Since Plato's only direct discussion of the drawings is his reference to these plans, this discussion must be carefully considered if we are to properly examine the problem of the idea as a concept shared by both Plato and Vitruvius. But first, given this possible link between architecture and philosophy, the limitations of Plato's anachronistic relationship with Vitruvius and his distancing from the concerns of architects and sculptors deserve attention. The gap of more than three centuries between Plato's death and the Ten Books of Architecture is evident, as is the lack of relevance of Plato's thought to those interested in design and construction. Plato's usefulness for this discussion is not how his philosophy affects later and later contemporary architects and sculptors. Rather, his usefulness lies in the status of his metaphors as established facts in his readers' experience, which allows him to manipulate those metaphors in meaningful ways for his own ends. Plato knew the activities of disciplines such as geometry, astronomy, music theory, construction, sculpture, poetry, painting, and other arts. This knowledge allowed him to shape his discourse based on the specifics of these disciplines. It is more than possible, then, that the beauty and goodness pursued by Polykleitos' intuitive adjustments to numbers is related to the type of manual thinking that Plato used independently of the specifically Pythagorean elements. At the same time, and despite the possible connections between architectural writing and Polykleitos' lost treatise, one can also see the usefulness and limitations of addressing our architectural design problems through figurative sculpture. Regarding the relationship between the reduced model and its imitation on a full scale (as in Plato

Sophist 235d), the practices in the classical sculptor's studio certainly suggest the possibility of parallel approaches in contemporary architecture. This parallel becomes clearer when one recalls the architectural context of marble sculpture, in which the design of friezes and pediments suggests close interaction, if not collaboration, between Greek architects, stonemasons, and sculptors. However, a close look at the sculptural practice also reveals an important difference. Contrary to the lack of need for reduced-scale drawings in classical temple architecture, as argued in Chapter 1, the successful creation of full-scale or life-size marble sculptures with any degree of naturalism and complexity of pose is just unbelievable. 19 Using the additive process of working with flaky clay allowed sculptors to specify form details in individual figures and larger groups that could be assembled as compositions in such a difficult setting as a pediment. Following these clay models in the subtractive chisel-on-stone method, portable casts of model parts made with negative casts of plaster parts ensure workability in the task of copying when full-size models are too heavy to carry. be moved. . . However, due to the structural limitations of the clay or wax, it is impossible to determine the pose and surface qualities on the full-size model. Metal armor is required. It is clear that the composition of this armor assumes a pose already prepared in advance by the sculptor, which can only have appeared in reduced models of the figures and their group composition. The alleged ignorance of scale models on the part of classical period architects would therefore be difficult to sustain, and the argument against equivalent building practice must continue to be based solely on our perception of differences in tradition. and the need as an Italian visitor ordering a fork in China. While there is a strong argument against the need for iconography, even in a relatively complex spatial composition like the Parthenon, as discussed in Chapter 1, Plato's reference to Daedalus' diagrams opens at least one small crack in the argument. against tradition. Daedalus was both a legendary sculptor and an architect.20 As a sculptor, instead of plastic models, diagrams would be of as little value as plastic models for Plato's purpose of representing the geometric patterns of the stars against the sky;

It is the graphic and geometric quality of the diagrams that evokes the architectural role of Daedalus (Republic 529e-530a). Ask what the architects might have measured their buildings by. It is possible that Plato's reference to Daedalus' diagrams supports the view that architectural drawings and not just written specifications (syngraphai) determined the dimensions and proportional relationships observed during construction. It is unclear whether such drawings were Vitruvian's reduced ideas (ichnography, orthography, and perspective), or the type of working drawings for ecstasy and column drum flutes discovered by Haselberger at Didyma (Fig. 33), or something else entirely. . Be that as it may (and as little as a casual phrase), Daedalus seems to have lost his way in his own maze without the aid of iconography.22 If the need for iconography for the classical period cannot be shown, then at least it can Discourse He bases our construction on the possible existence of antecedents of Vitruvio's ideas in the construction of traditions several centuries before. This possibility invites further reflection on additional similarities between Plato's and Vitruvius' narrative of doing. For Vitruvio, astronomy plays a very important role in architecture. In fact, Vitruvius integrates astronomy into the very definition of architecture (De architectura 1.3.1), whose three parts include not only the art of building (aedificatio), but also the arts of chronometry (gnomice) and mechanics (machinatio ). The entire Book 9 is devoted to the measurement of time, with entire chapters devoted to the structure and patterns of the rotating cosmos, the phases of the moon, the relationship between the course of the sun and the length of days and hours, the constellations, the contributions of the great astronomers, the figure of the analemma, sundials and waterdials.23 For Plato, the question of chronometry is central to the activity of the divine artificer, whose creation of the celestial bodies and their movements can be understood as the initiation of measurements in the universe, the measurement itself being the main role of ideas. In other words, the divine artisan is a watchmaker, and thus mediated, the measurement of time shapes the sense of order that underlies space.24 For Vitruvius (9.1.2), it is the force of nature that created the cosmos, but this is not the natural power of Aristotle (φ σι)

which produces phenomena through its own telic inner workings. Rather, it is the force of nature as architect that creates the cosmos as a machine in which wheels on a central axis spin celestial bodies in endless circular motion above, around, and below the earth, like if it turned a lathe.25 Interestingly, Vitruvius adds elsewhere this image of the machine as an underlying model for the shape and motion of the cosmos around an explanation of the cosmos as a model for machines (10.1.4). Dividing Vitruvian architecture into three parts (buildings, chronometry, and machines) results in a more unified corpus than might appear at first glance. Nature designs the cosmos like an architect, and by building machines and relying on the circular motions of machines to erect buildings, architects build like nature. Vitruvius is clear as to which of these creations occupies the exemplary position in the relationship between cosmology and construction: “...from nature [our ancestors] took models, and by imitating them the divine led them to display the pleasures of life ”. 26 For the Vitruvian passage here, the probable inspiration of Plato's divine craftsman has been noted elsewhere, and one can develop this connection along the lines of imitation (imitatio, μησι) of models.27 The intelligible mechanism and Eternal of the cosmos, Vitruvius describes how the creation of nature as an architect becomes visible in real machines. Likewise, Plato (Timaeus 28c–29a) describes the creator (π ιητ) of the cosmos as a maker (τ κταιν μ ν) who creates the cosmos according to a model or paradigm. Plato describes two types of models in this context (27d-28a): 1) the eternal type, or that of eternal being and without becoming, and 2) the generated type, or that of eternal becoming without being. He clarifies this distinction elsewhere (48e–49a) as the eternal, unified, and comprehensible idea of ​​the model (παραδ γματ δ) and the merely visual and phenomenal copy of the model (μ μημα παραδ γματ). For Plato, the eternal models are the ideas themselves, while the generated models with a developing rather than eternal ontological status include the revolving cosmos of the divine craftsman himself and the diagrams of Daedalus or some other craftsman or painter. In Plato's mind, Vitruvius' endlessly rotating cosmos, created by the power of nature as architect, would be a generated rather than an eternal model. This second-rate status is philosophically based on the phenomenal and even more remote nature of the status of machines.

However, imitating him should not have scared Vitruvius. In the Timaeus, it is the wrong movement of the planetary bodies that allows them to be contrasted with the uniformly repeated movements of the planetary orbits, allowing the bodies to serve as markers, and therefore as a measure, of the time numbers given in the clockwork mechanism. divine builder-architect of the revolving cosmos (38c). it is the origin of philosophy (Timeo 47a-b). By implication, Plato does not simply mean that knowledge follows automatically from visual experience. Rather, a correctly directed vision leads to reason and thought, which then allow the penetration of truth and the foundation of philosophy. Likewise, in the Republic "reason and thought perceive these (true qualities as number) but not sight" (δ λ γ μ ν κα διαν ληπτ, ψ ι δ, 529d). This apparent contradiction is actually a clarification that what is at stake is not sensory sight, but reason and thought as another way of seeing (instead of an opposition to sight), where arithmetic allows the intellect' see' (δ ν, Republic 524c ). Both sensory and viewable approaches come together in the revolving chronometric mechanism of the cosmos. The appearance of this mechanism in both Plato and Vitruvius suggests the possibility that both the philosopher and the architect were based on a discourse that preceded them both, rather than the latter's mere dependence on the former. A possible clue to this earlier speech is the testimony that in the sixth century Anaximander of Miletus made and wrote about a sundial, a sphere of the cosmos, and a drawing of the circular outline (π ρ μ τρ ν) of the earth and the sun. sea. .29 Interestingly, his cosmic sphere was supposedly a geocentric model showing the earth on its central axis in the form of a columnar drum, although our source for this architectural correlation goes back to the third century AD. and perhaps reflects a later elaboration.30 Through his verbal prose description of the cosmos and his models of representation, recent scholarship has argued for Anaximander's collaboration with and reliance on the work of contemporary Ionian architects involved in building and writing of the giant temples. archaic and began the traditions of architectural theory with his early treatises.31 Cosmological models remain relevant to Plato in both late classical and Western philosophy.

to Vitruvius in architectural theory in late Hellenistic times, and one can only assume a tradition of related principles in the lost architectural discourse of Khersiphron and Metagenes, Theodoros and Rhoikos, Iktinos, Pytheos, Hermogenes, and others cited by Vitruvius.32 Plato , then, may be useful as a possible reflection of the equally shared ideas of archaic architecture and philosophy that came to Vitruvius centuries later. Late classical and Hellenistic architectural writers such as Pytheos and Hermogenes may be Vitruvius' direct sources for sixth- and fifth-century topoi. Plato, a crude contemporary of Pytheos, may have drawn influences from the same nexus of archaic and classical sources of this famous architect who, according to Vitruvius, could at least boast of a great wealth of knowledge in many things (1.1.12). Although Pytheos may have read widely in various disciplines, it should not be imagined that Vitruvius studied Plato's descriptions of the cosmos or the related philosophical discussions in works such as The Republic or The Timaeus. Whatever sources Hellenistic writers on architecture have shared with contemporary philosophers, Plato's position outside of the ongoing discourse on architecture must convey subtlety and care, as one interprets the similarities that his writings might share with Vitruvian. . With this caveat, one might be wary of Plato's reference to Daedalus's diagrams. It may be tempting to read Plato's discussion as evoking what the Greeks called ideali (iconographies, orthographies, and perspective drawings), but Plato's reference to the beautiful geometry of these diagrams may have evoked more than just graphic representations of buildings. . As already indicated, the use of working drawings for the design of parts of buildings and their refinements (Figure 20) seems to apply to what Plato describes as nothing less than scale drawings of complete buildings. Furthermore, the clear astronomical context of the passage may suggest another possibility: that given the observable connections between classical architecture and astronomy preserved in Vitruvius, any architectural associations evoked by the name Daedalus would not preclude a simpler interpretation referred to by Plato. a kind of astronomical chart. A consideration of the details of Plato's argument might support this view. First of all he uses a metaphor established between the shining stars

and embroidered in a way that seems to emphasize a very specific point. In the Iliad (6.294-295) Athena receives a peplos whose embroidery shines like a star. in the manner of diagrams by Daedalus or some other craftsman or painter. In this way, the dialogue seems to depend on a rhetorical device to effectively match rotating celestial bodies (the astronomer's objects of interest) with an associated object in the field of the two-dimensional patterns created simply to stop visible motions, which it does not it's picking it up. correspond to real motions measurable "in real numbers" (ν τ λη ιν ρι µ). This binomial configures a comparison with a second binomial that focuses on graphs, which despite their beauty cannot serve as examples of this numerical truth, or "absolute truths such as equal values, double values, or any alignment" ( τ ν From the α τ ληψóμ ν ν σων διπλασ ων λλη τιν σ μμ τρ α ). But what is the counterpart of the rotating astral bodies that are woven into this second pair? One possibility worth considering is that Daedalus’ diagrams could be drawings associated with the kind of rotating machines of the cosmos described by Vitruvius (10.1.4). To understand how Plato's insinuation may have evoked mechanisms of rotation requires a detailed analysis of his comments on the specific characteristics of 'presocratic machines' both in character and function. In one possible interpretation, the sphere of Anaximander’s cosmos with the earth as a columnar drum at the center was itself a machine with rotating bodies, since in the cosmic model described by Vitruvius, the cosmos as a rotating machine would not really depend of the construction of a philosopher of this machine. In turn, the machines created by contemporary architects and described in their commentaries were already available to model the philosophical view of the functioning of the revolutions of the cosmos. Khersiphron and Metagenes, the architects of Archaic Artemision in Ephesus, who left comments on the construction of this building, described the mechanisms they devised to transport heavy stones from the quarry to the site. These descriptions are preserved in Vitruvius (10.2.11–12). Like the model of Anaximander, which represents the central earth as a pillar

drum,35 and like Vitruvius' description of the cosmos as a perpetual rotation of celestial bodies around a central axis centered on the earth, the khersiphron mechanism is the axis of a column attached to a wooden frame by pivots that allow that the column rotates incessantly In this way, the column is transported with precision through its ingenious transformation into part of the vehicle that contains it, and the load itself, in turn, moves the machine through its own rotation. The Metagenes mechanism modifies Khersiphron's design to transport the rectilinear blocks of the architrave, which he converts into axles by placing wheels at each end, which rotate above and below the ground like the wheels at the end of each axle in the rotating cosmic model described. by Vitruvius. . Once again, the rotating load becomes part of the vehicle that contains it, in this case, the axle that drives the machine. As part of a discourse on construction that survives from the Archaic to the Vitruvian period, these archaic machines may be useful in addressing Plato's obscure passage on astronomy that leads to his commentary on Daedalus's diagrams. Taking the reader from the phenomenal realm of the stars to their transcendent reality, he writes that visible cosmic bodies are far from the truth: in real speed, in real slowness, in real number, and in all true forms (π σι τ λη σι σχ μσι), charged because they are related to each other and, in turn, carry what they contain.36 In this difficult passage, Plato describes the difference between celestial phenomena and their true models in terms of the latter's character as carriers of what is inherent to them, related to the ideas of speed or slowness and numbers contained in the ideas of forms (σχ ματα).37 These forms themselves seem to be the models, the vehicles that sustain and carry them. The following commentary on Daedalus may refer to this meaning and serve as a particularly pertinent, though obviously unintended, invocation of the architects who built and wrote about the Ephesus Artemision; Like Daedalus and Icarus, Khersiphron and Metagenes were a father and son pair who left Crete to set up their creations elsewhere.38

Before characterizing how Plato's machines and Diadalos diagrams might relate to models of cosmic mechanisms, it is useful to consider how such models might relate to Plato's ideas. Immediately after his statement about true models as vehicles and in relation to how we can access these true models, Plato writes: "Reason and thought perceive them, but not sight." movement, to his proposal of a "real" astronomy that treats the night sky as a woven surface, a strategy that empties its physical presence and stops its movements in motion in favor of a solid, abstract image. Plato inserts here his commentary on the diagrams of Daedalus or some other craftsman or painter, equating them with the movements of the cosmos built by an anonymous craftsman (δημι ργ), anticipating the divine craftsman of the Timaeus who created the cosmos created from a model . (28c -29a). However, this equation should not imply that the divine craftsman builds his cosmos from blueprints that are the creation of his cosmic engine. An elevation of the importance of architectural ideas in comparison with complete architectural or astronomical structures is not immediately recognizable. Instead, something more subtle is at work. In Timaeus (47a-b) Plato claims that seeing in the right direction leads to knowledge, yet he ridicules those who lament the loss of sight. In these attitudes there is no contradiction because the true numbers - the comprehensible ideas of numbers - are grasped by philosophy, which is possible by observing the numbers as time in the mechanisms of the cosmic clocks of the divine Craftsman. Again, there are two types of paradeigmata: the generated models of becoming and the eternal models of being that mimic the generated models, their unified and intelligible ideas (Timaeus 27d-28a, 48e-49a). Plato carefully distinguishes between the apparent motions of turning vehicles and the actual speed in true numbers and true forms, 39 but these ideal numbers and forms are not found in the geometry of the diagrams he cites. Rotating vehicles are the generated models of the cosmos, following a tradition that seems to go back to Anaximander, a tradition that may have suggested such mechanisms as models for Plato and his readers. The eternal models that are Plato's unique contribution to Greek philosophy are the ideas for generated models, and Plato expresses them as accessible only through a different kind of vision. Thus understood both a graph and a

The machine that represents the cosmos would share the state of the generated models, as well as the associated embroidery and the pairing of stars. Each of them differs from the eternal models used in the construction of the cosmos by the divine craftsman. Apart from this difference, it is difficult to find a parallel between the ideali as models for the cosmos of the divine craftsman and the diagrams of Daedalus (or some other craftsman or painter) as models for any kind of machine. If such a parallel were tenable, it would be useful to have an indication that diagrams were part of mechanical production in the Archaic or Classic period. Without evidence, it cannot simply be assumed that the diagrams served a prescriptive purpose in this context. Rather, this assumption would result from reading Vitruvius with a modern perspective that associates the assembly of machines according to the descriptive diagrams found in Leonardo's tomes or on many toys today.40 A closer look at the passages relevant supports such an interpretation. Plato writes that Daedalus's diagrams contain compensations such as equality and doubling. From an engineering, rather than a philosophical, perspective, such proportions on vehicle diagrams would serve a practical purpose as a basis for the precision of the built mechanics, which in turn ensures the intended functionality of the device. According to Vitruvius, a well-designed machine was not just one that turned, but particularly one that turned in a way that covered distances in finite time. He relates a recent story of a certain Paconius who, in building a vehicle to transport the base of a monumental statue, did not follow the example of the architrave vehicle of Metagenes, which could cover the eight miles from the quarry to the building site in time. (From Architektur 10.2.13). The result of Paconius' flawed design was a vehicle that drifted, overloaded the oxen, and slowed down until poor Paconius wasted all his money. Vitruvius adds as many specifications and metric ratios as he has at his disposal, not only on Paconius's recent citron, but particularly on the vehicles of Khersiphron and Metagenes half a millennium earlier.41 Although these numbers appear to be for prescriptive purposes, it is important to note that Vitruvius omits any reference to the illustrations of the mechanisms in his account, and thus there is no indication that Khersiphron's treatise

and Metagenes contained such diagrams. Probably Vitruvius, these early architects relied on written descriptions with relevant metric and proportional specifications. Furthermore, even if such prescribed diagrams for transportation vehicles did exist, the idea that Plato would be amazed by the beauty of their geometry is somewhat unlikely. Daedalus's diagrams do not represent machines, but recognizing the element of mechanism to which they refer is important to understanding the world of manufactured objects known to Plato and the transcendent truth of the universe he describes. As visual phenomena, the diagrams form an apt parallel to the cosmic mechanisms mentioned in the same place: the revolutions of celestial bodies in their regular orbits and, in the case of "wandering stars", the repeated deviations in their locomotion. worldwide. What makes this parallel particularly interesting, however, is the cultural background that, in a discussion of vision, would make a craft diagram an apt parallel for these cosmic mechanisms. Considering the connections between vision, drawing, and graphic representations of cosmic machines, Chapter 2 examines these entities as links in the development of linear perspective, iconography, and constructions of order in the universe.

Appendix A Analysis of construction dimensions for Entasis at Didyma See Chapter 3 and Figures 60, 62. Measured from its central axis, the total radius of the construction axis (f-i) is approximately 1.01 m, with differences of only 1.5mm between the widths of the top and bottom dimension. The top of the shaft, where the arch intersects the chord, measures 84.3 cm +/- 0.1 cm (this part of the drawing does not survive, hence the uncertainty of 0.8429–8431 m for restoration) . Vertically, the drawing is divided into the 0.3128m base, shown at 1:1 scale, and the 1.1857m distance to the top of the drawing at d65, shown at 1:16 scale, which results in a total height of 1.4985 m. The reduced part on the base measures 1.1232 m at the height of the intersection of arc and chord on d61a. At this height, the horizontal line does not correspond to the regular dactyl intervals of 1.85 cm, but appears 1.25 cm above d61, which, according to Haselberger, could represent 2/3 of a single dactyl.1 As Haselberger concludes, the total height of the staff so far there are 60 2/3 dactyls drawn up to this point, which is roughly the height of the constructed shaft of 60 3/4 feet.2 The importance of this dimension is evident in relation to the other dimensions within the drawing. As b, its relation to y as the total height of the design from the bottom of the base to d65 is an integral ratio of 3:4: (1.123 m/3) × 4 = 1.4973 m, a negligible difference of - 1.2 mm from 1.4985 m, as measured in the drawing. The total radius of the axis d has a ratio of 2:3 with respect to the total height e. For greater precision, d is an average of the small difference between your measurements at the bottom and at the top of the drawing: (1.008 + 1.0095 m) / 2 = 1.00875 m With y of 1.4985 m ( its actual length is its ideal length of 81 dactyls), (1.4985/3) × 2 = 0.999 m, a difference of -9.75 mm from 1.00875 m. Perhaps this difference reflects the architect's addition of 1 dactyl to the overall lower diameter (not radius) of the shaft, resulting in an intended measurement of 1.00825 m or 54 ½ dactyls, a slight deviation from the ideal 54 dactyls or 0.999m. It is true, however,

The millimeter deviations that separate the actual design from the theoretical relationships proposed here make the interpretation of the intent extremely tenuous. A small error in the writing process cannot be ruled out. In this sense, the error starts at k and i' when determining the axis of the drawn axis (and therefore all measures of its radius) may remind you that drawing is not always a science, especially with drawings of this size, drawn vertically in a Wall to be executed in stone. For these reasons, the present analysis continues to focus on the multitude of proportional matches with tolerances on the order of millimeters, rather than trying to explain the motivations behind such close discrepancies. Another integer relationship is the 3:4 relationship between a as the radius of the axis at the end of the curve in d61a and b as again the height of 1.123 m for d61a: (1.123 m/4) × 3 = 0.8423 m, is that is, in the measurement range of 0.843 m +/- 0.1 cm for this measurement in the drawing. As a 3:4 ratio with b (= 60 2/3 dactyls), the ideal measurement for this distance should be 45 1/2 dactyls or 0.84175 m. Together, these integer equivalents demonstrate the graphical logic underlying the design as a whole: the 3:4:5 Pythagorean triangle. At the center of the design is a 3:4:5 Pythagorean triangle ABC that sets the height and radius of the axis to the level of the upper limit of curvature at d61a. In addition to this geometric definition, there is also an important modular element: the maximum height of the arc (g) over the chord (h) is 4.65 cm, which sets the modulus that describes triangle ABC at 18:24:30. :18 × 0.0465 m = 0.837 m, a difference of 2 to 4 mm from 0.843 m +/- 0.1 cm; 24 × 0.0465 m = 1.116 m, a difference of −7 mm at 1.123 m.

Appendix B Hypothetical Work Design Analysis for Platform Curvature at Segesta See Chapter 3 and Figure 61. Whether the Haselberger construction can be accepted as a method of creating euthyteria curvature along the flanks of the sien in Segesta (Figure 61), one might wonder, since the architect has reached a maximum height of 0.086 m. An attractive answer can come from the internal correspondences of the drawing itself. The maximum ordinate located on the center of the chord is 1.404 m from the center of the diameter of the arc: 1.49 m − 0.086 m = 1.404 m Given the 1.49 m size of the radius that has the same center as the endpoints of the chord, the Pythagorean theorem confirms Seybold's calculation of the length of the chord to be about 1 m: with a hypotenuse of 1.49 m, the lengths of the sides are 1.404 m and 0.499 m, the latter being 0.998 m for the total length of the doubled rope. Thus, the chord shares a 2:3 integral relationship with the radius of the arc: 0.998/2 = 0.499; 0.499 × 3 = 1.497 m Despite the similarity of integer proportions, it can be clearly seen that the 0.086 m sagitta does not establish modular relations in the sense of Didyma's plan; To be modular, the relations would have to be integers, being 0.985m/0.0845m = 11.166m and 1.478m/0.0845m = 17.491m, rather they are the eighteen equal divisions of the chord resulting from the succession of corresponding cross marks to the stylobate, establishing a modular relationship of 18:27 in the chord and circle of the design: 0.998 m/18 = 0.0554 m; 0.0554 × 27 = 1.496 m.

Appendix C Hypothetical working design analysis for platform curvature at the Parthenon See Chapter 3 and Figure 63. At the Parthenon, the long north flank of the stylobate has been preserved in a reasonable state of preservation to allow detailed study from the measurements of its curvature. GP Stevens produced seventeen coordinates documenting the incremental elevation of the stylobate to a maximum height of 0.103 m at the center of this 69.512 m long dimension.1 A minor complication in curvature analysis is that the two ends of the stylobate do not meet. flush with the Instead, the northwest corner of the temple increased by about 3 cm compared to the southwest. As discussed in Chapter 1, it is doubtful that this elevation and that of the southwest corner (5 cm) represent constructive inaccuracies or deliberate "refinements of refinements" intended to correct for an optically inferred convergence in the curved lines otherwise arising from the perspective of the Sacred Way (Figure 21). This will be the theoretical baseline under the camber with its slight diagonal elevation of about 3 cm over the distance of more than 69 m from east to west. Seybold resolves this inconsistency by analyzing the ordinates against the x-coordinates along a theoretically flat baseline corresponding to the easternmost point at 0,0. This method does not affect the results in any way, since ultimately the identification of the nature of the curvature (i.e., its optimal conic) is not affected by the fact that the slope of this baseline is less than 0.03°.2 The Seybold Nord calculation identifies the curvature of the stylobate as an ellipse with an exact measure of 2.141 m for its semi-vertical axis, that is, the radius of the smallest vertical dimension (as opposed to the largest horizontal) of the ellipse. If the Parthenon used the same method as Didyma to build the proposed curvature for Segesta (Figure 61), this measurement of 2,141 m would represent the radius of the working design. It remains to consider the importance of this radius in relation to the slope of the y-axis of the stylobate, which corresponds to the vertex of the semi-minor axis of the theoretical ellipse that defines the

curvature of the stylobate. This meaning is derived from the calculation of the chord length of the theoretical working drawing, from which the architect determined his ordinates when the architect viewed this central elevation (0.1205 m) in relation to the easternmost part of the line of base (Fig. 63).3 The rationale for The intention of this measure lies in the possibility that the architect intended that the highest level of the foundations further west (around 3 cm) was a "hyper-refinement"4 - a possibility that would call into question the meaning of the theory connecting the diagonal point with the lower northeast corner of the stylobate. The chord thus created shares an integer ratio of 2:3 to the radius, anticipating the identical ratio found in the proposed theoretical working design for the curvature at the Segesta flanks (Figure 64), see below: The height of 0.1205m subtracted the radius from 2.141m leaving a remainder of 2.02m along the y-axis. Using the radius as the hypotenuse, the length of half the chord a is calculated: a2 + 2.022 = 2.1412, resulting in a chord value of 0.711 m × 2 = 1.422 m So (1.422 m/2) × 3 = 2,133 m, a difference of -8 mm from 2,141 m, a tolerance of 0.6%. This result should be viewed with skepticism. As discussed in Chapter 3, such a possibility remains open as pure coincidence when Seybold's calculations are analysed. Therefore, I would only tentatively assume that the architect of the Parthenon (Iktinos?) could have proceeded in a very simple way by incorporating curvature in the flanks, similar to the following (see Figure 63): 1) Draw a baseline b (= length 1,422 m). 2) Make a 3:2 ratio to the baseline. b. 3) Center the compass on an arc that crosses the endpoints of the baseline. b. 4) Determine the westernmost point of the arc w, which corresponds to the highest level of the NW corner of the stylobate (about 3 cm). 5) Draw adjusted baseline (oblique) b' from the most easterly point to w; Bisect e and w with the a-axis. 6) Divide the drawing into equal sections (the twenty divisions in Figure 63 are hypothetical). 7) Divide the actual work into an equal number of equal sections. 8) Transfer the vertical measurements at 1:1 scale from the adjusted baseline b' to the arc in each of the subdivisions of the drawing with the same number

of steps defined in real work at a greater horizontal distance. These vertical limits fix the unequal curvature coordinates only along an extension of the major (horizontal) axis. 9) Repeat for the southern flank of the temple, adjusting to the westernmost point w at the top level (about 5 cm).

Notes Introduction: challenges of analysis and interpretation 1 Vitruvius wrote his ten books between 35 and 20 BC. see Fleury 1990: xvi-xxiv; Fleury 1994: 67-68; Howe and Rowland 1999: 1, 3; Wilson Jones 2000a: 34. After Brunelleschi's development of linear point perspective in the early fifteenth century, Alberti theorized it on geometric principles in his On Painting of about 1435; see Lindberg 1976:147-149. For a comparison of reduced-scale architectural drawing in the Renaissance and in antiquity, see Chapter 4 of this book. For architectural design in the Middle Ages and the Renaissance, see Ackerman 2002 and earlier studies cited. In a recent 2009 study of drawings by Bramante and others, Huppert argues that perspective played an important role in the design process for the new St. Peter's Basilica, despite the spelling privilege of Alberti and Raphael, whose rejection of perspective linearity in the worship of architecture tended to undermine the assumption that misled modern scholars about the system's limited use in the Renaissance outside of relief painting and sculpture. For Alberti's relevant testimony in his On Construction from about 1450, see Rykwert, Leach, and Tavenor 1988: 34. For Raphael, see Di Teodoro 1994: especially 123. 2 According to Suetonius's discussion of Julius Caesar in Gaul, Caesar concealed his intention to go to Rome to advance by pretending to be normal and supervising a plan, a form, of a gladiator school (Divina July 31). The context of the list clearly points to the normality of inspecting such plans. Essential for the purpose of this particular form is the future participle aedificaturus, and thus consistent with Cicero's metaphorical use in a letter to Caelius Rufus (Epistulae ad familiars 2.8) and again in Cicero Epistulae ad Quintum fratrem 2.5.3. See also number 24 of this chapter. However, strictly speaking, these passages do not necessarily refer to floor plans. The Vitruvian Greek term for a reduced plan is ichnographia, where its meaning is clear (De architectura 1.2.2). As indicated in connection with the passages in Suetonius and Cicero, we must understand the architectural drawings used in the planning process in the most general sense, whether they are plans, elevations, perspectives, sections, or whatever.

3 Cf. de Franciscis 1983: Plate I.3. See also the relatively unknown elevation of an arch found at Pola, where the circumferential intersections meet the axes of the buttresses: Gnirs 1915:37, figure 17; Haselberger 1997: Figure 7. As Haselberger also points out (#15), the modern scale bar in the original publication illustration is about 50 percent smaller. As an example of life-size (rather than to scale) drawings, this drawing survives because it was carved in stone, but Roman examples executed on ephemeral surfaces may have been common, as literary evidence suggests (see note above). For surviving full-size drawings from Hellenistic and Roman times executed at the site to work out details, see Wilson Jones 2000b: 56–57, 206–207. Senseney 2011 examines the design and planning process in Roman architecture. 4 See Wilson Jones 2000a:50, citing research on neurological and cognitive behavior related to drawing. I believe this view is contained in the earlier assessment of MacDonald 1982:5, 167-170. Taylor 2003 acknowledges the importance of Roman architectural design by dedicating much of Chapter 1 of his study of the Roman building process to the production of drawings. 5 See, for example, Ward-Perkins 1981: 100–101. 6 Of course, this suggestion does not contradict the longstanding idea that Roman builders gradually discovered the properties of opus caementicium in useful contexts such as warehouses and machine shops during the late republican period. Rather, it simply raises a motivation to use this material, as we find in projects as important as Domus Aurea, Domus Flavia, Pantheon, etc. 7. 7 On the functions of ancient architectural drawings as models, construction documentation, and votives, see Haselberger 1997: 83–89. 8 For a part, see Johnson 1994: 239–240, 338. For the development of the part from its early origins at the Ecole des Beaux-Arts, see Van Zanten 1977. A particularly intriguing study linking the architectural design traditions of Beaux-Arts in The part of American architects with design principles seen in ancient monuments (among those of later times) is Yegül 1991.

9 This text was initially serialized and appeared in 1897 as an integrated volume with around 2,000 (!) illustrations. 10 Ausonius (Mosella 306–309), Strabo (9.1.12, 9.12.16) and Pausanias (8.41.9) only mention Iktinos as the architect of the Parthenon, not the Callicrates mentioned by Plutarch (Pericles 13). The designer of the temple was therefore probably Iktinos; see Coulton 1984:43; Hurwit 1999: 166; wells 2001: 173; Korres 2001a: 340; Korres 2001b: 391; Schneider and Höcker 2001: 118; Barletta 2005: 95; Haselberger 2005: 148f. 10. For the sources and arguments of Iktinos, Kallikrates and Karpion (mentioned by Vitruvius De architectura 7.praef. 12 as Iktinos' co-author of a commentary on the Parthenon) see also Carpenter 1970; McCredie 1979; Svenson-Evers 1996: 157-236; Gruben 2001: 185–186; Korres 2001a, 2001b, 2001c; Barletta 2005: 88-95. 11 Lynch 1960. 12 MacDonald 1986; Favro 1993; Yegul 1994; Favro 1996. 13 Favro 1996. See also Favro 1993. For an interesting discussion of Ancient Roman models of virtual reality, representation, recreation, viewer experience, and visuality, see Favro 2006. For an experiential analysis of the street experience in Ephesus, see Yegül 1994 14 The identification of the Roman marble copy in the Museo Nazionale in Rome with the original by Myron is possible thanks to the precision of Luciano's description (Philopseudes 18). For a discussion of the copy and its possible relationship to the lost original, see Ridgeway 1970:84–85. 15 The work was probably an ex-voto dedicated to athletic competitions. For the most classical Hellenistic dating in stylistic and iconographic terms, see Kallipolitis 1972. For dating from the late 2nd to 1st century BCE. for pottery from the wreck, see Wunsch 1979:105–107. Hemmingway 2004: 83-114 speaks of a dating in the second half of the 2nd century BC. For a discussion see also Stewart 1990: 225 with figures 815-816. 16 However, the front view shown in Figure 30 from Hemmingway 2004 can be taken from a very high angle. The full effect is best developed in person at eye level. 17 Pollitt 1986: 149. See also Stewart 1990: 225 with illustrations 819–820 (copies in the Museo Nazionale, Rome and Louvre, Paris); Ridgway 1990: 329 with plate 166 (copy in Villa Borghese, Rome); Stewart 1996: 228-230; Stewart 2006: 175. The limitations of crowd control are currently seen

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the copy in the Villa Borghese does not allow the type of display described here. The specimens could be Hermaphroditus nobilis from the 2nd century BC. represent. Policles sculptor mentioned by Pliny (Natural History 34.80). Republic of Plato 346d, Gorgias 514b, Charmides 170c; Aristotle's Nicomachean Ethics 6.4.4. Architecture appears before Vitruvius in Cicero De officio 1.42.151. The Greek equivalent of architecture, ρχιτ κτ ν α, dates from the 2nd century AD. y is simply derivative; Liddel, Scott and Jones 1940: s.v. See also Greenhalgh 1974. For a discussion of the nature and role of architecture and the relevant primary sources, see Coulton 1977:15–29. In addition to Latin decoration (referring to practical considerations of tradition, function, and natural site), he mentions oikonomia (codes: oeconomia, the natural and financial resources necessary for work), taxis (order), diathesis (design or location). , eurythmy (pleasant shape) and symmetry (modular alignment). Lauter (1986: 30-31) speculates that Vitruvius is drawing here on fourth-century architectural theory. See Pollitt 1995. On this process see Bluemel 1969:34-43. Codices: ideae: Speciesdispositionis, quae graece dicuntur ideae, sunt hae: ichnographia, orthographia, scaenographia (De architectura 1.2.2). Haselberger 1997: 92-94; Senseney 2007: 560; Senseney 2009: 44-45; Senseney and Finn 2010: 88. Vitruvian's translation of ideali into species (from specio, "I see") preserves this connection to seeing. The same term appears in Aulus Gelio (Noctes Atticae 19.10.2-3). From the beginning, the Architettore la ragione e quasi Idea dello edificio nello animo suo cepe; Dipoi manufactures the house (secondo che e' può) tale, quale nel pensiero dispose. Chi negherà la case essere corpo? Et this essere very similar to the incorporated Idea dello artifice, to the cui similarity fù fatta? Certainly for a certain order integrate più tosto that for the similar material if it should be giudicare. Marsiglio Ficino, Sopra lo amore o ver convito di Platone (Florence 1544), or V, ch. 3-6:94-95. Original text cited from Panofsky 1968: 136–137, English translation by me. For the links between Neoplatonism and architectural design during the Renaissance, with particular emphasis on the Hypnerotomachia Poliphili published in Venice in 1499, see Moore 2010.

26 Heidegger 1967: 118-121. For a discussion see Wigley 1993: 37-41. 27 Diodorus Sikeliotes 1985–9. See Pollitt 1974:28-29; Bianchi-Bandinelli 1956. Elsewhere, in Filebo (56b-c), Plato directly addresses the art of value construction as a search whose measurement tools allow precision. For an analysis, see Chapter 1 of this book. 28 On this point of view see Davis 1979; Davis 1989: 106 and 225 n.1; and Bianchi 1997:37 44 f.38 for additional views and bibliography, including investigations into whether Plato may have visited Egypt. For an overview of Plato's guilt towards Egyptian culture, see Bernal 1987: 103-109. 29 See Mohr 2005:xv for comments on the recent "borification of Greek philosophy". 30 Nightingale 2004: 7–11, 111. On the difficulties of evaluating Plato's views on art, particularly through the lens of Nietzsche, see Janaway 1995: 190–191. 31 Nightingale 2004: 100-107, 113-115. 32 For a discussion of the relationship between Theoria and Thauma, see McEwen 1993: 20–25; Nightingale 2004: 253-268. 33 Nightingale 2004: 8–11, 99–100, 111. The partial views and perspectives of the human philosopher must be distinguished from the ideal philosopher, who does not exist in the mundane realm; see Nightingale 2004: 98–99. For the motivations of human potential, personal and political observations that led the philosopher to return to the cave, see Sheppard 2009: 119–124. 34 For an experimental analysis of Roman architecture, see MacDonald 1986; Yegul 1994; Favro 1996. For a detailed examination of the relationship between architecture and ritual at Didymaion (as well as at the Temple of the Oracle at Klaros) see Guichard 2005. 35 Pollitt 1986: 149. 36 Pollitt 1986: 149. This is one of several possible interpretations. offered by Pollitt. 37 For relevant passages from Plato and a detailed discussion of what follows, see Chapter 1 and the digression of this book. 38 On yin and yang, see J. Needleman's commentary in Feng and English 1989: xxii–xxviii. 39 See Needleman in Feng and Englisch 1989: x–xiv. 40 Socrates emphasizes that the idea of ​​good is the final experience of the journey (Republic 517b).

41 On theoroi and theoria, see Goldhill 2000: 166–167, 168. 42 Nightingale 2004: 40–93. 43 ti nd hip Daid l tin ll demirg graf o diff rndo g gram ni ka kpp pnim n i diagram (529e). 44 Roman Architectural Revolution was coined by Ward-Perkins 1981: 97-120, similar to MacDonald's New Architecture 1982: 167-183. Valuable recent studies of Roman concrete construction include Wilson Jones 2000a; cartoon 2003; Lancaster 2005. 45 Rowland 1999: 24. It is important to see also Thomas Howe's description of graphic principles shared among many disciplines in Howe and Rowland 1999: 144, Figure 6. 46 On this point see Wallace-Hadrill 2008: 147 47 Third Century: Critique of Heraclides 1.1. Roman Period: Strabo 9.1.16; Plutarch Pericles 13.4; Pausanias 1.24.5-7, 8.41.9; see Bart 2002:23–28. 48 For the range of emotional reactions of visitors to the Parthenon over the past centuries and decades, see Beard 2002: 1–12. For the reception of the Parthenon from antiquity to the present see Kondaratos 1994. Chapter One. The ideas of architecture 1 I distinguish between the process of architectural design and engineering, which worked from other points of view when a reduced-scale drawing was useful or even necessary, as in the 6th century Eupalinos tunnel on Samos. Here, would a reduced horizontal section of the mountain have helped to create a meeting point for the two northern and southern parts of the tunnel? see Kienast 1977, 1984, 1986/7, 1995, 2004. For arguments against small-scale drawings in the architectural design process, see Coulton 1977: 53–73, 1985. For detailed critiques of authors attempting to defend For the small-scale, geometric floor plans that underlie the Parthenon's design, see Korres 1994: 79–80. On the other hand, other scholars defend scale drawings during the Archaic and Classic periods; eg Petronotis 1972; Dinsmoor 1985. In his recent book on Propylaea, Dinsmoor (2003:4) explicitly suggests that Mnesicles should present a reduced plan in the planning process for his famous building 437-432. A contrary opinion has long been expressed, as in Bundgaard's depiction of Mnesicles as a

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An assembler of simple forms who "would not have projected his building in a modern way, that is, by drawing a precise geometric projection on a reduced scale" (Bundgaard 1957:91). Riemann 1959: 318-319 objected that Mnesicles was indeed an artist and must have made drawings given the sophistication of the design in the Propylaea. Vitruvius offers the only clear discussion of architectural design in the classical world; see Frézouls 1985. See in particular the critique of Riemann von Mertens 1984a: 175-176. For example, the width of the axis of the colonnade, stylobate or euthinterium and the height of the entablature including or not the cornice. Mertens 1984b: 137, 144-145. For a view that favors the importance of drawing in relation to such integral relationships in the process of designing buildings, complexes, and cities during the Hellenistic period, see Hoepfner 1984, which does not address the specific problem of reduced scale. These rational correspondences can already be found in the archaic temple of Hera I at Paestum; see Mertens 1993: 80–87, 2006: 143. For similar, though possibly more elaborate, numerical schemes in operation in the somewhat later Archaic Temple of Athena at Paestum, see Kayser 1958: 49–60; Holloway 1966:60-64, 1973:64-68; Nabers and Ford Wiltshire 1980. For a full analysis of the Temples of Segesta and Himera (Great Temple), the Temple of Athena at Syracuse, Temple A at Selinut, and the Temples of Luco-Lacinia and Concordia at Agrigento, see Mertens 1984a: 1–53, 65-116. For a detailed analysis of the design process for the temple at Segesta, see Mertens 1984a:45–50. Mertens (1984b: 145) comes to the conclusion that the planning approach of the fifth century, based on different internal relationships that do not have to correspond to each other, has given way to a new, simple and universal approach in the fourth century. According to Wilson Jones's (2001) study, this modular design approach was already effective in the fifth-century examples studied by Mertens. Wilson Jones 2001:679 and #24, referring to Claude Perrault's late 17th century theoretical distinction between schematic and coarse beauty, as discussed by Herrmann in 1973. Typical center-to-center distances between columns are 2.58 m; the width of the Euthynteria is 15.42 m; The commanded height or distance from the stylobate to the top of the horizontal cornice is 7.70 m 2.58 m × 3 = 7.74 m or 4 cm above the actual height. 15.42 m/2 = 7.71 m or 1 cm above the actual height. For

For measurements see Koch 1955. See also Dinsmoor 1941; Rieman 1960; Knell 1973; DeZwarte 1996; and De Waele 1998. For a more detailed discussion, see Wilson Jones 2001: 702. 9 Lawrence 1983: 230. 10 Stevens 1940: 4. 11 These views would have been blocked by both the Artemis Brauronia sanctuary and the Chalcothek, which may have come from the Age of Pericles; see Hurwitt 1999: 215–216, 2005: 13–14 with no. 10. 12 The ratio of the diameter of the lower Parthenon pillar (1.91 m) to the height (10.43 m) = 1:5, 46; Hephaestion (1.02 m and 5.71 m) = 1:5.60 m Height of the Parthenon column (10.43 m) at the height of the entablature without Geison (2.7 m) = 1:3.86; Hephaestion (5.71 m and 1.67 m) = 1:3.43. Measurements by Korres 1994 and Koch 1955. If the elongation of the columns of the Hephaisteion really reflects adjustments, this would be done in parallel with the addition of Mnesicles to the height of the western columns of the Propylaea to cope with the distortion effect created. tilting viewing angles on the final approach to the Acropolis; see Büsing 1984. Mnesikles' sensitivity to shaping perception through addition and subtraction anticipates some of Vitruvius's claims (as in De architectura 3.5.9, 6.2.2–5, 6.3.11 and some others). ; see in particular Busing 1984:29-32). See Haselberger 1999: 61–62 and footnote 233 for a more detailed discussion. See also Haselberger 2005:109–111 for a vivid visualization of the anxieties and debates that Mnesicles' innovations must have provoked for both Phidias and Iktinos. 13 The term "refinements" was introduced by Goodyear in 1912; see Haselberger 1999b: 22 with no. 78, 2005: no. 2. 14 This optical function is attested by Vitruvius De architectura 3.4.5, 6.2.2; Cicero Epistulae ad Atticum 2.4. In the Greek context, Philon Mechanikos On Artillery 50–51 anticipates this explanation of refinements such as optical corrections in the third century. For an excellent discussion of this topic, see Haselberger 1999: 56-60. For refinements, see Goodyear 1912; Dinsmoor 1950: 164-170; Robertson 1959: 115-118; Martin 1965:352-356; Coulton 1977: 108-113; Wycherley 1978: 110-111; Haselberger 1999a, 1999b; cusp 2000; Gruben 2001: 186-188; Bart 2002: 105-107; Hellman 2002: 185-191; Zambas 2002:127-134; Rocco 2003: 38-39; Haselberger 2005. 15 Cf. Korres 1999: especially 85–94. The term "ennoblement of an ennoblement" was


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coined by Wycherley 1978: 111, reflecting the intentionality of the elevations at the southwest and northwest corners first proposed by Choisy in 1865"), see Zambas 2002: 70 and Haselberger 2005: 145. The basis of this skepticism is the difference in the plane of the edge found also in the Hephaisteion and in the Temple of Aphaia in Aigina, equal to about 2 cm at 31¼ m and about 3 cm across 24 m respectively. For an analysis of the curvature of the Parthenon flank, these heights the levels are considered intentional deviations, see Chapter 3. According to Bundgaard (1974:18-24), the 'terrace' is strictly a dam built to contain dirt and debris.For discussion and dating see Korres 1997: 243; Hurwit 1999: 130, 132-135; 2005: 16-17.The adjustments at the northwest and southwest corners are approximately 3 cm and 5 cm, respectively.For measurements of curvature on the northern stylobate, with its maximum elevation at west of axis, see S tevens 1943: Figure 1. On the Parthenon, the measured height of the cornice rises only about 0.4 cm above what would otherwise form a theoretically perfect 4:9 rectangle: stylobate width = 30,880 m; Height from the top of the stylobate to the top of the geison = 13.728 m (30.880/9) × 4 = 13.724 m, a difference of only 0.4 cm. Dinsmoor measurements 1950. In the Hephaisteion the proportions are 1 cm and 4 cm below the theoretically perfect proportions of 1:2 and 1:3. For the term anagraph, see Coulton 1976a. For paradeigmata, see Jeppesen 1958; Pollitt 1974:204-215; Coulton 1975:94, 1977:54-58; and Hellman 1992. A tantalizing testimony of paradeigmata is found in a painted inscription on a monument from the Archaic period of the 6th century: the Eupolinos water tunnel, which is a section of tunnel more than five meters long with a painted inscription below it. Of the eye. enrolled level "Π Δ." However, there are difficulties related to the date of entry and how exactly the particular section of the tunnel is intended to function as a paradigm; see Kienast 2004 with the letter-by-letter photographic illustration on Plate 14 and the references cited above. An interesting study suggests how the anagraph process can be reversed as a model for architectural elements. take the scrolls


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the Ionic capital from the Temple of Athena Polias as a model, a modern machine can be assembled to duplicate its forms as a drawn model; Stevens 1956. Similar rules to those proposed by Stevens can be applied to vector-based computer-aided design software. These syngraphai are known from inscriptions and do not refer to drawings; see Coulton 1977: 54-55. Anyone wondering how a text can convey the specificity and clarity needed to create a building should consult the 340s syngraphai for the Arsenal at Piraeus by the architect Philo of Eleusis (IG2 1668). Engraved on a block of Hymettian marble, these syngraphai give precise instructions for the excavation and leveling of the site. the placement of the different parts of the foundation of the building and the leveling track; the masonry technique of the walls; and the exact number, size, and location of each architectural feature (columns, orthostats, jambs and lintels, cornices, windows, rafters and ridge beams, etc.). For an English translation with text and commentary see Ludlow 1882, with additional commentary in Marstrand 1922. See also the helpful reconstructed drawings in Davis 1930. Thanks to James Dengate for pointers. Coulton 1974:86, 1975:90-94, 1977:53, 55-56. Senseney 2007: 577. However, the exceptions are of great importance. See in particular the discussion of uniaxial protraction in fifth century temples in Chapter 3. Coulton 1974. See MacDonald 1986:250, who articulates the difference between Greek and Roman architecture in relation to the former's emphasis on qualities. 'sculptural and tectonic'. individual elements in contrast to his emphasis on an overall visual effect. I would propose this emphasis on the whole over the individual as the result of a design process focused on small-scale architectural drawing. The same is true of southern Italian examples, such as the "Temple of Hera II" at Paestum, which were created in an environment where numerical relationships clearly determined the relationships of architectural elements in both elevation and plan. Even Henri Labrouste's magnificent illustrations of this temple, executed in the 1820s in the Beaux-Arts tradition, fail to adequately convey the effect of its three-dimensional forms. For these drawings (published posthumously) see Labrouste 1877. Hahn 2001: 113. For the discovery of the chalk drawings see Kienast

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1985. Although this 1:1 chalk drawing technique was widely used in Greek architecture, its traces have, of course, largely disappeared. See Hahn 2001:112–113, based on Schneider 1996:27–48 with figures 14–16, 30–31. Hahn suggests that Peter Schneider, the excavator of the two buildings at Didyma, concluded that ichnography worked on these archaic buildings. However, Schneider makes no such statement. See, for example, Morris 1992: Figure 8a, where an Etruscan gold bull from 475–450 B.C. C. hired mercenaries under the command of Saite Psamtik in his quest to regain hegemony over Egypt, followed by the establishment of Naucratis as a permanent trading post for the Milesians in Egypt (Herodotus 2.151 -152). Evidence of scaled architectural drawings is well documented in the ancient Near Eastern world. For a recent and very comprehensive study examining the complexity involved in interpreting Egyptian architectural planning techniques, including surviving working drawings, see Rossi 2004. Evidence for the use of reduced floor plans in Mesopotamia is a little incised slab. known from baked clay in Berlin, representing a house in plan, with cuneiform inscriptions giving the dimensions of the rooms and the thickness of the walls (National Museums Berlin, Vorderasiens Museum, VAT 413). The seated statue from about 2150 B.C. C. also comes from Mesopotamia. in the Louvre with an incised drawing of an architectural plan on the lap of Gudea, the Neo-Sumerian ruler of Lagash; see Parrot, Tello 1948: 161, 163, plate 14. The image is appropriate for a chief who is known to have rebuilt some fifteen temples at Lagash, and surviving inscriptions tell of Gudea's dream in which the city's tutelary god, Ningirsu, appeared to express his wish that a temple be built; see Roux 1964: 165-167. If the folded hands in this and similar statues convey a gesture of piety, the work may show Gudea presenting the temple to the god, thus placing the function of architectural design in a votive context. For the gesture of folded hands as an expression of pan-Mesopotamian respect, see Cifarelli 1998. What we cannot know, however, is whether the image possibly represents Gudea offering the plan for approval to the god, who would thus take the place of drawing. in the context of planning. Definitely,

Gudea's design represents a complex group of rooms and thus belongs to a type of building that responds to a drawn plan, in contrast to the simple and prismatic temples and stoas of the Archaic and Classical Greek periods. For architectural drawings from the ancient Mediterranean world in general, including Near Eastern, Greek and Roman material, see Heisel 1993. 34 Vitruvius 1.2.2. It deals with iconographies, surveys and perspective drawings. 35 However, the absence of axial or orthogonal arrangements in groups of such buildings (as in the Propylaea, the Parthenon, and the Erechtheion on the Athenian Acropolis) should not in itself be taken as an indication of the absence of iconography. Rather, deliberate avoidance of these principles might characterize the decades-long, step-by-step process of designing old environments scaled down to flat scale. In Chapter 4 I discuss how in some settings ichnography could certainly have promoted the principles of axisymmetry and orthogonal arrangement, but this suggestion in no way implies that this result is necessary, that such principles depend on ichnography, or that none exist. The principles exclude iconography. at a specified location during a specified period of construction activity. 36 An excellent summary of the mixtures of architectural traditions, innovations in typology and planned proportions, and irregularities in the size of elements is Korres 1994: 78–91, who aptly characterizes the Parthenon as “the least dogmatic achievement of classical architecture” ( 79). Although my discussion here of the possible role of iconography in the Parthenon focuses on the stylobate, it is important to note Waddell's recent 2002 argument for the importance of krepis beyond the stylobate in Parthenon design. While Waddell does not believe that the drawings were a necessary part of the design process for the Parthenon (No. 34), his suggestion makes an interesting suggestion of how its floor plan may have determined the general spatial layout of the building. Based on the observation that the triglyphs are generally aligned with the joints of the krepis blocks, this argument speaks to the importance of krepis in determining the size of the triglyphs in fifth-century Doric temples, showing that the temples and all their Individual relationships had to be resolved as a whole.


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before construction begins, contrary to the notion that the Greek design process evolved through the various phases of construction. This explanation is consistent with an analysis that found that the vast majority of temples show a significant relationship between the proportion of number columns and the proportion of overall proportions on the short sides and long flanks of the crepis or stylobates. In the specific case of the Parthenon, the 8 × 17 columns give a ratio of 1:2.13. It is argued that this ratio deliberately refers to the 1:2.15 ratio of the overall dimensions of the krepis (33.68 m by 72.31 m). However, the difference between f/2.13 and 2.15 is more than 0.9%. With actual dimensions, this tolerance would correspond to 26 cm or 56 cm (!) on the short ends or flanks of the pancakes. This argument for the importance of pancakes in the design of the Parthenon is not in direct contradiction to other observable proportions, but the disorder of their related numbers should distinguish it from the more clearly supported proportional relationships in the stylobate. Therefore, we can safely set aside the suggested meaning of the Parthenon crepis and focus our attention on the stylobate and the functions it supports. See Korres 1994: 89. For arguments in favor of a hypothetical construction phase between the archaic Parthenon and that of Pericles, see Carpenter 1970: 44-45, 66-67; Bundgaard 1976: 48-53, 61-70. For a recent overview and literature sources on the relationship between the Archaic and Periclean Parthenons, see Barletta 2005:68-72. For the innovation of the pi-shaped colonnade, see Gruben 1966: 180–182; Gruben 2001: 199-202. For the ratio of column diameters at axial distances of 4:9: Stuart and Revett 1787:8; Penrose 1851: 8, 10, 78; W. W. Lloyd in Penrose 1888: 111-116. For the dimensions of the stylobate (30.88 × 69.5 m): Dinsmoor 1961; Gruben 1966: 167; Gruben 2001: 173–190; Barletta 2005: 72-88. For drawing surfaces available to early architects, see Coulton 1976: 52-53. See in particular the drawing for the calculation of the Entasis (approx. 1.23 × 1.82 m including the base) and the associated representation of the total height of the horizontal support of approximately 18 m long; Haselberger 1980: 191-203 and Figure 1. Other large format drawings of the Didymaion can be found in the working drawings of the pediment and cornice of the Didymaion.

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47 48 49

50 51 52


54 55

Naiskos, incised on the wall of the west plinth of the Adyton; Haselberger 1983: 98–104 and Figure 13. For a discussion and sources see Korres 1994: 84–86. For the complexity of the design of a Doric octastyle façade, see Winter 1980: 405–410. Korres 1994: 88-90. In contrast to the recent suggestion by Waddell 2002: 14-15 about the importance of the 1:2.13 ratio, recognition of the 4:9 stylobate ratio dates back to the eighteenth century, first mentioned by Stuart and Revett 1787:8 de contraction corner, see Coulton 1977:60–64; Gruben 2001: 42–43. For the exaggerated contraction of the Parthenon, see Gruben 2001: 179–180; Haselberger 2005: 124-125. Korres 1994: 90. See Pollitt 1974: 17–21; Pollitt 1995. Compare Janaway's observation of the longstanding notion of "the vision of art as the final route to a knowledge that Plato thought was reserved for philosophy: art as the revelation of eternal ideas or a 'higher reality'. '" (1995: 186). Codes: Idea (1.2.1-2). Haselberger 1997: 77, 92-94; Senseney 2007: 560; Senseney 2009: 44-45; Senseney and Finn 2010: 88. See introduction in this book. However, since the beginning of the 20th century there has been a convincing interpretation of Plato in Kantian language. See in particular Natorp 1903 and Stewart 1909. This passage begins with Plato's introduction to his well-known discussion of sofa construction (596e-597e), which clearly sets out his arguments for the relationship between intelligible ideas and sensual imitations. . The statement that no craftsman makes the idea does not entirely exclude another type of craftsman: the divine craftsman or Demiurge of Timaeus discussed below. For old usage, Liddel et al. 1940: sv Confusing the common and specifically Platonic use of the term can lead to unnecessary confusion, as in Janaway (1995: 112), who asks: 'Should we not be surprised that a humble craftsman can now catch a glimpse of the captured form? as a guiding principle? in the production of beds, when at the beginning of the republic there was much talk that only



58 59

60 61

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Do philosophers have access to forms? Janaway classifies Plato's claim as an anomaly. The following analysis is from Nabers and Ford Wiltshire 1980 and extends from Kayser 1958: 49-60; Holloway 1966: 60-64; Holloway 1973: 64-68. Interestingly, for a Doric order temple, the intermediate axes of the peripteron are uniform and correspond to eight Doric feet. In height, therefore, the long sides of the peripteron measure 96 feet axially, while the height from the stylobate to the top of the horizontal cornice measures 28 feet. The diagonal is 100 feet, resulting in a Pythagorean triangle where the hypotenuse has a whole number relationship to the sides. Also, in plan, the short and long sides of the peripteron measure 40 and 96 feet, respectively, axially. The diagonal is 104 feet, making a 5:12:13 triangle. Since the hypotenuse has an integer relation to the short and long sides, this again results in a Pythagorean triangle. Vitruvian 3.1.5. Porfirio Vita Plotini 20; Jamblichus Vita Pythagoreae 150; Auction 4 of Lucian Vitarum; Sextus Empiricus Adversus Mathematicos 7.95. See Pollitt 1974: 18, 421; Stewart 1978: 128-130; Nabers and Ford Wiltshire 1980: 280; McEwen 2003: 45-46. See Senseney 2007: 572-593. For a more detailed discussion, including the modular base of Temple A, see Chapter 4 of this book. More specifically, the graphic support controls the outer corners of the naos and the relationship of the antae of the pronaos to the outer rear corners of the temple (in Euthynteria). For a discussion of these terms and their implications for understanding Vitruvian iconography, see Chapter 4 of this book. Lauter (1986: 30-31) suggests just that: Vitruvius' discussion of taxis and diathesis is based on fourth-century architectural theories. Coulton 1977: 15-29. For an excellent and concise introductory discussion of the role of Pythagorean thought in the development of concepts of order in the Archaic and Classical periods and its influence on art, see Stewart 2008: 45–51. For number and truth see also Republic 525b.

67 See the passage on the "divided line" (Republic 510a-d), in which Socrates analyzes the place of geometric images in the search for real knowledge, grasped by the mind and not by the eyes. 68 On this passage see also Pollitt 1974:16-17 for a discussion of Plato's comments on beauty and the arts in Plato Statesman 284a-b. 69 Maguire 1965: 175-176. See also Janaway 1995: 69. 70 For Plato's concept of beauty or delicacy, see Brumbaugh 1976; Alexandrakis and Knoblock 1978; Janaway 1995: 58-79. 71 On the difficulty of determining whether παρ δ ιγμα refers here to a physical model (reduced scale?) or to a canon of ideal proportions, see Pollitt 1974:213–214. 72 On the interchangeability of beauty and truth in Plato, see Maguire 1965: 180-182. 73 Maguire 1964. 74 Maguire 1964; Maguire 1965: 171-172 with note 3. 75 Maguire 1965: 178-179. 76 For a catalog of Vision and Ideas citations, see Mohr 2005: 248–249. For a discussion see also Nehamas and Woodruff 1995: xlii–xliii. 77 Also “the eye of the soul” (τ τ ψ χ μμα, Republic 533d). 78 For an extensive discussion of the eyes and their relationship to the sun and the idea of ​​the good, see Nightingale 2004: 10–11, 112–113. 79 On the importance of sight for Plato see also Keuls 1978: 33-35. 80 Nightingale 2004: 88. 81 Nightingale 2004: 159. 82 In the symposium, the vision of the philosopher leads from the idea of ​​beauty to its birth to virtue (210e-212e); see Nightingale 2004: 84. For ideas see also Philebus 61e1. 83 On the relationship between Greek art and λ ια, see Irlenborn and Seubold 2006: 293–294. For the problematic relation of λ ια to the concepts of truth and Heideggerian “discovery”, see Helting 2006. One difficulty in bringing this discussion to an interpretation of Plato is the prominent Aristotelian character of the thought described by Heidegger. On the other hand, scholars generally use Aristotle to align themselves with Plato; for explicitly Aristotelian interpretations of Plato, see Johansen 2004: 5; Fine 2003: 41. For a critique, see Mohr 2005: xiv–xv. My own views are developed below.

84 85 86 87 88 89 90 91

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he does not sympathize with such interpretations. Rather, I find Plato and his cosmology useful as a possible reflection of the craft in the classical period, albeit modified to suit his own needs. Heidegger 1971: 159. For τ κτω as giving birth, see McEwen 1993: 55 and 146 n.6. This and all subsequent references to Philon's treatise cite the Marsden 1971 edition. See the analysis and sources cited in the excursus of this book. See Stewart 1990:20, 92; Haselberger 1999: 61 with no. 227. Mohr 2005: ix. God as π ιητ: Timaeus. 28a; Philebus 27a. God as δημι ργ: 28a, 29a, 41a, 42e, 68e, 69c; Philebus 27b. Benjamin 1968. See Derrida 1985. Plato's entire argument begins at Philebus 55e. For a discussion see Mohr 2005: 17. More specifically, the construction is 'scientific' in the sense that it is 'rather a techne', which means that for Plato his practices are based on a kind of knowledge that is measurable and measurable based on numbers. more than intuitive or empirical. For a consideration of how this reason for raising Plato's building might reflect the reduced status of poetry as an expression of being based on inspiration rather than precise measurement, see Janaway 1995: 16, 35, 174. In essence , for Plato, a true techne based on measurable knowledge, not just pleasure; Janaway 1995: 36-57. The architectural drawing material presented in Chapter 3 plays an important role in this question. For Plato's presentation of numbers in the Republic and Philebus, see Mohr 2005: 229–238. A full review can be found in the excursus accompanying this book. Soubrian 1969:ix–xi suggests that Vitruvius may have been the first writer to consider clocks under the heading of architecture, but this idea can hardly be affirmed since no extant comments on buildings designed by Vitruvius in 7.praef .12-were named. 17. McEwen 2003: 229–250 explains the emergence of a discourse on clocks in Vitruvius' work by referring to specifically Roman cultural concerns. While this explanation is compelling because it articulates how the gnome resonates in a Roman context, I see the clocks as being related for reasons I'll explore in the next chapter.

Architecture through probable links between astronomy and construction in a Greek cultural context. Chapter Two. Vision and spatial representation 1 Copernicus, De Revolutionibus 1.6. 2 For the diopter and its operations, see Lewis 2001: 51–108. 3 For the assumptions needed to explain Euclid's argument and additional comments, see Berggren and Thomas 1996: 54–55. 4 Berggren and Thomas 1996: 28–29. 5 For a general introduction to ancient Greek optical theory, shadow painting, and stage painting (including linear perspective), see Summers 2007: 16–39. 6 See Brownson 1981: 168. 7 White 1987: 249–258. 8 In attempting to distinguish between drawings for painting and architecture in the 15th century, Alberti emphasizes between the painter's use of shadows to convey an impression of depth and the architect's use of precise measurements (On Construction 2.1); see Rykwert et al. 1988: 34. 9 As Ackerman (2002: 64 n. 27) pointed out, it is not immediately clear why Vitruvius should have characterized linear perspective in terms of lines receding specifically toward the center of a circle, suggesting arbitrariness or artificiality. suggests construction. For possible confusion in our understanding of Alberti's pyramid as a necessarily rectilinear-based pyramid in contrast to his probable intention to continue the traditional notion of a vision cone, see Gadol 1969: 29–31; Lindberg 1976: 263–264 n.8 10 Previous studies emphasizing a disagreement between optics and linear perspective include Hauck 1897; Panofsky 1975. These arguments are superseded by Brownson 1981 on careful reading of Euclid's proofs. 11 For the distinction between Vitruvius' description of the scenery, which is comparable to that found in Campanian frescoes, and the significantly different Renaissance interpretation of the passage, see Thoenes 1993:566 12 Bär 1906:46–47. 13 See Lindberg 1976: 3–4. 14 Lindberg 1976: 13.

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Berggren and Thomas 1996: 28–29. For dating, see Mogenet 1950: 5–9. For a related discussion, see Evans 1998: 87–88. Timaeus 47a-b. On the relationship between human reason and the revolutions of the cosmos, Timaeus 90c-d; Plato's Laws 966e–967c. See Nightingale arguments 2004: 74-79. For the relationship between Plato's world soul and Parmenides, see Dicks 1970: 118. For the discovery of the circular motion of the planets, Plato Laws 821e–822a. Cornford's (1937: 73-74) insistence that Plato based his conception of the cosmos on three-dimensional objects such as an armillary sphere, an astrolabe, and a planetarium is anachronistic; see Dicks 1970:120-121. See Dicks 1970:108, 123, 152-153; Nightingale 2004. Eudoxo's phenomena are preserved in verse in the work of the same name by the didactic poet Aratos in the following century. Other works included his On Heaven and Mirrors; see Evans 1998: 75-76. For a detailed historical study with analysis of sources, see Dicks 1970: 151–189. Pollas 1970: 156-157. For Eudoxus, each division would simply be the twelfth part of a circle. The number 30° depends, of course, on the notion of a 360° circle, which Eudoxus did not use. For the possibility that Plato's emphasis on the twelve deities in heaven (Phaedrus 247a) reflects zodiacal imagery, see Dicks 1970:114-115. Pollas 1970: 156; Evans 1998: 75-76. Dicks 1970: 176 (emphasis on Dicks). In the earlier view of the retarding effect of philosophically based orbits, Dicks (n. 321) cites Africa 1968: 37: of the planets with their supposed circular motion. Dicks himself (1970: 169, 176) emphasizes this different approach to that of the Babylonians, as well as the Greek rather than Babylonian origin of the geometric conception of the universe, and the improbability that the zodiac represents Babylonian influence. For the concept of visuality, see Jay 1988: 16-17; Bryson 1988: 91-92. De Jong 1989. For an evaluation of De Jong's (1989) geometric analysis of Hermogenes' Temple of Dionysus at Teos (or more specifically its Roman restoration), see Senseney 2009:40–42.

28 On a related point, a recent attempt to see geometric proportions at work in an archaic Etruscan complex is inherently flawed. On my last visit in July 2007 it was still on display in graphic representation at the Museo Archeologico Nazionale in Palazzo Vitelleschi in Tarquinia. The monument in question is the "complesso sacrco-istituzionale" which contains the so-called Beta building, built in the 7th century BC. it started. The proposal finds a multiplication of √3 so that the shorter dimensions of the walls correspond to the more orthogonal dimensions in terms of length and width of the Beta Building itself, its surrounding wings and side walls, and the intermediate area in front of its façade; see the entries in the catalogs of two recent exhibitions: Invernizzi (2000), with more than 268 illustrations; Invernizzi (2001), with Figures 30–34 at 35. The main problems of this proposal are the selection of arbitrary points along incomplete foundations and the poor agreement between the real and theoretical dimensions. In particular, the proposed area in front of the Beta building does not correspond to any clear architectural feature to measure its shortest dimension. For the side areas, the width of approximately 9.20 m gives a length of 15.935 m multiplied by √3, a difference of more than 20 cm or 1.5% of the actual length of approximately 15.70 meters! That leaves us with the dimensions of the Beta building itself, whose longitudinal dimension of about 11.70 m is still more than 0.8% below the expected 11.605 m, since the product of √3 and the width of about 6, 70 m. This permission could be acceptable if this type of geometry was convincing at all in an archaic Etruscan complex. 29 For studies on the tholos see Charbonneaux 1925; Bouquet 1941: 121–127; Bouquet 1961: 287–298; Ito 2005: 63-133. Interesting, if not entirely convincing, is the recent analysis of his plan on the basis of three circumscribed pentagons; see Hoepfner 2000. 30 Horiuchi 2004: 136. 31 Horiuchi 2004. 32 Diameter of the stylobate (13.63 m/5) × 3 = 8.178 m, including a deviation of 1.8 cm from the actual diameter of 18.16 m from the cell walls. However, strictly speaking, the Vitruvian passage does not express the relationship in mathematical terms, such as a 3:5 ratio of diameters or the use of a compass, but simply the setting of the cell wall behind the edge by a distance of " about". . one fifth of the width of the

Stylobata: Cellae paries conlocetur cum recessu eius a stylobata circa partem latitudinis quintam. Geertman (1989) argues that circa could point to Vitruvian's reference not to 3/5 (or 0.6) exactly, but to the irrational ratio (2 − √2)/1 (or 0.586). Wilson Jones (2000a: 104) alternatively suggests that this may reflect Vitruvius's understanding that the precise thickness of the wall must be determined according to the nature of the project in question. However, this interpretation simply favors the inner diameter over the outer diameter of the cell; Although the thickness of the wall is variable, its location in relation to the stylobate edge remains unchanged, and there is no point in dismissing the stylobate edge as Vitruvius' primary consideration when he specifically says that was the case. I would suggest that both interpretations have a lot to do with "on" and that Vitruvius simply conveys a general rule consistent with late Republic tholoi, such as the one discussed below on the Tiber as well as Temple B in the "Sacred Kingdom". ". in Largo Argentina, whose original cell of approximately 9.3 m shared a 3:5 ratio with the stylobate of approximately 15.5 m For Temple B, see references in Marchetti-Longhi reports (1932, 1936, 1956 -1958). For excavations in the Area Sacra, see Marchetti-Longhi 1970–71. 33 On the tholos at Epidaurus, see Roux 1961; Burford 1969: 63-68, 114-116. 34 The most important archaeological publication on the tholos is Rakob and Heilmeyer 1973. For an almost certain identification of the building as the temple of Hercules Olivarius, see Coarelli 1988: 92–103, 180–204. For an alternative identification with the Mummius temple of Hercules Victor, see Ziolkowski 1988. However, as Coarelli points out, an inscription discovered near the tholos seems to read: [HERCVLES VICTOR COGNOMINATVS VVLG]O OLIVARIVS OPVS SCOPAE MINORIS, probably belonging to the cult of the temple statue. The date of the tholos is suggested by several parallels with the remains of the Temple of Mars in the Circus, commissioned by D. Iunius Brutus Callaicus after his victory over Callaeci in Spain in the 130s, and associated with the remains below the Church of S. Salvatore in Campo. The plan of this temple is now recognizable by its identification with the peripteral temple with an addit seen on Plate 37, Fragment 238 of the Severan Marble Plan; see Rodríguez-Almeida 1991-1992:3-26. Parallels to Tholos are the construction of Pentelic marble; lower column cut




38 39 40




Drums of the same block as the base, consisting of a single torus rather than the full Attic base common in early 1st-century Rome; the presence of a surrounding stepped crepidome instead of an axial staircase connected to a high podium, making these two temples the only known examples of a Greek character in republican Rome; and finally the use of the same Greek sculptor, Skopas the Younger, for the cult statues of both temples; see Gros 1973:151-153. For the attributions to the Greek architect Hermodoros, see Gros 1973: 158–160. Gros further interprets the combination of similarities and discrepancies between this tholos and Vitruvius's recommendations for round temples as evidence of a lost text written about the tholos that Vitruvius consulted, as opposed to the actual Italian workshop construction suggested by the Deviant Concept of the architect. Cell diameters, including wall thickness and total stylobate, averaged approximately 9.9075 µm and 16.517 µm, respectively. These figures give a ratio of 3:5 with a difference of only 0.1%. For these and other measurements, see Rakob and Heilmeyer 1973: Figure 1. This non-geometric understanding of the round temple is consistent with Wilson Jones' persuasive arguments that contradict Geertman's geometric interpretation of the late Republican tholos at Tivoli; Wilson Jones 2000a: 103-106. For Syngraphai, see Coulton 1977:54–55 and Chapter 1 of this book. For this argument about traditional temples, see Mertens 1984b:137, 144-145 and Chapter 1 of this book. As for the theater and other aspects of Vitruvius De Architectura Book 5, I regret not having access to a 2009 edition of Saliou before it went to press. For a discussion of questionable attempts to see the Vitruvian-prescribed Latin theater passage in later Roman theaters, see Sear 1990 and 2007: 27–29. Following Gros (1994:59–64) and McEwen (2003:326 n. 167), I quote this sentence from Harleian manuscript 2767 in the Loeb de Granger 1931 edition. Fensterbusch 1964:99–100. Gros 1994:64–65 supports the importance of the astrological reference, restoring the passage at 59 with n. 14 and Gros's comparison of Vitruvius' construction of the Latin theater with the contemporary astronomical diagrams of the Gemini of Rhodes in

44 45


47 48

49 50

65-66. As discussed in current and later chapters, the connection to astronomical diagrams refers to material much older than the Vitruvian Floruite. On Vitruvius and the training of architects, see Rowland 1999: 7–8. For general drawings, see Haselberger 1980, 1983, and 1985. For Haselberger's restoration of one of the rosettes, see 1991: especially 99-101 with figure 2. The earliest example I have found is Late Archaic, drawn on one of the pores. fragments bearing the small patterns of triglyphs and other features found in the building strata of the Temple of Aphaia at Aegina (ca. 500 BC) and on display in the site museum (Aegina inv. no. 78/157). However, we cannot expect such informal graphic exercises or steps in the design process to survive, and the rare examples do not begin to suggest the age and frequency of this form. For models of pores in Aegina, see Bankel 1993: 111 with Plate 35. See Bartman 1993: 64 for other examples of the reused lintel from the Badminton sarcophagus. Like other compass-based constructions, the six-petal rosette shape was eventually adopted for the geometric motifs of Roman floor mosaics, such as in the cabin of the surgeon's house in Rimini; see Gourevtich 2008:49, figure 1. Vitruvius describes the harmonic principles in 5.4.1–9 and refers to Aristoxenus's diagram and its specifications in 5.6.2–6. Construction of the Pompey complex as early as the 1950s is a certainty, probably beginning around the time of Pompey's triple triumph in '61; Sauron 1987. However, the exact date of the inauguration of the complex is disputed. According to Pliny (Natural History 8.20), the Templum Veneris Victricis of the complex was dedicated during Pompey's second consulate (55 BC), while Aulus Gelleio (Noctes Atticae 10.1. with Pompey's second consulate (52 BC) .) was devoted ). Hanson (1959: 43) prefers Pliny's testimony and credits the inauguration of Pompeianum 55, followed by Richardson 1992: 383–384 and P. Gros in LTUR 5, 35–38. However, Donald Strong (1968: 101) suggests a dedication date of 55 for the theater and 52 for the Temple of Venus Victrix. According to Boëthius (1978:205), the complex was “built during Pompey's second consulate in 55 BC. constructed. Y


52 53


dedicated in 52”, and the same dating is found in Sear (2007: 58). Coarelli (1997: 567-569) argues convincingly that the testimony of Gelleius on the dedication of an aedes Victoriae corresponds to the temple identified in the calendars only with the initial V, temple which joins that of Venus Victrix in the Pompeianum. as well as Honos, Virtus and Felicitas, all presumably at the apex of the cavea (Suetonius Divine Claudius 21.1); see the note below. Therefore, the Temple of Gelleius represents the fifth temple dedicated in 52 to Victory and is not synonymous with the Temple of Venus Victrix dedicated in 55. Tertullian (De spectaculis 10.5) cites Pompey’s intention that the combination of Veneris aedes and theatrum should be Veneris templum graduated with spectaculorum, and that the monument should be inaugurated as a temple instead of a theatre. According to Aulo Gelleio (Noctes Atticae 10.1.6-7), Tire also characterized the theater as the staircase to the temple. When describing the elaborate dedication ceremonies of the complex, Pliny (Natural History 8.7) never mentions the theater, but simply the dedication of the templum Veneris Victricis. In addition to the Temple of Venus Victrix, the Pompeianum included sanctuaries of Victory, Honos, Virtus and Felicitas. Given that the literary sources focus on the Temple of Venus as the reason for the existence of the complex, it could be said that these other shrines were less prominent. Its exact position within the complex is uncertain, but Suetonius (Divine Claudius 21.1) refers to the superior Aedes in his account of the reinitiation ceremonies under Claudius. Like the Temple of Venus, some of these probably appeared in the upper part of the cavea and were probably positioned radially from the orchestra. For the history of the monument and recent excavations, see Packer 2006 and 2007; Sear 2007: 57–61. On the location of the Curia in the Pompeianum: Suetonius Divine Julius 88, Divine Augustus 31; Dio Casio 44.16; Plutarch Brutus 14; Nikolaos de Demascus life of August 83. For fragments of Severan’s marble plan, see Rodriguez Almeida 1981: Plate 37. From Propertius (2.32.11–16) we know that the hypostyle room was a planted space in which there were trimmed bananas a uniform. height, fountains and statues; see Gleason 1990. Fragments of the marble plan include the central space of the Porticus Pompeianae





59 60 61 62 63 64

two long rectangles -perhaps pools of water- each of an actual size of about 23 x 100 m with a gutter about 12 m wide in the central axis with the Curia of Pompeii. Rectangles are defined by rows of small squares with a dot in each center. The excavations revealed the concrete foundation of one of these elements, which lacks the necessary strength of a monumental columnar foundation; Gianfrotta, Polia and Mazzacato 1968-1969. Coarelli (1997: 573) therefore identifies these elements as sculptures or sources of Propercio's testimony. According to Plutarch (Pompeius 42.4), Pompey's theater was specifically inspired by the Mytilene theater on Lesbos, a building of which we only know the approximate diameter of its orchestra (25 m) on the hillside; Sear 2007: 57. Roux (1961: 184-186) and von Gerkan (1961: 78-80) reject the attribution of Pausanias (or his sources) to the tholos and the theater, respectively. For a more smug view of the plausibility of at least having the same architect for both projects, see Winter 2006: 104. We can also consider that there is no reason to rule out that the design of the theater may have pre-dated its construction by several decades. Be that as it may, Käppel (1989) sees the geometry of theater design as the work of a single architect. The canon of the famous fifth-century Polykleitos is covered in Chapter 1 and its supporting digression. Akurgal 1973: 74. The relationship between buildings and theaters is perhaps best understood with reference to the restored model of the Pergamon Acropolis in the Pergamon Museum (National Museums, Berlin). For drama, see Radt, 1999: 257–262. The radial divisions of the Greek theater are built, therefore, by the ratio 1/√2 based on the square, as opposed to the ratio √3 of the triangular base of the Latin theater; See Gros 1994:332 for comparison with Euclid Elements 13, Proposition 12 at #19. An excellent study of Vitruvian Greek theater is Isler 1989, the results of which I summarize here. Liebe 1970: 152. Von Gerkan 1921: 116–118 with Plate XXIX.2. Isler 1989: 143-150. Isler 1989: 149. Isler 1989: 141.

65 Ferry 1960: 192-194. See also Trojani 1974–1975; Gros 1994: 63. 66 Goette 1995: 9-48. For a review of the literature on the Koilon, Skene, Bühnenhaus and Stoa, and the Temple of Dionysus, see Winter 2006: 99–100. 67 The theory that the first version of the Theater of Dionysus may have been rectilinear comes from Anti 1947. See also Anti and Polacco 1969: 130–159; Camp 2001: 145–146; Winter 2006: 97. This unlikely but likely suggestion was supported by Webster 1956: 6; Bieber 1956: 55. If correct, Anti's theory might suggest that the circular and radial form is not an obvious choice for the theater, but rather one created at a specific time and place for a specific reason, after which influence spread. As seen, for example, in the Minoan palace of Phaistos, as early as the Old Palace period (1900-1700), the seats for spectators to watch ritual performances were straight stairs. 68 For difficulties in separating Greek ritual and drama, see Csapo and Miller 2007. 69 See Thompson and Wycherly 1972: 127. 70 For this terminology in Sparta, see McEwen 1993: 58. 71 Liddel et al. 1940: sv 72 See Winter 1965: 104–105. 73 As Nightingale 2004: 50–52 and n.38 argues, this general meaning of the theory as seeing or observing is found in Herodotus 3.32, 4.46 and Thucydides 4.93.1 and is never used in relation to theatre. 74 On the character of the performances Stadtdionysien (dithyrambs, assemblies and processions of orators and chorêgoi) as a "political ritual" and not just as a dramatic art, see in particular Goldhill 2000: 162. Tragedy language (with instructive quotes in Sophokles Trachiniae 1079-1080 and Sophocles Oedipus Rex 1303–1305), see Goldhill 2000:174 and Zeitlin 1994. 75 See Nightingale 2004:3–7, 40–71. 76 Nightingale 2004: 72-138. Nightingale's argument is anticipated in Goldhill 2000:169-172. 77 I take this term for Plato's long and close association with Caine's 2007 art of drama. 78 See Winter 1965: 105. 79 Dunbar 1995: 1. 80 For speculations about its reception, see Dunbar 1995: 14.

81 For a consideration of this passage in the context of Vitruvius and classical urbanism in relation to the geometry of the winds, see Haselberger 1999c: 96. 82 For more examples see Dunbar 1995: 552. 83 For δα as a species or class, Liddel et al. Alabama. 1940: sv 84 This translation needs some explanation. On the authority of the manuscripts, Wycherly 1937:22, 23, 24 returns to κατ' γ ι and cites metrical motifs by shortening the penultimate of γ ιά before the final vowel, according to White 1912:§801. The benefit is to avoid the agricultural connotation of γ η in the sense of lot, privileging 'roads' in a way that better suits meton's purpose. In response, Dunbar (1995: 553–554) favors κατ' γ ιά as a corruption rather than the original. I agree with Dunbar's observation that even a city should begin as articulated lots rather than streets, avoiding the need to hold κατ' γ ιά. In other words, γη need not have a strictly agricultural connotation and, in the context of city planning, can be broadly understood as designated areas or sections. 85 See Wycherly 1937: 24–25 with Figure 1. 86 See Dunbar 1995: 555, with sources cited. 87 See Wycherly 1937: 25–27. 88 Wycherly 1937:26 successfully argues against the need to see Meton's lines as a reflection of the geometric problem of 'squaring the circle'. 89 Dunbar 2005: 556-557. 90 Our full understanding of the details of this process requires additional technical knowledge, which will be discussed with the introduction of additional material in chapter three below. 91 Dunbar 1995: 551. 92 Plutarch Nicias 13.7–8; Plutarch Alcibiades 17:5-6; Aelian Miscellaneous 13:12. 93 For a review of the idea that Meton represents Hippodamos, see Castagnoli 1971: 67–69. Von Gerkan (1923: 46-52) rejects the association of the Meton design with anything relevant to the question of surveying and orthogonal planning in the Hippodamous traditions. 94 See the discussion earlier in this chapter. 95 For a discussion see Dunbar 1995: 554–555. 96 Refutation of Hippolytus omnium haeresium 1.6.3-5; see McEwen 1993: 19 and 139 n.37, Hahn 2001: 177–218.

97 Evans 1998: 56. 98 Dicks 1971: 172. 99 See Dicks 1971: 84–85; Evans 1998: 39-40. 100 On the relationship between polis and cosmos in the Timaeus, see Adams 1997. The term demiurge for the divine craftsman with roots in deme and ergon can also designate both a civil servant and a craftsman; Adams 1997: 57. On the city as imitation of the cosmos in Statesman, Critias and Laws, see Voegelen 2000: 257–260. 101 For excavations from this first phase (Pnyx I) see Kourouniotes and Thompson 1932; Dinsmoor 1933. For the history of the Pnyx excavation see Calligas 1996. 102 Built 433/2 BC. BC, foundations 5.85 × 5.10 m; see Kourouniotes and Thompson 1932:207-211; Travlos 1971: 460; Dunbar 1995: 554-555. 103 Pnyx III dates from 404/3 BC. and increases the seating capacity to about 6,000; see Calligas 1996: 3. 104 See Beare 1906: 12, 44–47; Lindberg 1976:3-4, 13. 105 Goldhill 1998:106-107; Taplin 1999: 53. 106 Xenophon gives a clear description of voting procedures in the Ekklesia regarding an incident in 406 BC. 7-35); see Sennet 1994: 33. 107 The latest possible date for the invention of the 456 skenographia is given by Vitruvius' claim that Agatharkos built and commented on them when the late Aiskhylos 456 staged a tragedy (7.praef.11). For the alternative possibility that Agatharcus might have been working and writing in the 420s, as well as the drawbacks of this suggestion, particularly the impossibility of Agatharcus influencing the writings of Anaxagoras and Democritus on Vitruvian perspective, see Pollitt 1974: 244–245. For connections between Agatharcus, Anaxagoras, and Democritus, see Tanner 2006: 169–170. 108 For the application of less systematic approaches to linear perspective in vase painting before Agatharcus, see Richter 1970: 26–28. 109 If we insist on the evidence for a one-point linear perspective in vase painting, even this has been demonstrated on fourth-century Magna Graecian vases; see Christensen 1999.

110 vs. Richter 1970: 52-53. On this idea, see Beyen 1939; White 1987: 51; Keuls 1978: 65. 111 See Chapter 1. 112 For a discussion of this and subsequent passages in this section, see Halliwell 2000: 107–108; Senseney and Finn 2010. 113 Goldhill 2000: 174–175. 114 For drama pedagogy, see Goldhill 2000: especially 175. 115 For an examination of the relationship between Plato and drama, see Blondell 2002; Puchner 2010, especially 3-36. Chapter Three. The genesis of scale drawing and linear perspective 1 For whitewashed panels, see Orlandos and Travlos 1986: 167. Regarding papyri, surviving examples from the Middle and New Kingdoms do not exceed a height of about 45 cm, which would constitute a severe limitation for both reduced versions. -scale and drawing 1:1; see Coulton 1977: 53. 2 Haselberger 1980: 192; Haselberger 1991: 103. 3 Haselberger 1980; Haselberger 1983a; Haselberger 1983b; Haselberger 1991. 4 For dating, see Haselberger 1980: 205. 5 See Haselberger 2005: 104–107. Vitruvius 3.3.13 provides the Greek term éntasis. 6 Sixth-century examples: “Basilica” at Paestum (Mertens 1993:17), Olympieion at Athens (Korres 1999:98–101), and Artemision at Epheses (Hogarth 1908:272); see Haselberger 1999a: 25, 31; Haselberger 2005: 150 n.a. 28. 7 For an excellent discussion of the character, development, and historiography of ecstasy, see Haselberger 1999a: 24-32. For the related issue of realistic qualities in art as a concern of Plato, see Halliwell 2000: 102. 8 Haselberger 1999a: 28. 9 For the 0.294 – 0.296 m parapet foot, see Wilson Jones 2000b: 75 and 16 for the cited studies. 10 Cf. Haselberger 1980: 201 m.33a, where this achievement is attributed to Wolfram Koenigs. 11 Korres (1999: 101) proposes the use of the Parthenon procedure. 12 examples from the 6th century (Temple of Apollo at Corinth from ca. 550, Siphnian Treasury at Delphi from 525, reconstructed Temple of Athena Polias from

13 14 15



18 19



520–510, Temple of Aphaia at Aegina in the late 6th century) and bibliography see Haselberger 2005: 118–119. See Haselberger 1999a: 56-67 for a discussion of this age-old problem of "being and appearance." For the Athenian influence, see Mertens 1984a: 204-205. Mertens 1974; Mertens 1984a: 34–35 with Plate 33 and Supplement 21. These cross marks divide the fronts into eight 3,280–3,285 m sections, and thus eight 10-foot Doric sections across the full width of the 80-foot euntery. The flanks are divided into eighteen sections from 3,393 to 3,405 m. For the Doric foot used at Segesta, see Mertens 1984a: 44–45. For a full and well-documented discussion of "Scamilli odds' scholarly quest" from the Renaissance to the present, and a consideration of alternative explanations, see Haselberger 1999a: 36–56. Mertens 1974; Mertens 1984a: 34-35. The difference between a catenary and a parabola is negligible. Earlier, Oscar Broneer proposed the catenary as the basis for both the horizontal curvature and the entasis after examining the 4th-century South Stoa at Corinth. see Broneer 1949; Broneer 1954: 91-93. Mertens 1984a: 34–35 with Table 33. This proof is based on a computer-assisted quantitative evaluation of coordinate parameters, where ellipses were determined to be ideal conics describing curvature on both the Segesta and the Parthenon; see Seybold 1999. Haselberger and Seybold 1991; Haselberger 1999a: 52–54; Haselberger 1999b: 183-184. Dividing a string into eighteen equal segments can be accomplished relatively easily by dividing the string in half and using a pair of dividers to divide each half into three segments of three divisions each. "1 ½ meter round" based on Seybold's best fit curve in Haselberger and Seybold 1991: 179; Haselberger 1999b: 184 or 34 with figure 9.9. These figures should be considered approximate, as Haselberger assumed the ordinate values ​​to be 0.086 m, measured from a scale graph of Mertens 1984a: Supplement 21, Figure B (longitudinal 1:400 but vertical 1:2, the latter taking Haselberger measurements). The imprecision of the ordinates makes the calculation of the theoretical draft of work inaccurate.

22 23 24 25

26 27

28 29 30


Radio for purely mathematical reasons. Seybold (1999: 109-110) calculates a radius of about 0.916 m, but the large mean deviation requires a significant y-axis shift to a location about 0.45 m east of the center along euthyntheria, giving resulting in a revised radius of approximately 1,270 m for the theoretical design. However, shifting the y-axis in this way separates the cross marks from their intended function of producing a curvature with a maximum peak in the center. Then, given the imprecision of the ordinates, the calculation can serve to show that the ideal curvature fits an ellipse well, but the coordinates given by the crosses must be restored when reconstructing the radius of the working drawing. This last solution can be found in Haselberger 1999b: 184 n.34 with Figure 9.9. Haselberger 2005: 116. For the workflow of Entasis in the Parthenon, see Korres 1999: 94-101. See Mohr 2005: 14–15, 54–60 and Chapter 1 of this book. For Plato's terminology and example passages, see Mohr 2005: 248–249; Nehamas and Woodruff 1995: xlii-xliiii. See also Chapter 1 of this book. In a similar way (though not directly related to measure and proportion), Plato also criticizes "shadow painting" (skiagraphia): Republic 523b; Phaedo 69b; Theaetetus 208e; Parmenides 165c; Critias 107 c-d; see Bianchi-Bandinelli 1968; Pollitt 1974:1974:22-52, 217-224; Keules 1974; lawsuit 1975; Keuls 1978: 72-75, 118-119; Rouveret 1989: 24-26, 50-59. See Chapter 1 and the accompanying digression for discussions of these planning elements in Greek construction and relevant passages in Plato. See, for example, Plato's connection between philosophy and painting (Republic 500e-501c), in which philosophical rulers use a divine paradigm in the manner of painters; The architects are not mentioned here. Kirk and Rabe 1962: 248-249. See chapter one and the attached speech. For Plato's presentation of numbers in the Republic and Philebus, see Mohr 2005: 229–238. Architecture 3.5.14. As Haselberger (1983: 96 n. 21) discusses, the stripes here probably refer to fillets rather than carcasses. For linguistic considerations, see also Howe and Rowland 1999: 211. This consideration does not necessarily exclude further adaptations of the


33 34

35 36 37 38 39 40 41 42



Project. In addition to lines indicating "false starts" at end positions, such as at i', k, f, f', and f', there are creative deviations from the main geometry when working through the toral frames of Full Scale Base; see Haselberger 1980: 193-198 with figures 2 and 3. Both in the final plan and in the hypothetical scale drawing used to produce it, such changes can be made by erasing, chalking, and starting over. Other integral proportions in the plan include the 3:7 ratio in width and length of the euntinteria and the 3:8 ratio in width and length of the columnar axes; see Mertens 1984a:214, Table C. See Mertens 1984a:204; Haselberger 2005: 116. Gruben shows a similar method in the construction of capitals according to the principle of the circumscribed right triangle also in the archaic Artemision of Ephesus and in the late classic capitals of the Halicarnassus mausoleum; see Gruben 1963:126-129. Senseney 2007: 574-591. Galen De Placitis Hippocratis et Platonis 5.48 Philo Mechanikos on artillery 50.6. Haselberger 1980: 203–205 with supplement 1. Bergama Inv. #387; Haselberger 1980: Plate 89. Bergama Inv. In it. 2323. For second-century Stoic materials, see Shoe 1950: 351. Such as the radial pattern drawn in graphite over the ancient markings on the lower column and base (Delphi Inv. No. 8611) of the Corinthian columns on the inner wall of the Tholos Sekos from around 380 in the Sanctuary of Athena Pronaia in Delphi (Figure 38), restored in 2004. Thanks to Sotiris Raptopoulos of the Delphi Archaeological Museum for talking to me about this restoration. The fluted capital of the neighboring column continues to the ground. For comparison with another Roman example of this technique of making flutes on the curved outer surface, see the unfinished column shaft with its wavy markings in the central baths of Pompeii; Wilson Jones 1999: 248–249 with Figure 13.23. To Transfer Project Construction Markers to Visible Supports





49 50

on the site of Didyma, see Haselberger 1980: 204. Concentric radial patterns date back to the earliest vase decoration traditions of the Preminoan palace period (3200-2600), and are found most prominently on works such as the terracotta bottle with belly filled with a rosette of eight petals, circles, and radiating triangles from the Late Palace period 1400-1350 (Heraklion inv. no. 9039). From Hellenic traditions, such designs continue through the geometric period and beyond, finding monumental expression, for example, in the archaic period on the architectural acrotera at Olympia. From about 600-560, Ionic order stone columns feature twenty-four flutes, but other contemporary examples feature between 27 and 44 flutes. The canonical fillets, rather than the ridges, which characterize early Ionic capitals, first appear on Samos with the polycrat Heraion, initiated ca. 530; Barletta 2001: 98. As in Howe and Rowland 1999: 211 with the number 32 and 210 with the figure 53. Howe also suggests the possibility of starting with a hexagon and gradually dividing its six sides. It is not clear whether the craftsmen working on the columns (as opposed to the architects who made models for them) would have readily known of a method that constructs a precise hexagon. Also, the process would be cumbersome compared to the measures and procedures provided by something like the Didyma project, for example. A set of recognizable Doric capitals from various sites, dating to the late seventh to early sixth centuries, comprise our evidence for the rise of the Doric order during this period, spanning roughly two generations; see Barletta 2001: 54-63. In most of these examples, the stripes extend from the shaft to the neck. They often feature sixteen flutes instead of twenty, although this trend may have more to do with the smaller size of some specimens than with any chronological development, and indeed, as early as around 580-570, the capitals of the Temple of Apollo I at Aegina present twenty flutes. Barletta points to the link between the use of sixteen flutes and traditional Egyptian practices that may have been influential, as well as the ease of dividing a circle into sixteen parts. Gros 1976a: 688 with no. 4 and Figure 6. Let us take the hypothetical example of a 1 m diameter drum: From Figure 75.1 we find AB through AC − CO, with AC

found by the Pythagorean theorem. CO = 25 cm and AO = 50 cm. 252 + 502 = AC2, so AC = 55.902 cm. 55.902 cm − 25 cm = 30.902 cm = AB. AB/2 = 15.451 cm, corresponding to a difference of 2.57 mm at 15.708 cm and a cumulative difference of 5.18 cm (!) in circumference from 3.0902 m to 3.142 m or 1.65%. Therefore, this proposed geometric formula does not achieve the precision required to slot a column. 51 Ito 2004: 138 with nº 14. As in the previous note, we can test this proposal with a hypothetical drum of 1 m in diameter. 5/16 of the radius of 50 cm is 15.625 cm, compared to 15.708 cm, which is 1/20 of the circumference of 3.142 m. The circumference would be 3.125 m, which is a cumulative difference of 1.66 cm from the circumference of 3.142 m, or 0.55%. Therefore, this arithmetic formula is acceptable. 52 BergamaInv. N° 2323. 53 In addition, there are other possible techniques to perform these radial divisions on a curved ruler using compasses and rulers. For example, the shield of the Roman “Dying Gaul” marble copy from Pergamum or Delphi (220 BC) in the Capitoline Museums in Rome has a geometric diagram carved into the marble. Following Miriam Finckner's analysis, the design retains the construction process of a circumscribed pentagon. The termination of the strings in this drawing would produce a twenty-sided polygon which could demonstrate an ancient method of radial construction of such a figure, applicable to the current question of making a protractor for Doric flutes. Individual circles are broken and have inconsistent diameter and don't always line up with the lines they are meant to intersect. As has been reasonably explained, these imperfections probably result from transfer to the marble copy by means of a locator, followed by the application of a compass by a copyist who did not understand the intricacies of the geometry of the figure; see Finckner's comment in Coarelli 1995: 49. Coarelli (1995: 29-31) suggests that the main axes of this geometric form guided the composition of the sculptural group of dying and suicidal Gauls (Palazzo Altemps, Rome), who were together in the Circular Monument of Attalus I in the sanctuary. Coarelli (1995: 37-41) further argues that the same geometry may have determined the architectural composition of the sanctuary as a whole. See also Senseney 2009.

54 For alternative techniques, see Haselberger 1999a: 36–56. 55 Although among the earliest, these divisions along the perimeter of the column axes were probably not the first modules in Greek architecture likely to be identified with tiles. However, because the flutes were created as perimeter modules through design processes, they were arguably the most profound influence on the development of modularity in ichnography. For the role of terracotta tiles in developing modularity in Proto-Corinthian temple roofs dating back to the 7th-century "Old Temple" at Corith (as opposed to the 6th-century Temple of Apollo), see Sapirstein 2009 : 222–223 For fluting on Doric columns as early as the 7th and early 6th centuries, see Barletta 2001: 54-63. 56 Gros 1976a: 688. 57 See Chapter 2. 58 Hippolytus refutation omnium haeresium 1.6.3–5. See McEwen 1993: 9-40; Hahn 2001: 177-218. 59 The earliest surviving evidence of Anaximander's land as a column drum is Hippolytus, writing in the 3rd century AD. (Rebuttal omnium haeresium 1.6.3-5). 60 See, for example, Berryman 2009: 6–7. 61 Goldhill 2000: 174-175. 62 However, the method proposed by Rakob (1976: Exhibit 21) and endorsed by Gros (1976a: 94) for graphically producing this arrangement is faulty; see previous discussion. 63 For dates related to Hermogenes' works and career, see Kreeb 1990. For the sanctuary and its relationship to its broader architectural setting, see Humann, Kohte, and Watzinger 1904: 107–111, 130–141; Wycherley 1942:25-26; GE Bean in Stillwell 1976:554-557; Coulton 1976b: 253. Chapter four. Architectural Vision 1 Wallace-Hadrill 2008: 147. 2 Based on Rowland's translation in Howe and Rowland (1999: 47), with minor modifications. 3 For Leonardo's adaptations, see Wilson Jones 2000b: 81–84 with figure 8; Wesenberg 2001. McEwen (2003: 155–160) emphasizes in a more recent analysis that early modern images like Leonardo's were antecedents.

from the hand of Vitruvius, for whom the idea of ​​this reclining human form was nothing more than a textual description without accompanying illustration, such as the one used for the reference in book 3 to the construction of entasis (3.1.3), horizontal curvature (3.4 5) and an ion spiral (3.5.8). This lack of illustrations is unrelated to the present discussion, as my aim here is to analyze Vitruvius's description of his drawing in detail as to what it may contribute to our understanding of the traditions of Hellenistic iconography. McEwen links Vitruvius's discussion of geometry and solids with divinatory practices in this passage, an idea that is interesting but lacks direct support in Vitruvius' commentary. The analysis here maintains the specific role of the Vitruvian man as an analogy between temples and the human body in a discussion of temple design through the original Greek terminology that describes it. For illustrations in Vitruvius, see Gros 1988: 57–59; Haselberger 1989; Haselberger 1999: 28, 36; Haselberger 2005: 116. 4 McEwen 2003: 181–182 clearly links the Vitruvian man to iconography. 5 Loeb's translation slightly modified by H.L. Jones (1929: 89). Strabo here quotes Demetrios's account of the description of Attalus. 6 These philosophers include the founder of the Middle Academy, Arkesilaus of Pitane, Telekes of Phocaea, Evander of Phocaea, and Hegesinos of Pergamum; see Hansen 1971: 396. 7 For visuality, see Jay 1988: 16–17; Bryson 1988: 91-92; Elsner 2000 and 2007:xvii. 8 Rowland translation in Howe and Rowland 1999: 47. 9 Rowland translation in Howe and Rowland 1999: 47. 10 Rowland translation in Howe and Rowland 1999: 24, with minor changes. 11 For Vitruvius' emphasis on taxis and diathesis as active processes rather than complete products, see Scranton 1974: especially 496–497. 12 Compare with Plato's assertions that the beauty and value of a work depend on the measure and symmetry that its taxis define in its components: Filebo 64e, Republic 444e. Compare also taxis with Plato's κ κ σμ (Gorgias 506d); see Maguire 1964; Maguire 1965: 171-172 with nº 3. On the interchangeability of beauty and truth in Plato, see Maguire 1965: 180-182. 13 Translated from Rowland 1999: 24.

14 Based on Rowland's translation 999:25, with minor changes. 15 The Greek origins of this idea are underscored by Vitruvius' reference to the Greek term when speaking of quantity. 16 Architecture 1.2.3. For Plato, eurythmy (Republic 400e) allows art, along with music, dance, poetry, painting, and embroidery, to imitate ideas (Republic 400e-402b). 17 Aristophanes clarifies the distinction in the Clouds of him (638-641). In a passage of the comedy, Socrates fails to get Strepsiades to understand the concept of meter in its poetic sense rather than in its everyday sense. The humor of the scene derives from Socrates' later suggestion that Strepsiades should perhaps learn about rhythm, which is patently absurd to anyone who cannot understand meter. 18 McEwen 2003:157 affirms this view by contrasting Vitruvian 'how to' passages with the geometry underlying architectural features such as entasis and Ionic scrollwork. 19 Rowland translation, in Howe and Rowland 1999: 47. 20 McEwen 2003: 157. 21 For Vitruvian liberal arts education and training, see Howe in Roland 1999: 7–8, 14–17. For his mastery of Plato, see de Jong 1989: 101-102; Senseney 2007: 561-562. 22 Hermodorus is quoted in Cicero's De oratore 1.14.62; Priscian Institutiones grammaticae 8.17.4 (quoting Cornelius Nepos); Architecture Vitruvius 3.2.5. The classic study of Hermodorus and his influence on Vitruvius is Gros 1973. See also Gros 1976b. Recent studies summarizing current conclusions and hypotheses about Hermodoros include Müller 1989: 158–159; Anderson 1998, 17-19; Wilson Jones 2000b: 20. 23 This understanding is confirmed in several places in De architectura, as well as in Cicero (Epistulae ad Atticum 2.3). See Haselberger 1999: 56–58. 24 Again, more recently, see Haselberger 1999: 59-60 and earlier studies cited. 25 Inscription: von Gaertringen 1906: 143, no. 207. Coulton 1977 English translation: 70–71. 26 Architecture 3.2.6, 3.3.8, 4.3.1, 7.pref.12. For arguments against simply identifying the Hermogenes of the inscription with Vitruvian's Hermogenes, see von Gerkan 1929: 27–29. 27 As in the outlines of the footprints (Aiskhylos Libation Bearers 209); handle

28 29 30

31 32 33

34 35

36 37 38

and others 1940: s.v. In this regard, compare Plato's metaphorical use of the term (Republic 504d, 548d; Laws 737d); Lidel et al. 1940: sv See Coulton 1977: 71. The other inscription referring to hypographai is from Delos; cf. Dürrbach 1926: 41. Haselberger 1997: 92 discusses the function of building plans in antiquity as building symbols, "images" that can be found in dedications, ex-votos, and grave goods, and accordingly frames the Priene Hippograf inscription as a votive offering. Architecture 6.1.1. Rowland 1999: 56. De architecture 3.3.13; 4.4.2; 6.2.1; 6.3.11 For a discussion of the possibility of iconography in earlier temple designs, see Chapter 1. Despite his skepticism about iconography in Greek temple design, Coulton (1977: 71 n. 67) admits the possibility of its application in the temple of Athena. Polices in Priene. Coulton interprets Vitruvius' comments on the importance of architectural design and the beliefs of Pytheos (De architectura 1.1. . The original archaeological survey and temple restoration by Wiegand and Schrader (1904: 81-135 with figure 9) already recognized the base modular of the plan, based on a 6 ft 0.295 m module expressed by the pedestals. Important recent studies of the temple with important discoveries and observations on its design are from Koenigs (1983 and 1999). For an interesting suggestion on the role of Pytheos in the configuration of the wider urban context of Priene see Hoepfner and Schwandner 1994: 188-225 For additional considerations see Koenigs 1993 Gruben 2001: 416-423 For the relationship of such grids to drawing see Hoepfner 1984: esp 21-22 = 1.77 m or 6 ft by 0.295 m Wheelbase = 3.53 m Naos axes = 10.62 × 28.32 m Peripteral axes = 17.67 × 35.34 m Stylobate = 19.47 × 37.17m Krepis = 21 .21 × 38.91 m Koenigs 1 983: 165–68, with drawing by J.M. Misiakievicz in Figure 1 and photo in Figure 44.1. Haselberger 1980: 192; Haselberger 1991: 103. For the drawing in Didyma, see Haselberger 1983: 98–104 with figure 2 and plate 13. For the drawing in Rome, see Haselberger 1994.

39 For the uniqueness of Athena's temple grid during her time, see Martin 1987: 193–194; Koenigs 1999: 145. De Jong (1988) posits a connection between the Temple of Pytheos and the Temple of Hemithea at Kastabos from around 330 BCE. This connection is based on considerations of proportion and a proposed geometric construction for the column diameters related to the formula √3 − 1. This proposed relationship between the column diameters and this geometric design process is difficult to accept. Furthermore, the proportional relationships found in kastabos differ significantly from the Pytheos system, as they refer to the spaces between the walls and not to the axis of the walls. Therefore, the plan was probably drawn without a graphical component such as a grid or other geometry and probably unrelated to the reduced-scale drawing. For the Temple of Kastabos, see Cook and Plommer 1966. 40 For the now well-founded dating of Hermogenes' works and career, and a full account of the evidence, together with earlier arguments for a later dating, see Kreeb 1990. 41 For a mention of these lost writings by Pittheus and Hermogenes, see Vitruvius 1.1.12, 3.3.1, 7.1.12. 42 The Temple of Theos is a Roman restoration believed to reflect Hermogenes' original plan, although its precision is uncertain. For Roman fabrics, see Mustafa Uz 1990. For an evaluation of Jong Temple's (1989) geometric analysis, see Senseney 2009:40–42. 43 As suggested by Coulton 1977: 71. 44 Extended from 3.94 m to 5.25 m; Humann 1904: 39–49, with condition and restored plans in figures 29, 30. 45 Cf. Hoepfner 1990: 2–3. 46 Vitruvius 1.2.2. Rowland Translation 1999: 25. 47 As essentially stated by Onians 1979: 165-166. 48 See Koenigs 1983: 141–143; Koenigs 1984: 90. 49 This deviation is in addition to the larger center distance of 5.25 m along the central axis of the temple discussed above. See Humann 1904:39-49. 50 The horizontal curvature along the flanks of the three-layer crepe increases to about 4 cm. The curvature of the toicobato varies between 1.5 and 2.2 cm. The maximum deviation of the tip of the column is about 2 cm. There are very slight variations in the plans of the four corners of the Temple of Athena, but this is attributed to Koenigs (1983: 89–90, 1999: 143–145).

51 52

53 54 55

56 57 58 59 60 61



little mistakes. See Müller 1990: 21–34. See, for example, the progressive development of Bramante's iconography for Saint Peter in the years 1505-1509: Miller and Magnago Lampugnani 1994: no. Nos. 280, 283 and 288 (Uffizi 8A reverse and 3A right); Fromel 1994: 112. For the role of the grid in actual planning as opposed to polished 'presentation drawings' for clients (observable in a comparison between Bramante's Uffizi A 1 and the obverse of Uffizi A 20) see Huppert 2009: 161-162 on this distinction notably separated Filarete "disegno in grosso" from "disegnoproportionzionato", or a design with an overlapping lattice scaled to Braccia; Tigers 1963: 154-157. “It is imperative that the triglyphs are aligned with the central axes of the columns…” (Vitruvius 4.3.2). Rowland 1999: 57. Wilson Jones 2000b: 64-65; Wilson Jones 2001. Vitruvian 4.3.1. Rowland 1999: 57. For Vitruvius' close adherence to the Ionic design traditions espoused by Hermogenes, see Tomlinson 1989. For arguments against the popular notion of a decline of the Doric order in the Hellenistic period, see Tomlinson 1963. Senseney 2007. Vitruvius 3.3.1-8 followed by a discussion considering the heights of the columns along with their diameters and intervals. As essentially argued by Bundgaard 1957: especially 93-96, 113-114. For a discussion of paradeigmata and syngraphaphai and scholarly sources, see Chapter 1. For the sanctuary and its relationship to its broader architectural setting, see Humann, et al. 1904: 107-111, 130-141; Wycherley 1942:25-26; GE Bean in Stillwell 1976:554-557; Coulton 1976b: 253. Hoepfner 1990: 18. Elsewhere, the agora of Athens in the second century B.C. BC two new stoas on the south side and the stoa of Attalos on the east side, all oriented towards the cardinal points. Also, the sight lines of the Hephaisteion and the Metroon intersect at Bema in front of the Stoa of Attalos; see Onians 1979:165-166. Hoepfner 1997: 111–114, also with his Figure 1a, which suggests the possibility that Artemision and Agora may have been composed


65 66




by lines of sight. The main publication on the archeology of the Koan Asklepieion is Schazmann and Herzog 1932. For a full survey of Temple A and its dating, see Schazmann and Hergog 1932:3–13, Figs. 3-14 please. 1-6 For the history of the sanctuary see Sherwin-White 1978: 340-342, 345-346. For a detailed study of the ornament of Temple A, see Shoe 1950. For the design process underlying the form of Temple A, see Petit and de Waele 1998; Senseney 2007: 570. For an overview of shrine design as a whole, see Doxiadis 1972: 125–126 and reviews in Senseney 2007: 566. See Senseney 2007; Senseney 2010. Equal to 1,515 m The irregular spacing of the columns on the flanks introduces small imperfections in the intended uniform length of the column-supported pavers, which on the three surviving slabs on the western edge of the stylobate are only half a centimeter long. (1510-1515 m) vary. These variations in turn affect another small variation conserved in the two surviving axial spacings in the western pteron (3.034 and 3.05 m). To correct these irregularities, the excavators of the temple propose theoretical dimensions of 1,515 m for the plates and 3,050 m for the axial ones. Other imperfections include variations in the thickness of the east and west walls of the naos (1,028 and 1,016 m respectively) and distances from the east and west walls to the outer edge of the euthytery on each side (4,368 and 4,435 m respectively). . . This final asymmetry of 0.067 m on each side of the naos is clearly not intentional in the design of the temple. As I have shown elsewhere by three separate calculations, the three plausible corrections to this irregularity are too small to affect a proper geometric analysis of the temple plan; see Senseney 2007:588-593. While excavators suspect the cause of the irregularity was an earthquake that shook the entire ship, a small flaw in construction could be to blame. Total width of 18,142 m: 1,515 m × 12 = 18.18 m, a difference of 3.8 cm or 0.2%. Total length of 33.280 m: 1.515 m × 22 = 33.33 m, a difference of 5.0 cm or 0.15%. Small Circle: Radius 9.0615 m 1.515 m × 6 = 9.09 m, a difference of 2.85 cm or 0.3%. Largest Circle: Radius 15.1235 m 1.515 × 10 = 15.15, a difference of 2.65 cm or 0.2%. For the Temple of Athena Polias by Pytheos at Priene, see the discussion earlier in this chapter. See Chapter 3 and Appendix A.

70 For the dating of the sanctuary based on the inscription on its altar, see Coarelli 1982. For the following analysis and interpretation of the temple and its architect, see Almagro-Gorbea 1982; Jiménez 1982, especially 63–74; Almagro-Gorbea and Jiménez 1982. See also Coarelli 1987:11–21. 71 For the theatrical design, see Jiménez 1982: 61–63. 72 Almagro-Gorbea and Jiménez 1982: 121. 73 See Morricone 1950: 66–69, figures 13, 14, 16, 17. As in the case of the set of upper terraces of the Asklepieion, the marble and tuff architectural remains of the sanctuary of the port are scarce but enough remain for an archaeological reconstruction of the original plan. Built on an artificial platform about 2.5 m high (approx. 62.40 x 45 m in general plan), a complex of Doric porticos that open a central space with colonnades of approximately 33 x 38 m towards the sky. 74 On the excavations, see A. Viscogliosi in LTUR 1993–2005: 130–132. 75 On the influence of the Porticus Metelli in imperial forums, see Kyrieleis 1976. 76 Wilkinson 1977: 124–126. 77 For a linear perspective on Renaissance architectural design processes, see Huppert 2009. 78 Rykwert et al. 1988: 34. 79 Cf. the first lines of Book One of Alberti's On Painting of 1435-1436: 'To make my point clear in writing this short commentary on painting, I will first borrow from mathematicians the subjects with which my theme. it's about deals. .... In all these discussions I ask you not to consider me a mathematician but a painter who writes about these things. Mathematicians use only their minds to measure the shapes of things separate from all matter. Since we want the object to be seen, we use more reasonable wisdom." Translation by Spencer 1966: 43. 80 Marsiglio Ficino, Sopra lo amore or ver convito di Platone (Florence 1544), Or. v, chap. 3-6:94-95. See introduction in this book. 81 For a critique of Plato as a provocation for painters to use mimesis to express instrumental rather than intrinsic value (as opposed to the traditional interpretation that Plato rejects the value of painting and mimesis altogether), see Halliwell 2000 : especially 110. 82 For Manetti's work report and Brunelleschi's development and demonstration of linear perspective, see Wittkower 1953; Gadol 1969: 25-32; Lindberg 1976: 148-149; White 1987: 113-121.

83 See Halliwell 2000 and discussion in Chapter 2 of this book. 84 For a fascinating look at the role of drawing in the continuation of Michelangelo's work as an architect with his work as a painter and sculptor, see Brothers 2008. Excursus: Envisioning Cosmic Mechanism in Plato and Vitruvius 1 Kirk and Raven 1962: 248– 249. See also Pollitt 1974: 18. For an interpretation of the continuity between the Pythagorean traditions and Plato through a thematic connection between mathematics and warfare, see Onians 1999: 30-50. 2 Aristotle's Metaphysics 1092b8. For additional sources, see Kirk and Raven 1962:313–317. For the possible hint of the third dimension in Eurytus's flat representations, unlikely in my opinion, see Pollitt 1974:90 n.14.3 Thanks to Richard Mohr for pointing out the possible relevance of Plato's reference to Daedalus's diagrams to the issue. of architectural design. 4 Elsewhere, for Plato, moderation and adequacy constitute beauty and virtue in the work (Philebus 64e, Republic 444e). See previous discussion. 5 See Pollitt 1974:14–22. However, according to ancient sources, καν ν are rulers rather than instruments for measuring dimensions; see Coulton 1975: 90. On the importance of measure and balance particularly for fifth-century thought, see Politt 1972: 3-5. 6 This is the conclusion of Pollitt 1995:19–20. According to Galen (Kühn editions of De Temperamentis 1.566 and De Placitis Hippocratis et Platonis 5.48), Polykleitos titled both his treatise and his statue "Canon". 7 Plutarch mentions Callicrates together with Iktinos as the architects of the Parthenon (Pericles 13), while Ausonius (Mosella 306-309), Strabo (9.1.12 and 9.12.16) and Pausanias (8.41.9) only mention Iktinos. Therefore, I follow others in identifying Iktinos as the designer of the temple. See in this view Coulton 1984: 43; Hurwit 1999: 166; wells 2001: 173; Korres 2001a: 340; Korres 2001b: 391; Schneider and Höcker 2001: 118; Barletta 2005: 95; Haselberger 2005: 148 f.10 For sources and arguments on Iktinos, Kallikrates and Karpion see also Carpenter 1970; McCredie 1979; Svenson-Evers 1996: 157-236; Gruben 2001: 185–186; Korres 2001a, 2001b, 2001c; Barletta 2005: 88-95. 8 Lauter 1986: 27–28. For Vitruvius's confidence in the Greek theory, see Wallace-Hadrill 2008: 145–147.

9 For the sculptural career of Greek architects, see Pollitt 1995:20 and 12. 10 Pollitt 1995:20 postulated calculus; see Stewart 1978:126, together with a general description of the four possible classical meanings. 13 For this conclusion and the penetrating supporting analysis, see Philip 1990: 137–139. I strongly support the similar interpretation of Pollitt 1995: 21-22, which offers the architectural design process as a means of understanding the paramicron. Citing comments on Adyton de Didymaion's wall drawings (Haselberger 1985), intuitive deviations from the geometric basis of design characterize the very approach to intuitive fit. Haselberger 1999: 66-67 remains ambivalent about how much the statement might reflect the views of Polykleitos, focusing on its value for the views of 3rd-century Philo. 14 Studies interpreting a Pythagorean basis for Polykleitos' views include Raven 1951; Pollitt 1974:17-21; Butlers 1978; Pollitt 1995. 15 To be clear, I claim that, despite this discrepancy, the origins of this idea in Polykleitos's theory may well have been Pythagorean sources. Pollitt eloquently argues the possibility that the expression (τ) as used in the context of Aristotle (Metaphysics 1092b26) and Plato (Timaeus 68e) seems to demonstrate Pythagorean origins. However, I would like to emphasize that Polykleitos' possible deviation from the doctrine amounts to a deviation from Pythagorean philosophy. 16 Similarly, in 1955, Schulz analyzes Plutarch's description (Moralia 45c-d) of καιρ as an intuitive or accidental result rather than a product of numbers, and links this idea to the meaning of παρ μικρ ν, although this reading doesn't really work for the Plutarch passage; see von Steuben 1973: 50-53; Stewart 1978: 126. 17 As will become clear in Chapters 2 and 3, the reference here to painting may be an important clue to the nature of the type of diagram Plato is probably referring to. 18 However, for the distinction between appropriate and abusive mimesis (as opposed to inherently bad mimesis) in the field of painting, see Halliwell 2000.

19 The following account of the sculptural process of creation is from Bluemel 1969: 34-43. For the use and necessity of patterns and shapes in Greek marble sculpture in the Archaic and Classical periods, see also Palagin 2006: 243–244, 262–264. 20 The first explicit reference to Daedalus as an architect comes from the second-century Apollodorus (3.15.8,6), where the labyrinth is attributed to Daedalus. See Morris 1992: 190. However, as Morris points out, Apollodorus's description of the labyrinth seems to mirror that of Sophocles in the fifth century (Nauck, Fragment 34), which may have come from his lost drama Daedalus. Additionally, the black-figure painting on the 6th-century Rayet skyphos from Tanagra, Boeotia (Louvre MN 675) shows Adrianne with Theseus slaying the Minotaur, the rescued youths and maidens of Athens, and a belted figure (Cretan? ). in the air, which can only refer to Ikaros or Daedalus, linking Daedalus to the architectural setting of the labyrinth as early as the Archaic period; see Morris 1992: 190-191 and figures 10a-10d. For the probable identification of the winged figure with Icarus (and thus the connection between Daedalus and the labyrinth), see also Beazley 1927:222-223; Kokalakis 1983: 25. 21 As Keuls 1978: 124 pointed out, the term διάγραμμα generally refers to geometric figures. 22 Ovid (Metamorphoses 8.151–8.259) relates that Daedalus almost got lost in the labyrinth. 23 Two centuries later, Galen (ed. Kühn vol. 5, p. 68) repeats Vitruvius by including the gnomes under the heading “architecture”; see Soubiran 1969:x. 24 For this view of Plato as a watchmaker, see Mohr 2005: 14–15, 54–60. For additional discussion and references, see Additional Discussion. 25 Despite the differences between Vitruvius and Aristotelian teleology, here an influence of Aristotle's Mechanica may emanate. See Fleury 1993:324; Berryman 2009: 130-131. 26 … e rerum natura sumserunt exempla et ea imitantes inducti rebus divinis commodes vitae perfecterunt explicaciones (De architectura 10.1.4). 27 For the connection between the Vitruvian passage and Plato's divine craftsman, see McEwen 2003: 236. For the influential role of Timaeus during the late Republic, cited by McEwen, see Griffin 1994: 709. See also Loeb's edition for Granger's Vituvius 1934: 277 Note 6.

28 Cf. Mohr 2005: 18, 56–57, as well as 56 note 12 for an important discussion of Brague 1982: 66. The astronomical views on which Plato bases his dialogue are attributable to Plato and the astronomers influenced by him, among which Timaeus is probably only a fictitious speaker. see Dicks 1970: 116. 29 For an excellent discussion of Anaximander, see McEwen 1993: 9-40. Testimony of Anaximander's constructions: Diogenes Laertius 2.1–2. See Kirk, Raven, and Schofield 1983:100; McEwen 1993: 17-18. Testimony of Anaximander's writings in the 10th century: Suda s.v. Anaximander. See Kirk, Raven, and Schofield 1983:101; McEwen 1993: 18-19. Anaximander's own prose is recorded in fragment B1 of Aristotle's fifth-century commentary on Simplicio's Physics. This fragment contains between seventeen and fifty-six words from Anaximander himself. For a review and summary of previous studies on the B1 fragment, see McEwen 1993: 10-17. 30 Refutation of Hippolytus omnium haeresium 1.6.3–5. Anaximander's earth pillar form accepts McEwen 1993: 19 and Hahn 2001: 117–218. For the difficulties in interpreting Anaximander's model, see Berryman 2009: 32–33. 31 McEwen 1993: 9-40. Hahn 2001 largely addresses this thesis. 32 Architecture 7.praef.12–17. In the preface to his fourth book, Vitruvius notes that earlier architectural writers "left behind rules and volumes that were not arranged in order but were treated as if they were stray particles" (Rowland, in Howe and Rowland 1999). :54). McEwen 2003:236 correctly points out that, unlike these earlier writings, Vitruvius seems to have been the first to produce a complete corpus on architecture. However, this probability should in no way indicate that Vitruvius did not rely on an existing tradition of cosmological models scattered in earlier architectural commentary. 33 This connection between cloth and stars is repeated in Euripides (Helena 1096). 34 See McEwen 1993: 9, 18, 23–25. 35 Hippolytus 1.6.3. 36 Republic 529d).

37 Compare Shorey's Loeb translation, which inserts 'vehicles' to convey Plato's argument: 'but we must admit that they are very far from the truth, motions, d between themselves and as vehicles for the things they carry and contain. '. 38 Morris 1992: 169. 39 The question of the relative speeds of the astral bodies is particularly important for Plato. Compare Plato Gorgias 451c identifying the logos of astronomy. 40 For Leonardo's machine drawings, see Galluzzi 1996; Marinoni 1996; Scaglia 1996 41 For Paconius' vehicle, Vitruvius gives the dimensions of the base of the Apollo statue as 12 feet by 8 feet and 6 feet high, surrounded by 2-digit-wide slats and with wheels about 15 feet in diameter. . In addition to the metric specification of beams with a 4-digit width in Metagenes's machine, the specification of equal length in column and crossbeams is a surviving reflection of settings such as B. equal and double in Vitruvius's account of vehicles. Archaic at Ephesus from racks on Khersiphron's machine. For Metagenes' machine, Vitruvius's account gives a diameter of about 12 feet for the wheels, although he does not retain the important height and width dimensions of the architrave blocks (about 6 feet?) to imitate that vehicle. Appendix A. Analysis of design dimensions for Entasis at Didyma 1 Haselberger 1980: 199. 2 Haselberger 1980: 200. Appendix C. Hypothetical working design analysis for platform curvature at Parthenon 1 See Stevens 1943: Figure 1 These seventeen digits correspond to the column locations, rather than proving ancient coordinates in the form of crosses found at Segesta. 2 Seybold 1999: 108, where all y-coordinates in Table 4.2 are given at 111 with respect to the first x-coordinate in the 0-plane. See Stevens 1943: Figure

1.3 For calculation purposes, this height on the y-axis can be taken as the maximum height of the curvature, although technically the maximum height of 0.1215 m appears to the west of the y-axis at the highest level of the northwest corner. The negligible difference between these two measurements is irrelevant to the following calculation. In identifying the vertical distance from the center elevation to the level of the northeast stylobate as a significant measurement, I have omitted the alternative measurement of 0.103 m from the center of the diagonal baseline connecting the two corners of the sloped stylobate to a point 0, 0175 m on the northeast corner; see Stevens 1943: 137, Figure 1. 4 To quote the term used by Korres 1999: 92.

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Absolute Beauty Index 51, 52 Building 181 Aelian 212 Agatharkos 63, 98, 135, 172, 213 Agrigento 199 Temple of Concordia 199 Temple of Luco Lacinia 199 Aigina 209 Temple of Aphaia 209, 214 Aiskhylos 135, Leon 213 Alberti 1, Leon 213 Alberti 1 Battista 1 169. , 170 , 172, 195, 206, 222 alethea See Truth Alkmaion of Croton 63 Allegory of the cave See Plato Anagraphs 32, 112, 200 Analemma 99, 181 Analytical geometry 45 Anaxagoras 172, 213 Anaximander 94, 136, 175 , 183– 185, 224 Appearance 51, 55, 151 Areostyle system of proportions 160 Architects 1 Greek 8, 26, 32, 48–50, 58, 68, 80, 157, 158, 166, 167, 175, 183, 197, 209, 222, 223 medieval 169 renaissance 1, 143, 169, 170, 172, 195 roman 58, 83, 142, 153 architectural design, post-ancient 195 medieval 157, 195 modern 2, 3, 36, 44 renaissance 157, 195 architectural form 1 Greek 1, 39 , 49, 151 Rom 1, 39

Baroque 21 Byzantine 39 Mannerist 21 Architecture = Architecture 3, 8, 9, 17, 18, 25, 54, 58, 59, 64, 65, 68, 93, 99, 100, 138, 139, 141, 142, 145, 173 , 175, 197 Aristophanes 23, 61, 103 Aves 88, 95, 132, 161 Aristotle See Aristotle, Works of Aristotle, Works of Sensu 8 63 437b23-438a5 63 Mechanica 224 Methaphys 176 1080b16 176 109 3.6nachus 4 197 6.4.5 178 politics 8 1282a3 8 Aristoxenus 209 arithmetic 52, 111, 143–145, 160, 176 armillary spheres 207 astrolabes 2077 astronomical charts 2, 8 6, 2015, 645, 77, 98, 1, 7, 9 173 Astronomy 14, 17–19, 54, 56, 63, 93, 94, 113, 173, 179, 207, 225 Athens 184 Athens 3 Academy 144 Agora 28, 95, 221 Acropolis 3, 39 City of Dionysia 87, 88, 134 , 211

Erecteión 21, 202 Hefestión 28, 34, 200, 221 Calcoteca 29, 199 Colono Agoraios 28 Orquesta 86, 95, 134 Parthenon 3, 21, 29, 39, 44, 48, 54, 69, 70, 108, 109, 115, 134; 116, 129, 143, 156, 157, 196, 199, 200, 202, 203 Pnyx 29, 95, 132, 134, 212 Propylaia Heiligtum der Artemis Brauronia 199 Stoa des Attalos 221 Tempel der Athene 2 Polias Tempel des Dionysos 1345 Tempel des Zeus Olympier 213 Theater des Dionysos 21, 23, 86, 88, 95, 132, 134 Attalidendynastie 144 Attalos I. von Pergamon 144, 146, 149 Augustus 19 Aulo Gelleius 209, 210 Ausonius 2 1396, Autolykos de Pitane metrie 64 16sen2sym , 169 Schönheit 14, 17, 48, 51–53, 55, 56, 66, 112, 118, 179, 187 Benjamin, Walter 55, 56 Benthem, Jeremy 98 Geburt 53 Bramante, Donato 1 Broneer, 187; Oscar 214 Brunelleschi, Philip 3, 169, 170, 172, 195, 222 Brutus Callaicus, D. Junius 208 Caesar, Julius 195 Canon See capiteis Polykleitos 32, 34 Zimmerei 169 Chronometrie 60, 94, 181, 186

Cicero 195, 197, 200 circular buildings see buildings with radial design cities see fluted columns urban planning 118, 133, 164, 173, 216, 217 columns 34 adequacy 10, 11, 51, 112, 113, 118, 131–132, 143, 146 , 150, 151, 153, 164 compass and ruler 23, 27, 32, 33, 36, 49, 59, 64, 68, 69, 74, 75, 80, 92, 106, 108, 112, 114, 121 . , 165 corner triglyph problem 42 correction 14, 51–53, 151 Cosmic diagrams See astronomical diagrams Cosmic mechanism 57–58, 60–67, 75–77, 99, 137–138, 173–174, 185–187 Cosmology 55, 64 , 110 , 220 Curved ruler 23, 89, 92, 132 Decoration (Latin term) 197 Delos 83 Theater 83 Delphi 69 Siphnian Treasury 214 Tholos, sanctuary of Athena Pronaia 69, 134, 141, 215 Demiurge See Plato Democracy 95 Democritus 94, 172 , 213

Derrida, Jacques 55 Descartes, René 12 Descartes 14 Diastylic system of proportions 160 Diathesis 36, 47, 49, 50, 58, 142, 146–149, 151, 157, 158, 162, 164, 167, 197, 204 Didyma 14 Anta Building 34 East Building 34 Temple of Apollo 12, 14 Archaic Capitals 116, 117 Plants on the Walls of Adyton 40, 74, 104, 110, 114, 203 Diodorus Sikeliotes 10, 197 Dioptra 61, 206 Disposition See Diathesis Divided Line Ver Plato Divine Craftsman See Plato Doric Order 39, 156–158, 162, 203, 204 Dunbar, Nan 89 Agonizing Gaul (statue) 216 Durero, Albrecht 172 Egyptian architectural planning 34, 196, 201 Egyptian architectural planning 202 Egyptian art 10 height of drawing 1, 8, 17, 36, 38, 48, 89, 100, 101, 142, 146, 195 plans 198 entablature 34 entasis 34, 106, 113, 114 Ephesus 64, 196 215 Epidaurus 70 Theater 80 Tholos 70, 134 , 208 Eros 16 Essence 52 , 55 , 151 Etruscan planning 207 , 208

Euclid 60, 63, 98, 136, 137, 206, 211 Eudoxys of Cnidus 66, 67, 69, 74, 137, 207 Euctemon 94 Eupalinos 198 Euripides 224 Eurythmy 36, 52, 100, 142, 146, 1471, 1949 Eurytus 176, 222 Eustyle System of proportions 160 Ferri, Silvio 86 Ficino, Marsiglio 9, 170, 222 Subtlety See Beauty Fletcher, Railing 3 Florence 170 Baptistery 170, 172 Gabii 164, 167 Sanctuary of Juno 164, 167, 221 Galen 54 God 52 , 55 , 150, 205 Goldhill, Simon 102 Greek sculpture 4, 8 models and casts 8 Greek theater See Floor plans of Vitruvius (Marcus Vitruvius Pollio) See Ichnography (floor plans) Gruben, Gottfried 116 Gudea 202 Hadid, Zaha 3 Halicarnassus 215 Mausoleum 215 Haselberger, Lothar 23, 74, 104, 108, 110, 114, 116, 128, 150 Heidegger, Martin 10, 53, 54, 205

Criticisms of Heracles 198 Hermodorus of Salamis 166–168, 209 Hermogenes 48, 49, 133, 150, 151, 153, 162, 164, 183, 202, 207 Hero of Alexandria 89 Herodotus 211 Hymera 199 Great Temple of, 199 Miletus Hippodamus 66; 16, 16,16, 16,16 Hippolytus 217, 224 horse and jockey (of Cape Artemision) 5, 6, 14 hippograph 150, 151, 154 Iamblichus 204 ichnography (plans) 26, 34–44, 54–55, 58–58; 59, 65, 68, 71–74 , 79–86, 91, 100, 132–134, 143, 150–151, 153–168, 172–173, 175 Idea (Greek term) 8, 9, 22, 44, 175; 45, 47, 49, 50, 51 behold beauty Plato Idea of ​​the Good See Plato Idealism 9, 14, 15, 44, 45, 144, 149, 150, 151, 153, 170, 175, 176, 204 Ikaros 185 Iktinos 3, 39, 177, 183, 196, 200 223 Iliad 184 Intelligence See Reason Ionic Order 156, 157, 158, 161 Callicrates 177, 196, 223 Kant, Immanuel 10, 44, 204 Karpion 177, 196 Kastabos Hemithea 219 Temple of 219 Temple of Khersiphron 64, 136, 138, 18 85.17 – 18 Cnidus 82 tea base 82, 84 knowledge 53, 55, 56, 176, 205 Corinthians 214

South Stoa 214 Temple of Apollo 214 Kos 45, 48 Sanctuary of Aphrodite 167, 222 Stoa, Agora 119, 129, 132 Temple A, Asklepieion 45, 48–50, 69, 74, 117, 162, 164, 172, 221 Kouroi ( Statues) 5 Labrouste, Henri 201 Latin theater See Vitruvius (Marcus Vitruvius Pollio) Leonardo da Vinci 143, 172, 186, 217, 225 Light 52, 53 Linear perspective (Skenographia) 1, 4, 8, 17, 36, 62, 63 , 89, 98 –101, 105, 134, 142, 146, 169, 172, 175, 195, 206 Lobachevsky, Nikolai Ivanovich 61 Lucian 196 Lynch, Kevin 4 machines See Magnesia-on-the-Maeander 36, 161 Agora 161 machines bar 51 52, 110, 112, 222 Mechanics 58, 181–182, 184–187 Mertens, Dieter 108 Mesopotamian architecture 202 Metagenes 64, 138, 177, 183–185 Athenian methon 88, 94–96, 132, 135 metrological analysis 26, 204 Michael Angel Buonarroti 172 Mimesis 44, 52, 53, 55, 56, 179, 182 spirit See the why of Minoan art form 215, 216

Mirror analogy see Plato Mnesikles 199, 200 models see paradeigmata modern architecture 3 modules 114, 162, 164, 204, 217 music theory 18, 52, 56, 176, 179 Myron 4, 196 Diskobolos 4, 196 Mytilene 210 theater 242.10 nature , 144, 148, 149, 181 Naucratis 202 Neoplatonism 9, 170 Nero 173 Nietzsche, Friedrich 11 Nightingale, Andrea Wilson 11 noumena 44 nous See base number 26, 45, 47, 49, 50, 54–56, 70, 110, 111 , 113, 114 , 116, 118, 142–147, 160, 162, 164, 176, 177, 179, 182, 183, 186, 199 oikonomia 100, 197 Olympia 120 Temple of Hera 120 optical theory, Greek 4, 17, 199; 18 , 22, 62, 96, 136, 150, 206 or 142, 144, 146, 148, 162, 175 ordinatio See taxi orreries 207 Ovid 224 Paestum 45 Temple of Athena 45, 48, 49, 176, 199 Temple of Hera I. 199 , 213 Temple of Hera II 201 Painting view Linear perspective (Skenographia) Palmanova, Italy 95

Panoptic 98 Paradigm 10, 16, 17, 32, 34, 51, 54–56, 58, 61, 101, 112, 119, 160, 176, 179, 180, 182, 186, 200, 201, 223 Parapegmata 94 Parmenides 207 Part 2, 196 pattern 34 Pausanias 80, 196, 198, 210, 223 Pergamum 80, 119, 129, 132, 144 theater 80 Perrault, Claude 199 Persian war 39 Phaistos 211 Phidias 8, 39, 200 Philo Mechanikos , 1 5 , 150 , 156, 178, 200, 205, 215 Philo of Eleusis 201 Greek philosophy 4, 22, 55, 68, 149, 150, 186 Piero della Francesca 172 The Piraeus 201 Arsenal 201 Place de l'Etoile, Paris 95 Plato See also Plato , Works of the Cave Allegory 10–12, 16 Split line 102, 176, 205 Divine craftsman 17, 52, 98, 99, 181, 204 Idea of ​​beauty 53 Idea of ​​good 44, 52, 53, 205 Mirror analogy 170 , 171, 222 World Soul 207 Plato, works of 8 Charmides 197 170c 197 Critias 95, 212 115c 95 Gorgias 197 451c 225

506e 52 514b 197 Leis 95, 212 778c 95 821e–822a. 207 966E-967C 207 Meno 51 82b-86c 51, 151 Phaedrus 14 247a 207 250b-D 53 251a 14 251b 53, 63 252d 14 254b 14 254b-C 14 Philebus 51 27a 205 27b 205 51C 51 51C--D 51, 52 55E 55E 51 C 51 51C-DE 51, 52 555E 205 56b–c 54, 56, 112, 129, 170, 179, 181 64e 51, 222 República 10, 23, 56, 58, 60, 65 346d 197 402b 52 444d 52 444e 52, 0202 53, 102, 111 500e–501c 101 507b 52 507c 52 507e–508a 53 508b 53, 63

508e 44, 53, 102 509d - 511e 102, 176 510a - d 205 514–517 10 517b - c 44, 102 517c 53 519b 16, 52 524c 52, 183 525C 52, 111 525e 1, 111 525E B 65 527B 11, 14, 51, 65, 102, 111 529a 14 529b 65, 111 529c - E 17, 57, 99 529c - 530a 184 529c - 530c 65 529d 179, 182, 225 329e, 180 530d - 531c 56, 113 531c 56 56 56 56 56 53 53d 16d 16d 16d 16d 16d 16d 16d 16d - 531c 56, 113 531c 56 56 56 53d 16d 16d 16d 16d 16d 16d 16d 16d 16d 16d 16d 16d 16., 205 540a 101 596b 17, 44, 45, 52 596d - 170 596e -597E 204 597E 179 598B - 170 SOFISTA 10 235D 10, 51, 597e. , 55, 112, 170 235e 10, 56, 177 Estadista 8, 212 259e 50 261c 8 284a–b 205

Symposium 9, 88 210e–212e 205 Timaeus 16, 56, 58, 60, 65, 204 19b–c 101 27d–28a 102, 113 28a 205 28c–29a 17, 102, 186 38c 182 45b 45.25 53 53 b 176, 182, 207 48e–49a 66, 102, 113 53e–54a 51, 52 68e 223 90c–d 207 Pliny the Elder 197, 209 Plutarch 196, 198, 2210, 23 (Pula,179 Croatia) 195 page drawing at 195 Pollitt Amphitheater, J.J. 10, 14, 15 Polykleitos 54, 80, 117, 138, 142, 151, 156, 177, 179, 211, 223 Polyklei 197 Pompeii 215 Central Baths 215 Porphyry 204 Porticos See Stoas Poseidonia See Paestum Posotes 36 Priene 36, 16 Athena 49, 50, 150, 153, 154, 156–158, 160, 219 Propertius 210 Proportion 26–28, 31, 143 protractor See curve ruler

Psamtik 202 pseudodipterous Typus 156 Ptolemäus 68, 137 Proportionssystem Pyknostil 160 Pythagoras 45 Pythagoräer 45, 50, 51, 55, 56, 63, 117, 151, 152, 176, 177, 179, 204, 223,6, 47, 1 49, 133, 153, 162, 172, 183 radiale Verlängerung 118, 132 radiale projizierte Gebäude 69, 73, 78, 93, 105, 138, 145, 172 Raffael (Raffaello Sanzio da Urbino) 195 Raptopoulos, Sotiriso 515 2. 15 razáso. . 78 Circus Flamminius 23, 78 Curia Pompeii 79, 210 Domus Aurea 172, 173 Forum Augustum 79 Forum Julius 23 Trajansforum 168 Kaiserliche Foren 23, 168 Trajansmärkte 79 Neue St. Peter 195 Palazzo Pio Righetti 79 Pantheon 59, 145, 173 Porticus Metelli 167 Porticus Pompeianae 79, 209, 210 Region Prati 95 Rundtempel 71, 141, 208 Tempel B, Largo Argentina

Temple of Mars in the circus 208 Temple of Venus Victrix 79, 209, 210 Theater of Marcellus 82 Theater of Pompey 78 Round buildings See radially projecting buildings Rule of the second pillar 41 Sacrificial ritual 134 Samos 34, 177, 198 Temple D, Heraion 34 Temple of Hera 177 Tunnel of Eupalinos 198 Sardis 119, 120 Temple of Artemis 119, 120 Scamilli inpares 108 Science, Greek 68 Sculpture, Greek 51, 54–56, 143, 179, 180, 223 Sectional drawing 195 Vision See Vision Segesta 27 Without finish Temple 27, 114 , 116, 129, 199 Selinut 199 Temple A 199 Seybold, Hans 109, 110, 114 Uniaxial protraction 104, 108, 116, 118 six-petalled rosette 74, 75, 128 Skopas the Younger 208 sleeping hermaphrodite (sculpture ) 6, 8, 14, 197 Socrates 14, 16, 51, 103, 205 Sophocles 135, 211 soul 9, 10, 12, 52, 53, 205 Sparta 86 kind (Latin term) see idea (Greek term) show see vision spirituality 9–11, 16 Stevens, G.P. Stoas 33, 164, 167, 169, 221

Strabo 143, 144, 149, 196, 198, 223 Suetonius 173, 195, 210 Suicide Gaul (Statue) 217 ​​52, 205 Sundials See Analemic Symmetry See Syngraphai of Commensuration 32, 34, 38, 160, 181, 201 19. Syracuse Temple of Athena 199 system of proportions 160 Tao Te Ching 15, 16 Tarquinia 207 shrine complex 207, 208 taxis 36, 47, 49, 50, 52, 58, 100, 142, 146–149, 151, 157, 158, 162, 208; 164 , 167, 197, 204 techne 129, 205 teleion 45 teleology 224 temples 33 Theos 207 temple of Dionysus 150, 207 Tertullian 210 tetraktys 45, 47, 49 thauma 12 theatai 97, 102, 213,97 theater the , 98 Greek culture at 4 Theodore 177, 183 Theodore of Phocea 69, 134 Theoria 16, 17, 19, 87, 88, 95, 98, 102, 103, 138, 198 Theoroi 61, 87, 88, 97, 103 Thucydides 55, 56 Triglyphs 32, 56; 34 , 203, 220 truth 50 , 51 , 53–55 , 176 , 205 t-square 35 , 36 , 74

Urban Armor 4 City Planning 61, 78, 161, 162 Van der Rohe, Mies 3 Vehicles 186, 187, 225 Virtual Reality 196 Vision 3, 5-7, 9, 16, 17, 19, 38, 52-53, 56, 60–65, 87–88, 96–103, 108, 111, 134–139, 172, 182–183, 185 Vitruvian Man See Vitruvian (Marcus Vitruvius Pollio) Vitruvian (Marcus Vitruvius Pollio) 1, 10, 11, 18 , 22 , 44, 45, 49, 58, 97, 98, 100, 101, 142, 146, 151, 183, 195, 199 Greek theater 82, 86, 94, 95, 136, 172, 211 Latin theater 73, 75 , 80 , 94, 95 The Vitruvian man 23, 143, 144, 146, 151, 170, 218 Of architecture 8 10.1.2 146 1.1.2–4 36 1.1.4 111, 146 1.2.1–4 146 1.2 .3–4 147 1.2.4 146–148 1.3.1 181 3. 5.14 106, 215 3.1.1–4 142 3.1.2 149 3.1.3 143 3.1.4 149 3.1.5 204 3.3.13 106 3.3.1 –8 34 3.4.5 108, 150, 200 3.5.14 121

3.5.9 200 3.praef.2 143 4.3.2 42, 220 4.8.2 70, 134 5.6.1–4 73 5.7.1–2 82, 92 5.9.4 108 6.1.1 151 6.2.2 150, 200 6.2.2–5 200 6.3.11 200 7th pref. 12 69, 133, 196 7th pref.11 135, 172 7th pref.12–17 224 9.1.2–3 64 9.1.3–5 74 9.1.5 75, 95 1.2.1–9 8 1.2. 2 8.°, 9 , 143, 146–148, 197, 202 1.1.16 18 Wallace-Hadrill, Andrew 142 War 222 Weaving 184 White, John 62 Bleached Drawing Boards (λ χωμα) 40, 104 Wilson Jones, Mark 27 World Soul See Plato Xenophon 213 Yegül , Fikret 119 Zodiac Signs 66, 68, 75, 77, 136


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