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The semiotics of the Vitruvian city*

ALEXANDROS PH. LAGOPOULOS

Abstract The Vitruvian city in De architectura is founded on an eight-part windrose. Vitruvius describes how to trace the direction of the eight winds astronomically and relates the tracing of the street network of the city to the form of the windrose, but his description is extremely laconic. Ever since the Renaissance, the customary interpretation is that the form of the proposed city is radial-concentric, a pattern that exercised a powerful influence on the Renaissance model city. However, a close reading of the text shows that the Vitruvian city has a grid plan, following the general Roman model. But the city also has a symbolic significance for Vitruvius. This has escaped the great majority of scholars, because they isolate Vitruvius’s description of the city’s form and orientation from its immediate context, that is, his general urban discourse, and further from the entirety of his work. Interpretation has focused on the practical dimension of the city, since Vitruvius pleads for a salubrious city with a specific relation to the direction of the winds. But the winds have strong connotations, since they correspond to one of the four cosmic elements, and these elements are such an essential part of Vitruvian planning theory that they even define the site to be chosen for a city. I argue that the Vitruvian windrose, in addition to being an aesthetic device, is an abridged cosmogram. The windrose is founded on numbers considered perfect, and the city emerges from the perfect geometrical figure of the circle and the marked qualities of the square. Since the geometrical complex of the windrose-cum-city almost coincides with Vitruvius’s geometry of the human body, the city also has an anthropomorphic connotation. Keywords:

Vitruvius; semiotics of space; history of urban planning; symbolic anthropology.

Semiotica 175–1/4 (2009), 193–251 DOI 10.1515/semi.2009.047

0037–1998/09/0175–0193 6 Walter de Gruyter

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There is no doubt that Vitruvius’s De architectura represents the actual zero point of Western architectural theory.1 There is also no doubt that his text could not have been written without the earlier written works of a whole series of Greek architects, which have unfortunately all been lost. Vitruvius makes repeated references to their names and uses their ideas, although he seems to know their works from secondary sources (Fleury 1990: XLI); he also makes abundant use of Greek technical terminology. In his discussion of urban planning, he proposes a city founded on salubrity, to be achieved through the avoidance of the prevailing winds, and it is the salubrity factor that until recently has attracted the almost exclusive interest of the scholars who have commented upon the Vitruvian city. I shall try to show, however, that this factor, of the order of the material, cannot for Vitruvius be detached from two other crucial components, this time belonging to the order of the symbolic: the cosmic and the aesthetic codes. Vitruvius was a professional architect who lived in the first century BC. It is generally assumed that he dedicated his work to Octavian, at a date that is uncertain. Philippe Fleury, applying the concept of stratification to the redaction of the text, observes that, on the basis of the textual evidence, the work is composed of di¤erent, not clearly distinguishable but interpenetrating strata, and concludes that the text was written over a period of time from the end of the Republic to the very beginning of the Empire (the date of this transition is 31 BC), more specifically between 35 and 25 BC According to Fleury, the dedication of the book is not prior to 29 BC and most likely took place in 25 BC or immediately after (Fleury 1990: XVI–XXIV). However, even if De architectura springs from Greek architectural knowledge, that is, even if Vitruvius may be considered as the end of the line of late Classical and Hellenistic theoretical thought on architecture, transmitted to him through vulgarized manuals (Gros 1988: 50, 53), his book is not a copy of a Greek model. Vitruvius states that he is the first to have written an integrated work on architecture, and Fleury subscribes to his view and the originality of the book; it seems that the Greek authors were limited to the writing of case studies. Vitruvius, using the logic of classification, attempts to integrate in a single work the whole of the architectural knowledge of his times, the Classical and Hellenistic Greek tradition as well as the Roman and Italian. This synthesis is, according to Fleury, of a specific nature: he believes that Vitruvius primarily addresses the public or private architectural client, o¤ering a knowledge that, though it would not elevate the client to the level of a professional archi-

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tect, nevertheless would allow him to understand the operations of the architect and even on occasion to guide the workers. For Fleury, though the book is original, its conception of architecture is inscribed within the Hellenistic current of architectural thought; the architect — the architectus of the beginnings of the Empire — is simultaneously what we today mean by an architect, and also a civil engineer and a military engineer, with a domain of competence including matters such as hydraulics, horology (related to astronomy), and mechanics. The book is thus also related to a certain Latin tradition of technical literature (Fleury 1990: XXXI– XXXIX; see also Callebat and Fleury 1986: XIII–XVI).

2.

The theory of architecture in De architectura

De architectura is a normative work, composed of ten books. Architectural theory is treated with respect to volumes, plans, and architectural elements in Books I, III, IV, V, and VI, and with respect to building materials and colors in Books II and VII. The core of architectural theory is discussed in chapters II and III of Book I. Urban planning theory is included in chapters IV to VII of the same Book, chapter VI being the pivotal chapter. It is this chapter around which the present discussion will revolve, but in order to illuminate the meaning of the Vitruvian city it is necessary to draw on clues from the whole of De architectura. A key to this understanding is chapter II of Book I, presenting the fundamental concepts of architecture, to which I shall now turn. Vitruvius (I.I: 1, 3, 15, and 16) opens his analysis of architecture by stating that the knowledge of the architect derives from practice ( fabrica) and theory (ratiocinatio). We conclude that the aim of architectural practice is the realization of the architectural project, which falls exclusively within the competence of the architect; the same holds for every other art. The project is one of the two aspects found in all arts and especially in architecture, namely ‘‘that which is signified’’ (quod significatur). The other aspect involves theory, which is common to all arts, and it is ‘‘that which signifies’’ (quod significat). Theory is a demonstration according to systematic principles, allowing the interpretation of practical realizations (for a discussion of these concepts and their later interpretations, see Rykwert and Hui 1998: 1330–1333). Carl Watzinger (1909: 205, 207) relates this di¤erentiation to rhetoric and the distinction between form and content. However, semiotically speaking, quod significatur refers to the project and quod significat is the metalanguage used for this project (cf. Gros 1982: 670). Still in the context of semiotics, we may consider

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the second term as comparable to ‘‘competence’’ and the first as comparable to ‘‘performance.’’ Continuing, Vitruvius writes in chapter II that architecture consists of ordering (ordinatio — he refers to the Greek word t´axiv), disposition (dis, positio — he refers to di´ayesiv), eurythmia (he transliterates euruym´ia), symmetria (from summetr´ , ia), appropriateness (decor) and distribution (distributio — he refers to oi konom´ia). He defines ordering as: a. the right adjustment of the measures of the individual members of the work — which for Fleury (1990: 106, n. 2) is inseparable from the proportions between the measures of the members of the work — and b. when applied to the whole work, as the establishment of proportions resulting in symmetria (see also Watzinger 1909: 210–211; Fre´zouls 1968: 445). It is constituted by quantity (quantitas — he refers to the Greek pos´othv), which is the choice of modules based on the whole work and the harmonious realization of the whole work due to the di¤erent parts of its members (cf. Falus 1979: 257). Disposition is: a. the right placing of the elements of a work and b. the tasteful realization of a work of quality that results from this. The reference here is to the process of drawing of the future building, in plan and front elevation — both in scale — and in perspective. Watzinger (1909: 212–213, 214; see also Falus 1979: 258) points out that this right placing corresponds to the right adjustment in ordering, and that both the former and its consequence, tasteful realization, are activities. For Vitruvius, the aim, but also the e¤ect, of disposition as an activity is eurythmia, since disposition is accompanied by quality (versus quantity); eurythmia should be related to the e¤ect of the architectural composition on the eye of the viewer. Edmond Fre´zouls (1968: 445), on the other hand, argues that proportion is the foundation of the plans included in disposition. However, Vitruvius uses the concept of disposition to indicate, not only the arrangement of the elements of an architectural whole in such a manner that it is rightly done, thus leading to a tasteful result, but also the positioning, consciously chosen by the poets, of a word in a poem with the same aim (see also Kessissoglu 1993: 55). Eurythmia implies: a. a graceful semblance (venusta species) and b. a proportionate appearance, residing in the composition of the members. It is achieved when the relations between the height, the width and the length of the members are right, and in the whole when all elements correspond to the proper symmetria. Vitruvius further defines eurythmia — which as here presented may be misleading — in Book VI (II: 1–5). There he explains that the eyes do not achieve accurate results, and he gives as examples the optical illusions created by paintings of stage settings and the oars of ships in the water (in the latter case, owing to the

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transparent thinness of water, the oars send back images that, floating at the topmost level of the water, are disturbed and produce in the eyes of the beholder the broken appearance of the oars). In the case of architecture, attention must be given to its appearance, this is why we must adapt the form to the nature of the site, since appearance is di¤erent if something is near, if it is elevated, if it is in a confined or an open site. Vitruvius follows a very similar reasoning in Book III (V: 8–9), when writing on architraves. I shall not deal with the contradiction that marks the relations he presents between the heights of the architraves and the dimensions of the columns (see on this contradiction, Gros 1990: 177– 179, n. 4). The weight of the discussion is given to the formulation of the height of the architrave as a proportion of the height of the column, in such a manner that the proportion increases as a function of a denominator that decreases with the increase of the height of the column. The interpretation he gives for this regularity is di¤erent from that for the oars. The higher, he writes, the ray issuing from the eye is raised, the more difficulty it has in piercing the dense layers of the air; because of the distance the ray has to travel upwards, it is dispersed and loses its power. The result is that it reports to the senses imprecise information relative to the existing symmetria. According to the passage in Book VI, since certain things appear to the eye as other than what they really are, the architect must make (subtle) adjustments, i.e., add to or subtract from the symmetria of the building (cf. III.III.11) according to the nature or requirements of the site. When discussing architraves, Vitruvius generalizes his argument: for all members obeying the proportional system, we must add to the proportion one supplementary element in cases when the member is either situated at a very great height or is itself of large dimensions (see also III.III.13). In Book VI, the operation of adding or subtracting leads, according to Vitruvius, to a balanced appearance, and presupposes not only theory but also a fine judgment: first we define the symmetria and then, on its basis, the modifications are correctly deduced. In this manner, he writes, eurythmia will be convincing to the viewer. We note that in a few cases eurythmia abandons proportions2 (see also Fre´zouls 1968: 443–444, 445). Pierre Gros (1990: 120, n. 3, and 179, n. 8.4 and n. 9.1) believes that the initial project of Vitruvius referred solely to symmetria and the treatment of eurythmia is foreign to this project. Undoubtedly this view is related to his conclusion that the examples of optical illusions Vitruvius gives are heterogeneous and of a level not beyond that of the school (Gros 1982: 672). What seems clear is that the close, and forced, bridging of these two incompatible approaches is possible if eurythmia is understood as a

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symmetrical property (I.II.4). Eurythmia, for Vitruvius, compensates for the apparent deficiencies, due to the eye and the action of the air (III.III.11), of an otherwise perfect symmetria (see also Gros 1990: 121, n. 4). It corrects by increasing when there is a false appearance of reduction (cf. III.III.13) and vice versa. Thus, it leads to the restitution of true symmetria (VI.III.11 — see also Gros 1990: LVII, n. 139 and 120, n. 2). Eurythmia is thus founded on and deduced from symmetria.3 Now, if we compare chapter II of Book I and chapter I (1, 3, 4, and 9) of Book III, symmetria is conceived: a. as the commensurability of each member of a work — that is, of its dimensions — to the whole work, whence (see Gros 1990: 60, n. 4) b. the commensurability between the members (see also Watzinger 1909: 211). We understand that these two kinds of relation, that are considered as established by nature, or by art which imitates nature, are the foundations of beauty (Fre´zouls 1968: 442, 443, 445–446). Symmetria is founded on proportio — Vitruvius gives the Greek term , analog´ia — and is linked to the definition of a common unit of measurement, a module. Thus, symmetria is a system of proportions4 (see also Falus 1979: 256, 259, 260, 262, n. 23, 264). A closely related term is compositio (III.I.1) — probably from the Greek s´unyesiv — which refers to the system established between the components of a building, a system founded on symmetria (Gros 1990: 55–56, n. 1). In Book I, Vitruvius gives examples of objects showing symmetria. The symmetrical property of eurythmia is found in the human body, deriving from the small parts of the body such as the forearm (cubit), the foot, the palm and the finger (digit). A system of symmetria is to be found in all buildings and first in sacred buildings, in the ballister, based on (the diameter of ) a hole, or in ships, based on the interval between two oarlocks. According to Watzinger (1909: 210–212), each of the two parts of the definition of symmetria corresponds to a part of the definition of ordering. He observes that symmetria corresponds to an e¤ect, that it is the aim and e¤ect of ordering and quantity, these two being the activities leading to this e¤ect; proportion, which accompanies symmetria, also corresponds to quantity. The di¤erence between ordering and symmetria is comparable to that between dispositio and eurythmia. Appropriateness is generally the carefully worked-out aspect of a work of art of high quality realized with approved elements (members following the principle of symmetria? — see Fleury 1990: 116, n. 3). It is achieved by rule or by custom, or through adjustment to nature. In the first case, the type of a temple is adjusted to the nature of the god adored therein, and in general a building is adjusted to the status of its owner (VI.V.3). In the second case, the parts of a building must fit together and thus, on the one hand we should create elegant vestibules to go with mag-

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nificent interiors, on the other we should not mix elements of di¤erent orders, i.e., we should respect tradition. The last case concerns the use of salubrious orientations for specific functions and the selection of appropriate sites, due to their resources, for the location of temples. These three cases show us that appropriateness is based on matching, including the matching of architectural elements with architectural elements, of natural elements with the natural element in which an architectural whole (the temple) will be located, and of architectural elements or the whole building with a natural element (sun) or the status of the owner of a building (see also Pollitt 1974: 68–69). According to Frank E. Brown (1963: 106), appropriateness manifests the morality of architecture, a domain ruled by the ethics of the universe. In his discussion of the above cases, Watzinger points out the relation of appropriateness with dignity (auctoritas) and that of the latter with the classical, understood as something with inherent value and generally appreciated, as well as its closeness to pr´epon in rhetoric (Watzinger 1909: 215–217; see also Brown 1963: 106–107). Distribution is: a. the suitable use of materials and the plot, and b. the wise equilibrium of expenses for the work: use must be made of local materials. Thus, it follows from Vitruvius (see also VI.V) that distributing also includes the architectural response to the needs of the owners, their fortune, profession, and social status, their personality, the uses required, the geographical character of the site (urban versus rural ) and the status of public buildings — factors that are combined in di¤erent manners. This response concerns the arrangement of the building and its zones, the uses planned, the location of rooms, the ampleness of the building and the size of its rooms, and the splendor of the building and its rooms. According to Watzinger (1909: 217–219, 220), the adjustment of the type of a temple to the kind of god it is dedicated to formulated in the context of appropriateness corresponds to the present response to the needs of the owner, with the di¤erence that the first seems to be more aesthetic (it is considered by McKay (1978: 19, 54, 55) as ‘‘formal functionalism’’), while the second is practical (see also Gros 1989: 127). Watzinger believes that there is in general a close relation between distribution and appropriateness and that they are related as activity to its e¤ect. We see that Watzinger proposes the following organization by pairs of the six concepts that Vitruvius discusses: ordering-symmetria, dispositioneurythmia, and distribution-appropriateness (Schlikker (1940: 72) expresses objections in respect to the last pair). He classifies this organization as two sets of concepts, the one grouping the first term of each pair and the other the second term. For him, these sets represent two identical architectural wholes, with the only di¤erence that they correspond to two di¤erent viewpoints: the first sees architecture as a professional

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activity, while the second as a state that is the aim and e¤ect of this activity (Watzinger 1909: 211–212, 214, 220; see also Scranton 1974). There are overlappings between Vitruvius’s concepts (see also Fre´zouls 1968: 445; Knell 1985: 30), but Watzinger attempts with his above proposal to discover their correspondence and coherence. I find his proposal generally convincing, though not perhaps throughout; for example, while the nature of appropriateness corresponds to a state, the suggested manners of achieving it are processual. On the other hand, the order according to which Vitruvius presents the six concepts founding ‘‘his’’ theory of architecture poses another problem. Heiner Knell (1985: 34, 168), while believing that the concepts belong to a holistic conception, does not try to explain Vitruvius’s sequence. Robert L. Scranton (1974: 499) proposes a logical sequence, but it is not convincing.5 Vitruvius’s theory of architecture has been approached from four different perspectives: as a loose whole; as an integrated whole; as a whole composed of two repetitive (sub-) wholes, corresponding to di¤erent viewpoints, since they are considered to be related as processual cause to desired e¤ect; and as composed of concepts that may be organized in a significant sequence, di¤erent, however, from the one proposed by Vitruvius himself. It is reasonable to think that Vitruvius, in his attempt to systematize architectural theory, would have a tendency to harmonize the concepts used. This integration would certainly imply some intellectual acrobatics, given that the three pairs discussed by Watzinger are related to di¤erent Greek schools of thought, with a di¤erent origin and historical development (see Schlikker 1940: 55–112; Pollitt 1974: for example, 24–31, 67–70). However, in spite of the eclectic nature and the triple aesthetics of De architectura, and without discounting the insights of other scholars, I believe we may assume that the actual order of presentation of the concepts is in accordance with the following rationale. Appropriateness and distribution, two ‘‘lateral’’ concepts according to Fre´zouls (1968: 45), share the common characteristic, which also di¤erentiates them from the other four concepts, that they involve factors external to architecture, which are heterogeneous, or otherwise external constraints that influence the architectural project. Distribution covers only such factors, appropriateness mainly such factors, with the addition of the matching of architectural elements with architectural elements. We may thus agree with Watzinger that the two concepts are closely akin. Furthermore, the fact that Vitruvius presents them sequentially and puts them at the end of the discussion of his fundamental concepts perhaps gives us a clue as to the logic underlying the whole sequence of the concepts. In fact, in architectural practice the architect has to start with the constraints, which o¤er a context within the limits of which it is then possible

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to elaborate the proposal. If Vitruvius is presenting his concepts on the basis of practice, then he should have started with the above two. On the other hand, if he has adopted a theoretical viewpoint, he could start with the internal factors, which correspond to architectural composition, and conclude with the constraints, considered as determinant but secondary to the previous main work of the architect. This is the case with the actual sequence he gives us. If we assume on this basis that Vitruvius had a theoretical order in mind, we may give a possible explanation of the sequence of the other concepts as well. Vitruvius starts with the two activities, ordering and disposition, covering what is for him the essential part of the whole of architectural practice, which stretches from conception to drawing. He next presents the desired e¤ects of architectural practice, eurythmia and symmetria. He rightly starts with ordering, because it is the activity leading to the crucial symmetria. What seems awkward is the discussion of eurythmia before symmetria, since the former cannot be understood without the latter. Maybe this logical reversal is due to a desire to focus first on the final result of the design. Finally, there is another reversal if Vitruvius thought of the relation between distribution and appropriateness as one between activity and e¤ect, because in this case the e¤ect is presented before the activity. A possible explanation would be that the aesthetic considerations included in appropriateness attached it to symmetria. There are two related overriding ideas in Vitruvius’s theory of architecture, the one explicit, the other implicit. The explicit one is proportion, starting with symmetria, i.e., the subordination of the members of a building, their relations, their relations to the whole and of the whole to numerical proportions, providing the objective quality of architecture. But also, symmetria is a principle of quantitative matching, starting from a common measure and e¤ected at di¤erent levels of a work. Eurythmia would also be a quantitative and proportional — though only on paper (see Gros 1990: 124, n. 4 and 179–180, n. 4) — intervention on symmetria, an intervention that has as its goal the perception of the viewer, differs according to the situation, and provides the ‘‘subjectivizing’’ quality of architecture. In this case, there is a qualitative matching between the quantitative conversion of symmetria e¤ected by eurythmia and the specifics of the situation. Finally, the adaptation of the building to the client and the environment are other cases of qualitative matching. We deduce that the implicit principle of the Vitruvian theory is matching, the grouping and tight correspondence of things that ‘‘go together.’’ After the discussion of the six concepts in chapter II of Book I, Vitruvius introduces three more concepts in the following chapter. They follow a reference to the three branches composing architecture and a brief

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presentation of the two subdivisions of one of these branches, building (see below). They correspond to the triple aim an architect must have when building and are strength ( firmitas), utility (utilitas), and beauty (venustas) — see also III.III.6. The last term is later complemented by dignity, auctoritas (III.III: 6, 8, and 9). Strength relates to the solid foundation of a work and the use of materials without parsimony. Utility refers to the appropriate distribution and functional organization, as well as orientation. As to the complement of beauty, dignity, in the later phase of the redaction of his work Vitruvius came to relate dignity to the increase in size, more particularly height, of a building and to an e¤ect of relief. This concept is related to the visual impression created by a building, an extroverted factor, as opposed to the introverted factor of its canonical organization. Dignity complements grace with prestige and majesty. In addition, dignity is accompanied by the meanings of power, sovereignty, royalty, and submission of the citizen (Gros 1989 and 1990: 114, n. 6). In sum, Vitruvius’s theory of architecture covers a wide range of the factors involved in architectural design. They are not, however, all equally represented. For example, the functional factor is present, but there is no theory on uses and their location. As Fre´zouls notes, the discussion of the functional is limited and does not refer to fundamental issues. The emphasis of the above group of nine concepts is on beauty, i.e., aesthetics — which, for Vitruvius as for the Greeks, was not an independent realm as it is today. Fre´zouls observes that, while symmetria is restricted to the same level as the other concepts, in reality it rules them, as is attested by its omnipresence in De architectura. The appearance of beauty is eurythmia, but the essence of it is symmetria (see Fre´zouls 1968: 444–445). In the last instance, the rule, symmetria, is legitimized through its foundation in nature and function, or to put it otherwise, necessity (Gros 1982: 679–680). Symmetria is, as it were, objective beauty. There is beauty when we give to the work a pleasing and elegant aspect, and correctly calculate the relations of the measures of the parts of the work according to symmetria. Subjective beauty, the beauty that relates to the eye of the beholder, is eurythmia, which results from the combination of the rules of symmetria with visual corrections (see also Gros 1990: 120, n. 2, 123, n. 3 and 125, n. 6). The principle of symmetria was the nuclear concept of the classical Greek worldview. For Pythagoras and the Pythagoreans, numbers and their relations are the essence of all things, indeed of the universe (k´osmov), and through them the order of the latter is constituted. In this manner, numbers in Pythagorean philosophy acquire an ontological status and a sacred nature. The equivalent of this philosophical cosmic order in the domain of the arts was symmetria, namely the commensurability of

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the parts of a work to each other and to the whole (Pollitt 1974: 15–16, 17, 26, 162, 167; Grassi 1962: 49–53; Raven 1951: 147–148). Symmetria is an aesthetic (or rather quasi-aesthetic) and cosmic principle, through which the work of art is imbued with and participates in the cosmic harmony. As we shall see, the concept is used by Vitruvius in exactly the same sense (see also Gros 1990: LVI–LVII and 57, n. 2); indeed, this is not the only case in which Vitruvius’s thought shows Pythagorean influences (Kessissoglu 1993: 89–90, 100). Symmetria is the nuclear concept of De architectura (see also Gros 2001: 16, 22) and, as I shall try to show, of the Vitruvian city.

3.

The windrose and urban planning theory

The city proposed by Vitruvius is related to a windrose. He starts by stating that according to certain authors there are four winds: solanus blowing from the equinoxial sunrise, auster from the south, favonius from the equinoxial sunset, and septentrio from the north. But, he says, those who have studied the subject more profoundly teach that the winds are eight, and he gives as example the octagonal ‘‘Tower of the Winds,’’ as it is called today, in Athens. Vitruvius also presents a windrose with twentyfour winds, which is unique in ancient literature (I.VI: 4–5, 10; see also Nielsen 1945: 95; Fleury 1990: 182, n. 16; Paulys Realencyclopa¨die 1958: Winde, 2372–2373) and perhaps was related to the hours of the day (Hamberg 1965: 114), but he focuses on the eight-part windrose.6 The directions of the eight winds, according to Vitruvius (I.VI), are found in the following manner. A horizontal marble slate is placed in the middle of the city (it can be replaced by a well-prepared and leveled ground). In the middle of it is placed a bronze gnomon — an instrument consisting of a vertical rod on a horizontal base (Figure 1). About the fifth hour before midday the extreme point of its shadow is marked, and then a circle is traced through a compass with the position of the gnomon as center and the distance between it and the above point as radius. A second point is marked when after midday the extremity of the shadow again touches the circle, this shadow being equal in size with the morning shadow. With these two points as centers, two intersecting arcs are traced, and the straight line passing through their intersection and the center, and extending to the opposite part of the circle, gives the N-S direction. In this manner, Vitruvius locates true north and the meridian line. Vitruvius then asks us to take the 1/16 of the circumference of the circle and, with as centers the two intersections of the meridian line with the circumference, make marks on the latter both to the right and to the left

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Figure 1. The gnomon on the levelled marble slate (according to Fleury 1990, reprinted by permission of Les Belles Lettres)

of this line — he manifestly means for us to take as radius the chord corresponding to the above arc, but he does not clarify how to perform this operation7 (Plommer 1971: 161). Two diameters should unite these points by twos and thus the two eighths corresponding to the south (auster) and the north (septentrio) wind will be defined. The remaining parts of the circumference should be divided in equal parts, three to the right and three to the left, and with the tracing of the appropriate diameters the equal divisions of the eight winds will be obtained. The remaining winds (and sectors) are solanus (E), eurus (SE) coming from the winter (solsticial) sunrise, favonius (W), africus (SW) from the winter sunset, caurus (NW) and aquilo (NE) — Figure 2. The number of the winds (eight), writes Vitruvius, is related to both their names and the orientations from where they blow (I.VI: 6–7, 12–13). This analytical description of the tracing of the eight-part windrose is linked, as we shall see, to a tantalizingly laconic description of the tracing of the street network of the city — manifestly a new city (see also Fleury 1990: XCVI). But let us start from the beginning. In the chapters on urban planning theory (I: IV–VII) — the most complete left to us from antiquity and to which the tracing of the windrose belongs — Vitruvius opens the discussion with the walls of the city and begins with the selection of the site, which must be ‘‘very healthy.’’ The site must be elevated (which does not necessarily mean on a summit), free from fog and frost, exposed to a temperate orientation, neither hot nor cold, and must not be next to marshland, since in this case the morning breezes which reach the city at sunrise will be conjoined with fog and thus the bodies of the inhab-

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Figure 2. The eight-part windrose of Vitruvius according to the most ancient extant manuscript of his work, Harleianus 2767. Three manuscripts of his text include a figure of the eight-part windrose. If this figure were derived from the original text, it would be the only one extant among his figures (reprinted by permission of the publishers and the Trustees of the Loeb Classical Library from Vitruvius: vol. I, Loeb Classical Library8 volume 251, translated by Frank Granger, Cambridge, MA: Harvard University Press, copyright : 1931 by the President and Fellows of Harvard College. The Loeb Classical Library8 is a registered trademark of the President and Fellows of Harvard College)

itants will receive the poisonous exhalations of the beasts of the marsh. Vitruvius continues with the orientation of the walls; he is against orientation towards two of the cardinal directions, south and west, on the grounds that they involve too much heat.8 Alternation of heat and cold damages bodies and inanimate objects. Organisms are constituted, as Vitruvius writes (I.IV: 5–8), by the elements, the ðstoiwe˜iaÞ of the Greeks, which are heat, humidity (water), earth, and air, and the qualities of living beings are determined, according to their species, by mixtures of these elements naturally proportioned. We , recognize here the Pythagorean principle of isonomia ðisonom´iaÞ, that is,

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the right proportion and equilibrium of the opposing elements of the body. Isonomia was for the Greeks the manifestation of the cosmic order in the domain of biology and closely akin to symmetria (see Raven 1951: 150). It is clear from the very nature of the elements that they are cosmic also for Vitruvius. Much later in his work (VIII. Praef.: 1–2) he is explicit on this point. Another term used there for the elements is ‘‘principles’’: they are the principles of all things and, not only are all things born from them, but they are also nourished, grow and are preserved by their power. Too much or too little of one of them seems to destroy, for Vitruvius, the necessary equilibrium of the four elements. Francesco Pellati stresses the existence of a strong, though not direct, impact of Empedoclean theory on the views of Vitruvius concerning the elements, while also indicating the Pythagorean influence on both. Pellati observes that part of the Empedoclean theory is founded on mathematical proportions, that this approach is due to the early Pythagoreans and that proportional relationships are clear in the case of the salubrity of sites, where Vitruvius refers to the theory of the four elements. Pellati rightly writes that for Vitruvius sites are composed solely of the four elements and are related to their various combinations (Pellati 1951: 243– 244, 245, 254, n. 1, 256, 258, 259; cf. Steckner 1984: 264). In fact, the four elements are introduced from the very beginning of Vitruvius’s planning theory: he refers, as we saw, to the topography of the site (earth), fog, frost and marshes (water), temperature (fire), and breezes (air). He then first discusses heat in connection to orientation. Still in the context of the salubrious site, after the theory of the elements (I.IV: 9–12) he passes to the quality of water, and pasture (earth), which he proposes to study through the inspection of entrails according to the Ancients (this kind of procedure was used by the Etruscans); then follows a discussion of the combined conditions under which the establishment of the walls on a marsh is acceptable, one of which is its being in contact with the sea.9 After discussing the positive and negative characteristics of sites, and the orientation of the city walls, Vitruvius turns to the construction of the walls and to their towers, passing thus from salubrity to the military factor (I.V), but he returns to salubrity with the next and crucial chapter. Operating from the outside inwards, he refers to ‘‘the division into lots . . . and the orientation of the avenues ( platearum) and the alleys (angiportuum)’’ — elsewhere he also uses the term vicus. These — and here we have the reference to the street network and its relation to the winds — ‘‘will be rightly oriented if we plan not to let the winds blow through the alleys’’ (I.VI.1); the winds can be cold, hot or humid. Thus, after the discussion of the salubrity of the site in respect to three of the four elements

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— and that of the military factor — Vitruvius comes now to the last element, air. Protection from the winds allows a site and an organism to be healthy. This protection is achieved if the tracing of the avenues and alleys is not oriented in the direction of the winds, but follows the ‘‘angles [he means the vertices] formed between two directions of the winds’’ (I.VI.7). Thus, we shall be able to protect the dwellings and public streets from the violence of the winds, which break on the angles of the buildings and are dissipated. Otherwise, the rush of the winds coming from the open spaces of the sky and their abundant blowing constrained in the narrow alleys lead to their circulating with violence. Vitruvius closes his urban planning theory (I.VII: 1–2) with what we would call today ‘‘location theory’’ applied to the urban level (the selection of the site is also related to location theory, but on the regional level). He writes that, after the creation of the network of alleys and avenues, what must be studied is the choice of the locations for the sacred buildings, the forum and the other public places, thus concentrating on what he manifestly considers as the main unitary elements of the city (see also Tosi 1984: 427). These constructions, together with the walls and their accompanying towers and gates, constitute the public spaces of the city, which are one part of ‘‘building’’ — itself one of the three parts of architecture together with horology and mechanics — the other being private building (I.III.1 — the above items are the subjects of Vitruvius’s books). If the wall is on the sea, the forum must be near the port, otherwise it must be located in the center of the city — the typical location of the forum in Roman cities. He prescribes that the capitolian triad, Jupiter, Juno, and Minerva, must be located at the highest place — in this manner, the gods can see and thus protect, and can be seen and thus addressed; the elevation of the Capitolium is also typically Roman. He then proceeds to location prescriptions for temples of other gods, which follow the Etruscan tradition but not the practices of his times.

4.

The Vitruvian city: A radial-concentric plan

Before analyzing the deeper meaning of the Vitruvian city, we need to examine its pattern. On this point, Vitruvius is laconic in the extreme. We just saw above that the streets are oriented to the ‘‘angles’’ between two directions; these are the points marked on the circumference of the windrose, which according to Vitruvius are also the vertices of an octagon. He adds one more piece of information: in order to orient the network of the alleys, one should place the gnomon ‘‘between the vertices of the octagon’’ (inter angulos octagoni) (I.VI.13); he adds a drawing

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showing, as he says, the way to avoid the harmful winds by moving the alignments of the avenues and the alleys out of their course — unfortunately, the drawing has been lost. Fleury (1990: 186, n. 2) poses two crucial questions in respect to this puzzling description of the tracing of the street network: what is the instrument called a ‘‘gnomon’’ and what does ‘‘between the vertices’’ mean, that is, to what kind of operation does this expression refer? There have been di¤erent interpretations concerning these questions. As to the first, Fleury’s interpretation of the gnomon in this expression is literal: a gnomon is a right angle. How then is this angle used? And finally, what is the pattern of the street network? The customary interpretation of Vitruvius’s description goes back to the Renaissance. Alberti, the well-known theoretician of architecture of the quattrocento, in his De re aedificatoria is well aware of Vitruvius’s work. I have argued elsewhere (Lagopoulos 1993: 128–132, 1998: 388– 397) that, although Franc¸oise Choay (Choay 1980: 12, 15, 16, 107–108) maintains that Alberti in this work does not have recourse to an urban model, he actually does propose such a model, a radial-concentric one, exemplified by the city of the tyrant. I based my reconstruction of this plan (Figure 3) on information given by Alberti himself in di¤erent parts of his ten books, starting from his description of the tyrant’s city with its emphatic concentricity. I proposed that he introduces the radial pattern both because he knew it from urban reality and because he was inspired by Plato’s cosmic ideal city-state in the Laws. Finally, I suggested that his proposal integrates both the Roman tradition of the cross-shaped cosmic complex of the cardo and decumanus, the two principal streets of the Roman city, and the Christian cosmic city, the heavenly Jerusalem. We should add to this many-layered intertext Alberti’s interpretation of the Vitruvian city, since the circular contour and the radial form of the street network may be derived from Vitruvius: the first from Vitruvius’s statement that ‘‘cities are not to be planned square, nor with projecting angles, but curvilinear, so that the enemy may be seen from several sides’’ (I.V.2), and the second as an interpretation of the expression ‘‘inter angulos’’ in the passage discussed above. Alberti’s proposals were fundamental for the establishment of the Renaissance model city; though other architects of the quattrocento, such as Filarete and Martini, also contributed, both followed Alberti’s work and all of them were influenced by Vitruvius (Lavedan 1959: 12, 14, 23). Martini proposes an ideal octagonal city with four gates situated in the middle of four sides of the octagon and on the extremities of the two main streets of the city, which cross at right angles. There are eight towers at the vertices of the octagon. The radial street network also includes two axes bi-

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Figure 3. Reconstruction of the city of the tyrant as proposed by Alberti (according to Lagopoulos 1998)

secting the right angles of the two main streets. The resulting eight streets converge on a central octagonal square; between this square and the city walls three octagonal rows of blocks and three narrower octagonal streets are situated, the whole plan thus consisting of a set of three consecutive octagonal rows of buildings, embedded the one within the other. Four secondary squares are situated between the blocks forming the rows and on the secondary radial streets (Figure 4). It is clear that we are again

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Figure 4. The ideal octagonal radial-concentric city of Martini (from Lavedan 1959, reprinted by permission of E´ditions Jacques Lenore)

dealing with an interpretation of the Vitruvian city: the street network is radial, as is the case with Alberti, and the founding and repeated form is the octagon, the figure attached to Vitruvius’s windrose. It is to be noted that each side of the octagonal streets is perpendicular to one of the eight radial streets, showing that Martini conceived of the angiporti as perpendicular to the plateae, manifestly a compromise with the ancient Roman grid plan; also, that the orientation of all the streets goes against Vitruvius’s prescriptions. The radial-concentric interpretation of the Vitruvian city is not limited to Alberti, Filarete, and Martini. It was promulgated by the group known as the ‘‘Vitruvians,’’ most of whom belonged to the circle of Bramante and his disciples, active towards the end of the fifteenth and the beginnings of the sixteenth centuries (see Lavedan 1959: 23–25). The interpretation continued through the following centuries and is still alive today. To give some examples, Fra Giocondo, who had relations with Bramante and published an edition of Vitruvius in 1511, designed an ideal city surrounded by two concentric walls and having at its center a large monument, also circular; radial streets, probably twelve, extend from the central monument to an equal number of gates (Figure 5). Galiani, who published his edition of Vitruvius in 1758, proposes placing the vertex of the right-angled gnomon in the center of the windrose and its sides between the center and the vertices of the octagon, but this operation does not follow the precept ‘‘between the vertices’’ (cf. Fleury 1990: 186, n. 2).

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Figure 5. The ideal circular radial-concentric city of Fra Giocondo (from Lavedan 1959, reprinted by permission of E´ditions Jacques Lenore)

Figure 6. Galiani’s reconstruction of the Vitruvian city as an octagonal radial-concentric city (from Portoghesi 1969)

His reconstitution of the Vitruvian city is shown in Figure 6. The plan is strongly influenced by Martini’s proposal, with the main di¤erence that the radial streets unite the center with the vertices, and not the middle of

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Figure 7. The reconstruction of the Vitruvian city as octagonal and radial-concentric (reprinted by permission of the publishers and the Trustees of the Loeb Classical Library from Vitruvius: Vol. I, Loeb Classical Library8 volume 251, translated by Frank Granger, Cambridge, MA: Harvard University Press, copyright : 1931 by the President and Fellows of Harvard College. The Loeb Classical Library8 is a registered trademark of the President and Fellows of Harvard College)

the sides, of the octagon. In the middle of the central octagonal square is a circular element, and there is a set of four consecutive octagonal rows of buildings, embedded the one within the other; eight secondary squares are situated between the blocks and on the bisectors of the street angles. This plan gives the main, radial streets the right orientation according to Vitruvius, but it fails to do so for the secondary ones, because the latter are not perpendicular (and parallel) to the former. Frank Granger, in his 1931 translation of De architectura, gives the octagonal plan reproduced in Figure 7, a close variant of the Galiani plan, which also fails to accord with Vitruvius in the case of the secondary streets.

5.

The Vitruvian city: A grid plan

If we assume that Vitruvius instructs us to put the vertex of the gnomon in the center of the windrose, thus paraphrasing ‘‘between the vertices’’ to mean ‘‘between the center and the vertices,’’ then we come up with a radial plan. Admittedly, the temptation to do so and to arrive at a radial

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plan is strong, since the circle, its center and the symmetrically disposed diameters are the elements of the Vitruvian windrose. Put another way, the pressure of the text pushes us towards the radial plan. The fact, however, that this reading violates the literal text prompts us to seek for another reading, which, as we shall see, is not only literal, but also in line with the external environment of the text, that is, the urban ideas and realizations, preceding or surrounding it, that were known to or could have been known to Vitruvius. Let me first briefly present this environment. Among the ancient Greeks, there had never been any newly created city with a radial plan. However, there existed a semiotic urban model composed of a center, the agora, and its circumference, on which all citizens are ideally supposed to be located; all citizens should be located at an equal distance from the agora because of the democratic — here political — principle of isonomia, equality of political rights. Thus this model, which is not only political but also cosmic, essentially emerges from an unspecified number of radii. The model is a sub-model of a wider model consisting of concentric circles and covering urban and regional space up to the confines of the earth (cf. Lagopoulos 1978: 109–110). This kind of isonomia is the political equivalent of the biological isonomia, and they both derive from the cosmic order, from which symmetria was also derived. Both the above and the Platonic radial-concentric model were, however, purely theoretical models, while the actual model, realized in a great number of cases, was the Hippodamian grid plan. The grid plan was also the Roman urban model. It has the advantage of a quick and easy division of the land, and is convenient for infrastructures. But for the Romans, as for the Greeks, it was also filled with cosmic connotations. When constructing a new settlement during the empire, the Roman surveyors, the agrimensores, would trace two perpendicular axes, the decumanus (W-E) and the cardo (N-S), intersecting in the middle of the future settlement (Figure 8). The decumanus connoted the course of the sun and the cardo the axis of the universe. Facing east, they called the region to their right regio dextrata (DD: dextra decumanum) and that to the left regio sinistrata (SD: sinistra decumanum). The region in front of the cardo was regio ultrata (VK: ultra k[c]ardinem) and that to the back regio citrata (KK: kitra k[c]ardinem). Streets parallel to both axes were then traced and each section of the perpendicular streets was labeled according to the quadrant in which it was located and its relative distance from each axis. The point of intersection of the two axes, DMKM (decumanus maximus - kardo maximus), was considered to be the center and the navel of

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Figure 8. The geometrical system of the Roman surveyors for the tracing of the street network and the blocks of a settlement (according to Mu¨ller 1961)

the quadripartite universe. This is the point where the groma, the instrument with the help of which the two axes were traced, was placed; at and around this point were located the mundus (the sacrificial center of the settlement, created during the foundation rite), the forum and the capitolium. This point was considered as the origin of the settlement: as Hyginus Gromaticus writes, ‘‘ab uno umbilico in quattuor partes omnis centuriarum ordo componitur’’ (from a navel into four parts follows all the order of the blocks — for the above, see Mu¨ller 1961: 11–27, 33). The grid plan was the pattern used universally and for centuries by the Roman surveyors and it is utterly improbable that an architect-engineer like Vitruvius, who also addresses himself to clients of architects and tries to communicate an operational knowledge, would propose an urban plan totally independent from this practice and tradition. But if, for some reason contradicting all of his work, Vitruvius had indeed decided to do so, he would surely have had to be — and he certainly would have been in his text — explicit about his unorthodox proposal, while simultaneously

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Figure 9. The gnomon and the operation e¤ected with it

trying to legitimize it. It is precisely the absence of any insistence on the description of the plan that indicates that it is so predictable that no comment is necessary (cf. Hesberg 1989: 134–135). Is there, then, some reading of ‘‘between the vertices’’ which could lead to a grid plan? We are thus confronted once more with the question already posed: how is the gnomon, the right angle, used? Fleury (1990: 186–187, n. 2) is firm that Vitruvius proposes a grid plan and thus agrees with the position of Schlikker (1940: 42-43, n. 26). He concludes that the vertex of the gnomon is placed on a vertex of the octagon; the result is that each of the sides of the gnomon will pass below the next vertex of the octagon and through the second vertex (Figure 9). On the basis of this operation, Fleury traces a grid plan (Figure 10) that also establishes, in the spirit of Vitruvius, a hierarchy between the streets, including two types, the main streets or plateae and the secondary angiporti, and gives the latter an orientation perpendicular to the former.10 Of course, this is the case only if the gnomon has sides of equal length, since it is possible to inscribe within the circle a gnomon with unequal

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Figure 10. The grid plan as traced after this operation (both according to Fleury 1990, reprinted by permission of Les Belles Lettres)

sides, the one side passing through two consecutive vertices and the other below the two next vertices and through the third. But only the first case is consistent with the requirement that the streets should be oriented between the directions of the winds, because the orientation of the street it prescribes coincides in fact with that of a pair of perpendicular diameters of the windrose. In the second case, on the contrary, the orientation of each pair of sides is towards either the cardinal points or the intermediary points, which goes against the Vitruvian prescription. Fleury’s proposal is aligned with the views of Per Gustaf Hamberg. Starting from the idea that the use of two di¤erent terms for the streets correspond to a specific and known type of plan, Hamberg argues that Vitruvius cannot be referring to the ‘‘typical’’ Roman plan (cf. Figure 8). This plan is seen, for example, in Aosta (Augusta Praetoria), in which the streets, intersecting at right angles, have an approximately equal width (the streets uniting opposite gates are slightly larger, according to Hamberg) and the blocks are almost square. For Hamberg, in this model there

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Figure 11. Knell’s (1985) proposal for the Vitruvian city (reprinted by permission of WBG)

is no essential distinction between two di¤erent types of streets (Hamberg 1965: 106–107, 112). Fleury disagrees with Knell (1985: 40–41) on the same issue. Describing the steps Vitruvius would follow from the windrose to the street pattern, Knell concludes that a square is inscribed within the octagon, and then he fills the latter with a grid plan having streets of equal width and equal square blocks (Figure 11), acknowledging that this last point is an addition of his own. Fleury also makes reference to the plan of Thourioi, where he follows Georges Vallet (1976: 1031–1032) in believing that there was a di¤erentiation between large avenues ðplate˜iaiÞ and alleys ðstenopo´i Þ, the latter being located in the interior of the areas bordered by the avenues. He observes, however, that Vitruvius does not seem to have had this plan in mind, because his plan should be interpreted as involving large avenues all following the same direction

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(but he does not substantiate his argument) — Fleury 1990: C–CII and 146–149, n. 2). Fleury also agrees with Hamberg that Vitruvius was inspired by the planning principles presiding over the Greek colony of Naples. The urban model of this city is labeled by Hamberg ‘‘per strigas.’’ Its street plan seems to date from the second half of the fifth century BC and includes three principal avenues at equal distances, traditionally called plateae, which are intersected at right angles by about twenty lanes, also at equal distances; the proportion of the sides of the insulae is 5:1 (Figure 12). Hamberg thinks that the model per strigas is the typical Greek form for a regular city, and that the plan of Naples was the application of this at the time quite modern model. The plan would belong to the period when

Figure 12. The plan per strigas of Naples (from Lavedan and Hugueney 1966, reprinted by permission of E´ditions Jacques Lenore)

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Greek urban planning, under the influence of philosophy and medicine, begun to concern itself with practical problems. The plan is also ‘‘scientific’’ — in the sense that it takes into account astronomical and meteorological orientation. The issue concerning orientation presupposes a theoretical background. Thus, Vitruvius would have been inspired by a now lost early classical Greek treatise concerning urban planning, climate, and orientation, a treatise that could be contemporary with the planning of Naples and would have expressed ideas similar to, but also di¤erent from, those (already current) of Hippodamus of Miletus, but that would not have been written by any personality known to us (Hamberg 1965: 108–109, 112, 113, 116, 122). If the ‘‘between the vertices’’ operation is meant to define orientation, then it is theoretically superfluous, because the directions arrived at through it are already present in the two pairs of perpendicular diameters of the windrose. We should, thus, conclude that its aim is the delimitation of a perimeter. There are then two possibilities: either it takes place just once, as we may deduce from a scholastic interpretation of Vitruvius, in which case only the two sides of a square perimeter are defined (cf. Figure 9); or at most it is e¤ected twice, in a symmetrical manner, so as to complete the square (cf. Figure 10) — a non-symmetrical repetition would be non-sense. There is an increasing and thus rewarding visualization of the pattern of the city from the first case to the second, because this square together with the two axes makes four squares, a configuration rendering with fidelity the grid pattern. It is not possible to know if Vitruvius filled the internal space of this perimeter with a finer grid plan — as Knell does — but, if he did so, then he would have drawn a complete Roman city with its cardo and decumanus, one, however, contradicting his view about the avoidance of the square contour. In the first case, the two sides would reveal the will to relate them to a virtual square and focus on a unitary block of the city. In the second, the pattern of the city is given and the square form emphasized by repetition. Both cases show that the Naples model was combined with the pattern of equal square blocks, a pattern proposed by both Fleury and Knell. That in the case of the square we should exclude a reference to the perimeter of the city seems clear, since Vitruvius is explicitly against square cities and in favor of curvilinear ones. At the same time, this last view of his could perhaps allow a slight bridge between the two interpretations of the Vitruvian city, the grid and the radial-concentric pattern: we could hypothesize that the circumference of the windrose is an allusion to, not a precise geometrical model of, the suggested contour of the city (cf. Knell 1985: 41). The two interpretations given to Vitruvius’s city led, thus, to two different city plans: a radial-concentric and a grid plan (see also Lavedan

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1959: 23). This oscillation may even appear in the views of one and the same person. I already made reference to Fra Giocondo’s ideal radialconcentric city. However, as Fleury (1990: CI) reminds us, the very same Fra Giocondo included in his drawings an ideal plan close to that of Naples — where he had worked between 1489 and 1495 — accompanied by meteorological orientations derived from Vitruvius (Figure 12); the similarity of this plan to Vitruvius’s city was already noted by Hamberg (1965: 124–125). But we shall not oscillate here; we shall close the Vitruvian case with a verdict for the grid plan, the traditional Roman cosmic plan, with special emphasis on the cosmic, as I shall try to show. In addition to oscillations, there have been unconvincing compromises of di¤erent sorts. I already referred to the first kind of compromise, which is early and is exemplified by Martini and Galiani, as well as Vasari the Younger (1598), who attempted to reconcile in one plan with an octagonal contour the two opposed plans (see Lavedan 1959: 25–26) — Figure 14. Two recent compromises are due to Hugh Plommer (1971: 160, n. 4 and 161–162, n. 2) and T. Kurent (1972). The first gives a variant of Galiani’s plan (Figure 15), which has the triple advantage that it follows

Figure 13. The ideal square grid city of Fra Giocondo (from Hamberg 1965, reprinted by permission of Blackwell Publishing)

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Figure 14. The compromise of Vasari the Younger between the radial-concentric and the grid plan (from Lavedan 1959, reprinted by permission of E´ditions Jacques Lenore).

Figure 15. Plommer’s (1971) compromise proposal for the Vitruvian city (reprinted by permission of Cambridge University Press).

only the orientations prescribed by Vitruvius — indeed all of them — has the angiporti perpendicular to the plateae, and is in accordance with the observation on the breaking of the winds, but nevertheless it is still a radial plan. Kurent, on the other hand, believes that the Roman surveyors had a secret knowledge of proportions, derived from an ‘‘octagram’’ or eight-pointed star (created by the four rectangles that can be traced on the basis of the four pairs of the diametrically opposite sides of a regular

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octagon), but would not use the encircling octagonal figure. Vitruvius, who would not have been privy to this knowledge, would incline hesitantly to the octagonal form. The only settlement which to some extent follows Vitruvius’s octagonal plan would be Calleva Atrebatum (Silchester), which however also follows the logic of the octagram, implanted by the surveyor who was in charge of the tracing. Kurent attempts, in the name of Vitruvius, to reconcile a by-product of the radial plan, the octagon, with the grid plan, by using as his example Silchester, which, however, is almost precisely oriented to the cardinal points (Figure 16). Both the operation with the gnomon that Fleury reconstructs and the diameters of the octagon define the orientation of the city plan. They can only lead to two di¤erent pairs of orientation: one E/NE-W/SW and N/NW-S/SE, and another E/SE-W/NW and N/NE-S/SW. Each of these two pairs is related to two perpendicular axes, which derive from the rotation, clockwise or anticlockwise, by 22.5 degrees of the meridian line with the E-W axis; this angle is due to the fact that the axes coincide with the bisectors of the angles formed by the cardinal and the intermediary directions (see also Hamberg 1965: 116; Paulys Realencyclopa¨die 1958: Winde, 2366). If, on the other hand, the plan proposed by Vitruvius was radial, the street network would follow simultaneously all eight orientations. Granger (1931: 63, n. 1) observes that at Dougga (Thugga) in Tunis there is a large windrose — about 9 m. in diameter — with twelve winds, which agree closely with those given by Vitruvius. During about eighty years of the second century, a monumental forum was built in this African city. Toward the end of this period, during the reign of Commodus in the last quarter of the second century, the Pacuvii family was responsible for the construction of an extension of the forum, a complex including the rebuilding of an older market, a temple of Mercury and a porticoed square between them (Figure 17). On the white pavement of this square, the above windrose was inscribed in the beginning of the third century (Gros and Torelli 1988: 261; Poinssot 1958: 12, 32–33; Golfetto 1961: 20, 36). The two axes of the circular windrose are oriented to the cardinal points with a divergence of about 6 degrees (clockwise, i.e., from the east southward). These axes are diameters of three concentric circles (Figure 18). The narrow zone between the two outer circles is divided, by lines following the radii, into 24 equal parts. These parts are grouped by pairs so that 12 equal groupings are obtained; the four central groupings are divided into two equal parts by the axes of the windrose. The names of 12 winds are inscribed on the groupings. These names are from north clockwise as follows: Septentrio, Aquilo, Euraquilo, (Vul)Turnus, Eurus, Leuconotus,

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Figure 16. The compromise of Kurent (1972) between the octagon and the grid plan (reprinted by permission of Zˇiva Antika)

Auster, Libonotus, Africus, Fa(v)oni(us), Argestes, Circius (Poinssot 1958: 33; Golfetto 1961: 15, 36; Khanoussi and Maurin 2000: 102). Though there are di¤erences between this windrose and that by Vitruvius,

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Figure 17. The forum, the Windrose square and the market of Dougga (from Poinssot 1958, reprinted by permission of the General Director of the Institut National du Patrimoine, Ministe`re de la Culture et de la Sauvegarde du Patrimoine, Republic of Tunisia)

the two have six winds in common whose regions overlap. Both Arthur Golfetto (1961: 36) and Heiner Knell (1985: 43, n. 126) observe that the Dougga windrose is in accordance with the Vitruvian windrose, though Knell is not certain that it has its origins in Vitruvius. Before Knell, R. Bo¨ker (Paulys Realencyclopa¨die 1958: Winde, 2355–2356) had expressed the opinion that the Dougga windrose has its origins in the twelve-part windrose of Timosthenes (see also Khanoussi and Maurin 2000: 101). The Windrose square and the market are later than the forum, together with which they form an L-shaped whole. The southern side of the square is exactly parallel to the southern side of the forum and we may thus consider that their direction corresponds to the intended W-E axis. The western side of the market is exactly perpendicular to this axis and thus its direction should correspond to the N-S axis. The two axes are actually oriented E/NE-W/SW and N/NW-S/SE and diverge from the cardinal points by 15 degrees, but from the axes of the windrose, by 21 degrees, which according to Knell (1985: 43) represents a very good approximation to the Vitruvian prescription.

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Figure 18. The Dougga windrose (Khanoussi and Maurin 2000, reprinted by permission of Ausonius)

What conclusions can we draw from the above data? From the viewpoint of the names and locations of the winds, the Dougga windrose is close to both the eight-part (and the 24-part) Vitruvian and the Timosthenian windroses, in fact closer to the former. On the other hand, from the geometrical viewpoint, it is identical to the latter. However, beyond these formal comparisons, it is reasonable to assume that an urban windrose in a Roman city of the Imperial period should be related to Vitruvius, whatever its specific form and organization. It should also be noted that the Dougga windrose is connected to Vitruvius, not only through its form and organization, but also through its use. The Dougga windrose is attached to (open) spaces and not streets, but manifestly the former should

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obey the health factor as much as the latter. Given this, the 21 degrees divergence of the axes of the complex and the forum from those of the windrose could in fact be a reference to Vitruvius. I shall come back immediately to this point. But their divergence from the actual cardinal points is of 15 degrees, and it is quite improbable that the Roman surveyors would have made a mistake of 7.5 degrees, as would be the case if they had wanted to achieve the Vitruvian divergence of 22.5 degrees. We must assume that they deliberately sought to achieve a divergence like the one actualized. We can show that this divergence is absolutely compatible with the Vitruvian modus operandi. The windrose is not operational, but commemorative and decorative, since it was constructed some years after the construction of the complex and about a century after the construction of the forum, which both had its own orientation and dictated that of the complex. What is remarkable about a twelve-part windrose is that the ‘‘between the vertices’’ operation allows for the use of three di¤erent types of gnomon. In the case of the first type, one side of the gnomon passes through two consecutive vertices and the other below the next four vertices and through the fifth vertex. In the second case, one side passes below the next and through the second vertex, and the other below the next three vertices and through the fourth (see acb, Figure 19). And in the third case, each side passes below two vertices and through the third, the sides of the gnomon being equal (ac’b, Figure 19). The sides of this last isosceles gnomon correspond, depending on the position of the gnomon, to three di¤erent pairs of perpendicular axes, which in all cases pass through the middle of the arcs of the winds and thus do not follow the prescriptions of the windrose (the position ac’b of the gnomon exemplifies one of the three possible cases of orientation). Exactly the same observation is valid for the first type of gnomon (which is not shown in Figure 19). Only the three pairs of perpendicular axes to which correspond the sides of the second type of gnomon are in accordance with the directions dictated by the windrose (the position acb of the gnomon shows one of the three possible cases). Thus, this it the type of gnomon, which is suitable for the Vitruvian prescription in the case of the twelve-part windrose, and this type does not generate square city blocks. On the basis of a twelve-part windrose, the E-W axis of urban space has three possible orientations with reference to the east. In the first case, it diverges from the east by 15 degrees to the north (which gives for the perpendicular axis a divergence of 15 degrees from the north towards the NW); in the second case, it diverges by 45 degrees to the north or south (both leading to the same pair of perpendicular axes); and in the third, it diverges by 15 degrees to the south (which gives for the perpendicular axis

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Figure 19. Diagram of the twelve-wind and 24-part Dougga windrose. n: The windrose’s north. N: Real north. AA-BB: Main axes of the windrose. XX-YY: Orientation of the axes of the forum and the whole central complex. acb and ac’b: two possible results of the ‘‘between the vertices’’ operation; the first case corresponds to the actual operation

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a divergence of 15 degrees from the north towards the NE). It follows that the dominant divergence of the urban axes from the cardinal directions prescribed by the twelve-part windrose is of 15 degrees. But 15 degrees is the actual divergence (from east to north — cf. acb, Figure 19) of the axes of the complex and the forum from the cardinal points. This fact would lead us to the hypothesis that already at the time when the forum was built, a twelve-part windrose was used as a guide to its orientation. This hypothesis becomes all the more plausible if we take into account that the ratio between the sides of the ideal block generated by the pertinent gnomon is about 0.57, which is almost exactly the same ratio (about 0.53) as that between the sides of the internal, open-air square of the market; incidentally, this ratio simultaneously corroborates Fleury’s interpretation of ‘‘between the vertices.’’ The commemorative windrose would thus be a repetition of an earlier, operational windrose. The last point that remains to be explained is why the correspondence between the urban axes and the earlier windrose was deliberately obscured with the false cardinal points of the new, commemorative windrose — and I use these expressions because an involuntary mistake of 6 degrees is unthinkable. A probable answer is that, through a clockwise turn by 7.5 degrees of the axes of the windrose in respect to the cardinal points (which was not achieved perfectly, since it was limited to 6), it was possible to accomplish a double aim: to preserve the initial guide to urban orientation and at the same time to hint at the Master’s orientation of 22.5 degrees. In Naples, the orientation of the three plateae is E/NE-W/SW and diverges by 24 degrees to the north from the W-E axis — and the same orientation is shown by Alexandria. In each of the Vitruvian pairs of orientations, the plateae may theoretically follow either the meridian or the solar course. In Naples, and Alexandria, they follow the latter, and, as we saw, Fleury believes that this is also the orientation recommended by Vitruvius (on the above, see also Fleury 1990: 173, n. 5). Both Fleury’s interpretation and the hypothesis concerning Naples converge in a solar direction for the plateae, and the latter is in accordance with the fact that, while earlier the cardo was the main axis of the Roman settlement, in the imperial period priority was given to the decumanus (see Mu¨ller 1961: 15– 16). We observe that in Dougga also, the main element of the center, the forum, has a solar direction — while the market is perpendicular to it. 6.

The cosmic man and the cosmic site

According to Empedocles, the four elements form three di¤erent structures. In the first structure, fire as the dominant element — located at the center of the universe — is opposed to the three remaining elements. In

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the second, fire and air, which correspond to light, are opposed to earth and water, darkness. The third structure is not a simple dualistic one, but dualistic and ternary: there are two opposite poles, fire (day) and water (night), and a middle term, air and earth (in-between gradations — Bollack 1965: 238–239). As we already saw, when first referring to the elements, Vitruvius grouped them as fire and water, and earth and air. In the preface of Book VIII, he starts with a brief historical account of the theories on the original element or elements and his reference to the elements follows the sequence water-fire-air-earth (also present in II.II.1). This sequence is comparable to his original grouping. Then he presents the elements in the order air-fire-earth-water, which is totally di¤erent from the above (elsewhere the sequence is again di¤erent). This order is comparable to the grouping of the elements in the second Empedoclean structure, but it is itself unstructured. Vitruvius’s first grouping of the elements could also be considered as related to the third structure of Empedocles: the relation would be that in both cases earth and air compose one group, and Vitruvius’s grouping of fire and water would unite in a single group the two opposite poles of Empedocles (cf. Fleury 1990: 129–130, n. 2); however, no easy justification exists for this latter conjunction of two opposite poles. We may conclude, then, that even though Vitruvius is well acquainted with the Greek theory of the elements, he is not aware of their qualitative structural bonds. Living organisms in general and man in particular constitute for Vitruvius, as for the Greeks, mixtures of the four elements. These mixtures have specific and di¤erent proportions for birds (cf. the element air), fish (cf. water), and terrestrial animals (cf. earth), proportions, which secure their equilibrium and thus their good health. We may conclude that, since man is a composition of the four cosmic elements, he is a microcosm. The condition of this microcosm is dependent for Vitruvius on two kinds of orientation, each of which represents a relation to a cosmic element. The first element is fire, attached to the heat of the sun; when out of proportion, heat destroys the equilibrium of the elements. The second is air, which acts in a similar way: the winds must be well proportioned, that is, not violent but sweet. The tracing of the windrose and the street network, and that of the walls in respect to the sun, are, then, the urban planning devices through which one can regulate the right dose of the corresponding element and thus maintain the cosmic equilibrium in man. Man-as-microcosm also depends on the other two cosmic elements. For Vitruvius, humidity may fill the pores of the body and destroy equilibrium, because the other elements are altered by the liquid element and end up diluted and thus the qualities derived from their correct proportion are dissolved. Exposure to the humidity of the winds may be

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damaging to the organism. But also the natural proportion of earth in the latter may be excessively increased, due to an excess of food, or decreased, and then the other elements are weakened. In general, organisms su¤er or are dissolved by excess or defect of the elements. Thus, the cosmic equilibrium of the substance of man-as-microcosm is secured by the elements and, in relation to them, by the orientation and form of the city. But the site in which the city is located is also of the same nature as man. For Vitruvius (I.IV.4), there are healthy and unhealthy sites, and even in the former organisms become weak from the heat in summer, while even the very unhealthy sites become healthy in winter, because cold strengthens. Fleury (1990: 127, n. 4.1) observes this shift from organism to site and considers that there may have been an omission in the text of a second reference to the organism, because for him it is not literally sites that become solid from cold, but men living in them. But it is quite possible that there is no word missing and the shift is due to the close analogy for Vitruvius between sites and organisms. Such an analogy appears in respect to the winds, since Vitruvius (I.VI.3) writes that protection from them renders a site healthy for organisms in good health. Sites, like organisms, are in fact discussed by Vitruvius in relation to the four elements. As we saw in the beginning of this essay, a site is a function of: – –

– –

Earth, because it must be elevated and provided with good quality pasture. Water, because it must be free from fog and frost, far from marshes (except if certain conditions are fulfilled, including contact with the sea), and provided with good quality water. Fire, because it must be exposed to a temperate orientation, neither hot nor cold. Air, because, when the city is located near marshes, the morning breezes bring to the city the poisonous exhalations of the beasts of the marshes, and because if the winds are cold they wound, if hot they infect, and if humid they are injurious.

We see that the site is in its substance homologous to the organism, since it is composed by the very same four elements and each element must show specific properties. Not only man is a microcosm, but also the site on which the city will be founded. 7.

The cosmic windrose and the cosmic city

In chapter VI on the windrose and the street network, Vitruvius inserts a passage on the calculation of the circumference of the earth. He writes

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that Eratosthenes of Cyrene, using the gnomon, found that the circumference of the earth is 252,000 stades, that is, 31,500,000 paces, and thus the eighth part occupied by each wind is 3,937,500 paces. We may deduce that the circumference of the windrose stands for that of the earth, and its eight-part division figures the distribution of the winds on earth. We also saw that for Vitruvius the winds and the orientations from which they originate constitute an inseparable whole (see also Fleury 1990: 168, n. 8). These orientations are related to celestial phenomena and mainly the course of the sun; the origins of four winds, solanus and favonius, and eurus and africus, are explicitly related to the sunrise and the sunset. We also note that aquilo (the NE wind) is symmetrical to eurus (SE) with respect to the east and, since eurus is associated (very approximately) with the winter sunrise, aquilo was surely associated with the summer solsticial sunrise. For similar reasons, caurus should have been associated with the summer sunset. The remaining two winds, auster and septentrio, are both associated with the meridian line, traced in function of the course of the sun (but north was also the direction of the pole star). In Book VI (I.5), Vitruvius gives an image of the universe, according to which the upper and lower parts of the universe meet on a circumference located on the plane which also includes the horizontal section of the earth (and passes through its center); this circumference is the celestial horizon (see also Gros 2001: 22). The horizon extends as a circle between east and west and is naturally level. We may deduce that the trajectory of the sun touches this horizon, the sunrises and the sunsets being points on it. After the reference to these two cardinal points, Vitruvius traces a straight line from north to south. The fact that the circumference of the earth is concentric to the celestial horizon, and the similarity between the windrose and the circle of the horizon including the cardinal points, lead to the conclusion that the windrose also connotes the horizontal section of the universe, that is, it is an abridged cosmogram. It is on this circumference that the origins of the winds and the trajectory of the sun meet. Describing the windrose, Vitruvius uses the right versus left opposition. After the definition of the eighths of the south and of the north on the windrose, the rest of its circumference is divided into three equal parts to the right and then three to the left. When referring to the 24-wind windrose, he also uses the same opposition in order to define the positions of the new winds he adds. In the case of the eight-wind rose, if Figure 1 was drawn by Vitruvius himself (which is however debatable; see Gros 1988: 58), and since north is above, the eastern part corresponds to the right and the western to the left. In the case of the 24-wind rose, he is looking from the periphery towards the center and, using as reference the eight

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directions, he relates to each one of them two winds, always starting with the one to the right (see also Fleury 1990: 178, n. 1). In both cases, there is a middle term between right and left, the meridian in the first case, one of the eight winds in the second. In this latter case, he starts from the south, as he also does with the tracing of the parts of his windrose, and proceeds clockwise, both in his general movement and in the partial right-to-left movements. He follows the same movement in his description of the four winds, only that here he starts from the east; and a neighboring starting point together with the clockwise direction are used in his description of the four intermediary winds that leads to the eight winds. According to Frontinus and Hyginus, the Etruscan augurs, the haruspices, divided earth into a right northern part and a left southern part; thus, we can deduce that the dividing line, the E-W axis, corresponded to the apparent course of the sun (see Fleury 1990: 160, n. 4). According to Pliny the Elder, the Etruscans divided the celestial circle into sixteen parts — i.e., an eight-part division subdivided into equal halves — arranged around two main axes orientated N-S and E-W, the former being the principal one; the angles of the sectors are equal to 22.5 degrees. The line of view was from north to south, and there was a left, eastern and favorable part and a right, western and unfavorable one (Figure 20). The same north-to-south direction, or one towards the east, was used by the Roman priests during the foundation rite of a settlement, when they projected the celestial templum on earth, as well as by the surveyors (Mu¨ller 1961: 26, 38–45).

Figure 20. The Etruscan division of the celestial circle: 1: Left, eastern and favorable part. 2: Right, western and unfavorable part

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If we compare Vitruvius’s windrose with the above, we see that: a.

b.

c.

d.

The Vitruvian windrose is geometrically close to the Etruscan celestial circle as described by Pliny, and the divergence of 22.5 degrees from the cardinal directions for the streets that derives from his windrose corresponds to divisions of this circle, that is, the directions he prescribes are in a manner related to tradition (see also Paulys Realencyclopa¨die 1958: Winde, 2 373). The clockwise movement accompanying this and the other windroses can be associated with this Etruscan circle, because it coincides with the apparent movement of the sun. However, the tracing of the moat dug around the Roman and probably the Etruscan settlement (sulcus primigenius) followed an anticlockwise direction (sinistratio). The emphasis on south, and generally in his windroses on south or east, is comparable to that on south or east by the Etruscans and the Romans. His right-left opposition, while in its general form the same as the one of the Etruscan circle, seems to valorize semantically the right,11 while the Etruscans valorized the left. However, in both cases, the valorized part is the eastern part, provided Figure 1 is due to Vitruvius or at least corresponds to his own figure.

The similarity of the Vitruvian windrose with the Etruscan celestial circle, on the one hand adds new evidence for its cosmic nature, and on the other shows its integration into the Etruscan and Roman tradition. Simultaneously, this integration reveals the continuity between his windrose and the Italian urban planning tradition. In fact, during the traditional foundation rite of a settlement, the augur was seeking to project the celestial templum on earth. To do that, he would sit on a stone, which was thought of as attached to the center of the universe. The form of the earthly templum, the projection on earth of the celestial templum, included two perpendicular oriented axes, symbolically identical with those of the celestial circle. The templum was one of the elements linking the settlement to the universe. The Roman foundation rite was in all probability the continuation of the Etruscan rite. It was composed of three parts: inauguratio, limitatio, and consecratio, and the creation of the templum was the nucleus of inauguratio. The cardo and the decumanus of the settlement followed the axes of the templum. Given the contiguity of the forum with the intersection of these main streets of the settlement, the templum was linked to the forum (see, for example, Mu¨ller 1961: 17–21, 24–35, 39–45; Rykwert 1976: 46–50, 90–91). It becomes, I believe, clear that not only the form of the windrose, but also its function derive from the templum tradition. The windrose

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represents Vitruvius’s reinterpretation and rationalization of a long tradition, a kind of technocratic view on tradition. It is intended to replace the traditional templum with a new one, having a similar form, the same function — to guide the orientation of the street network — and the same location in relation to the forum, as the example of Dougga indicates. The templum was intended to bring the order of the universe down to the earth, and into the street network and the settlement. The cosmic windrose of Vitruvius should have the same aim, with the di¤erence that it is explicit about a practical matter, the salubrity of the city, and leaves in the background the symbolic matters and the cosmic code. In the same way as the traditional settlement emerges from the cosmic templum, his grid-plan city — but even if it was radial-concentric the case would be the same — emerges from the cosmic windrose. This city then is cosmic, and ought to be so, because, as we saw, the Roman city was cosmic.

8.

The laws of nature: The cosmic and the aesthetic

Vitruvius’s windrose intends to show the distribution of the winds and this was also the interpretation of its commentators. I have tried to show that this denotative ‘‘aeolian’’ code was the product and the vehicle of a connotative cosmic code, a relation mediated by orientation, which is mainly related to one astral subcode of the cosmic code, the solar code. Hence, we may restate the nature of his windrose: it shows the dynamic structuring in the universe of the element air, in close connection with the movement of the sun. Before dealing with another crucial connotative code of the windrose, the aesthetic code, I shall try to show the indissoluble link between the cosmic and the aesthetic, by having recourse as a privileged standpoint to the conception of the laws of nature in Vitruvius’s work. Following the Greeks, Vitruvius explains the nature and the birth of the wind (I.VI.2). Wind is a flux of air and air has waves (VIII.II: 1 and 2). Wind rises when heat strikes the humid element and this pressure produces a violent current. Vitruvius refers us for verification to spherical (see Fleury 1990: 154, n. 6) Aeoluses of bronze. These Aeoluses represent, as Vitruvius writes, the divine reality of the secret laws of the celestial system, the great natural causalities, which regulate the skies and the winds. Vitruvius here elaborates on the relation between the cosmic elements: the movement of the air is produced by an internal dynamics of the couple of fire and water. We also see once more that the dynamics of the wind is coextensive with the universe; it is ruled, together with the skies, by the laws of the universe.

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From the sphere to the cube. Vitruvius (V.Praef.: 3–5) writes that Pythagoras and his sect formulated their rules in texts, which were related to a cube. He defines the cube as a body with all its edges equal and its faces square, which, when it is thrown, remains stable and immobile whatever face it rests on. For our author, the Pythagoreans related the length of a written work to a cube: the work should have no more than three cubes, the cube equaling 216 lines. This number of lines makes the memory stable in the manner of the stability of the cube. These things, he writes, have been observed by our forefathers in the order of nature. The latter term thus refers to a geometrical figure and its properties, as well as to a number attached to the cube. After the above preface, Vitruvius (V.I: 1–3) describes the forum. In Italy, he writes, the forum is used for gladiatorial shows and is surrounded by colonnades, and balconies on the upper floors. The upper columns must be a quarter less than the lower ones, because the latter bear more weight. Writing on the foundation of buildings (III.IV.1), he states that we must seek if possible to reach solid soil. Above the ground, we build walls and on these columns. These walls must be thicker by one-half than the columns, because they receive a greater load. Both these prescriptions aim at solidity and this latter is legitimized with a metaphor from nature (Gros 1990: 128, n. 6). Thus, in the first passage Vitruvius explains that the change in the diameter of the columns imitates the natural growth of trees and, if the higher part of a thing is narrower than the lower, it is rightly arranged both as to height and thickness. According to J.J. Pollitt (1974: 69–70), Vitruvius holds in general that art must seek its prototypes in nature, and this idea is a corollary of the Hellenistic decor theory, which he applied to architecture. The solidity of a building, then, transfers to the building a regularity found in trees, and thus we are dealing with the imitation of a natural model. According to Vitruvius, this model is thicker at the roots and then gradually diminishes towards the summit. Not only is thickness a function of height, a fully formulated qualitative proportional rule, but also in the modeled object this rule takes on a quantitative expression. The regularity embodied by the tree is not vague, but it is a rule of a specific kind, which can then be applied to a building using mathematical proportions: it has all the necessary characteristics with which Vitruvius would define a law of nature. From the trees to the animal world. We saw that the good health of the various kinds of leaving creatures is due to the specific proportions in each of them of the four cosmic elements. Thus, the cosmic interplay of the elements, active in the universe, is transferred into the individual organisms, including man, and acquires in each case a di¤erent structure.

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We may speak about structural variants and transformations. The organism is the field of a specific structuring of the cosmic elements: the laws of nature are integrated into the laws of the universe, as was also the case with the wind. Similarly, as I tried to show, the site is a composition of the four elements and thus it is governed by the same laws. The cosmic order is manifested in man in its aspect of isonomia. Man is also the vehicle of symmetria. We read in chapter I (1–4) of Book III that a temple cannot but follow symmetria, which characterizes the members of a rightly shaped man. Nature has shaped the human body according to certain norms. The navel is the center of the body. If a man lies on his back with hands and legs spread diagonally, and we consider his navel as the center of a circle, the circumference will pass from the extremities of his fingers and toes. As Gros observes (1990: 66, n. 3 and 2001: 22), the inscription within a circle or a sphere demonstrates the accomplishment and perfection of a composition. But also, writes Vitruvius, we discover a square: the height from the soles of the feet to the top of the head is equal to the width of the outstretched hands (III.I: 3–4). Gros (1990: 67, n. 4) notes here that Vitruvius establishes an implicit relation of equivalence between the two geometrical figures, but does not specify any kind of geometrical relation between them; Gros comments that their relation, i.e., the squaring of the circle, is one of the obsessional themes of ancient geometry. The conclusion that Vitruvius draws from the presentation of the rules that the body obeys is twofold: first, that nature has composed the body in such a manner that its individual members hold proportional relations to its total form; and second, that this is why the Ancients established the principle that there must be a perfect proportional correspondence between the members and the whole of a work (see also III.I.9). Gros (1990: 70, n. 3) also points out that Vitruvius’s views on the circle and the square add meaning to the concept of the totality of a work; the inscription of a facade or volume within a simple geometrical form reveals to the eyes of the observer the value and harmony of symmetria. To come back to the main line of the argument, nature shaped the human body according to symmetria, and buildings, especially temples, must imitate the body by following the principle of symmetria (see also Gros 2001: 17). The laws of nature thus have an aspect, which is quantitative and proportional. They give to the body the symmetrical property of eurythmia, that is, a graceful semblance, and lay the foundations for the beauty of buildings: (quasi-) aesthetics derives from the laws of nature (see also Brown 1963: 106). From the body and the building to the machine. For Vitruvius (X.I.4), every machine originates in nature and its principle is based on the rota-

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tion of the universe. The observation of the planets shows that their rotation is regulated by mechanical laws. The forefathers imitated the precedents of nature and were inspired by the divine works, developing useful applications. We thus learn that the laws of the universe are of a mechanical nature and they are incorporated into machines. Let us examine these machines more closely. Writing about the machines of traction, that is, for raising loads, Vitruvius (X.III.1) states that the principles of their motion are two di¤erent and cooperating principles: the straight line and the circle. Louis Callebat and Philippe Fleury (1986: 114–115, n. 3 and 115, n. 1) note that these two concepts are not used here in their dynamic sense, but the straight line coincides with the axis of rotation and the circle with a circumference. If we relate the line-axis to the universe, we recognize in the line the cardo, the (immobile) axis of rotation of the universe, the one extremity of which is in the north, in the highest point of the universe relative to the earth and beyond even the stars of the Great Bear, and the opposite extremity under the earth in the south (VI.I: 5 and 6, and IX.I: 2–4) — cf. Soubiran 1969: 75–76, n. 8 and 10. But then we may relate the circle to the rotation of the universe and the planets. For Vitruvius, the universe is the supreme container of everything that belongs to nature and is coincidental with the spherical heavens (cf. Soubiran 1969: 74–75, n. 6 and 7). The two poles of the cardo were placed as centers by the power of nature. Nature also installed the (immobile) earth — and the sea — in the central place of the universe, and placed a wide circular zone, transversal to the cardo, equidistant from the poles and inclined towards the south, which is constituted by the twelve signs (of the zodiac), that is, the distribution of the stars into twelve equal parts. The movement of these signs is subject to the immutable laws of the rotation of the heavens. The inventions, which protect against danger are the scorpions and the ballistae (X: X and XI). They are both regulated by symmetria. Concerning the scorpions — which throw arrows — all their dimensions are calculated on the basis of the length of the arrow used: the ninth of it defines the diameter of each of the four openings in the frame of the scorpion — in front and above the ground — in which twisted cords are stretched. This diameter is in turn the unit for all the measurements of the scorpion. The same logic is applied to the ballistae: their measurements are again referred to a unit that is the diameter of holes, this diameter depending now on the weight of the stone to be thrown. Vitruvius adds that the necessary calculations cannot be done by just anybody, but only by those who have a sound knowledge of the geometrical treatment of numbers and their multiples. In his very first book, he had already stated the same presupposition, there accomplished through music: the architect

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must know music in order to be familiar with mathematical relations and be able to adjust the ballistae, catapults, and scorpions (I.I.8).12 As in the case of architecture, where symmetria is complemented by eurythmia, the system of symmetria for the scorpions is complemented by a similar principle of adaptation, allowing for corrections through addition or subtraction. The discussion above leads to the following conclusions concerning the universal laws of nature: a. b. c. d.

e.

f. g.

The laws of nature are the laws regulating the skies and the universe, which have a divine origin. They are attached to the four cosmic elements. Dynamically, they are natural causalities and of a mechanical nature. Statically, they consist in: i. Proportional relations, quantitative and qualitative; ii. numbers with characteristic properties; iii. geometrical figures and qualities. More specifically, they regulate the rotation of the planets and the stars, the winds and the sites, the animal world and the trees, and the health and form of man They must be imitated by the works of man: buildings and machines. They cause the beauty of the human body and by extension of buildings, which imitate it. (see also Gros 1990: LIII)

The conclusion is that, exactly as for the Pythagoreans, so for Vitruvius there is a cosmic order connected to the four elements and founded on number and proportion, of which symmetria is the (quasi-) aesthetic aspect; quasi-aesthetic, because this is not a pure aesthetics but a cosmic aesthetics: objective beauty is not a subjectively pleasing quality, but the result of the application of the laws governing the cosmos. Vitruvius’s city, as a work of man and as a cosmic city, cannot but incorporate the laws of nature and symmetria, and as a model for built space it should have the attribute of beauty. The model for this city, the windrose, since it shows the dynamic structuring of the cosmic element air, should also show symmetria (cf. Steckner 1984: 269). I shall examine these matters in the next and last section.

9.

The aesthetic city and the aesthetic windrose

It is common knowledge in semiotics that a text delivers its complete meaning only when it is read within its context. The isolation of the urban planning theory of Vitruvius from the rest of his work, understandable as it is due to the specialized interests of the scholars working on this matter,

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has led to a partial — to say the least — understanding of the meaning, the layers of signification that envelop his proposed city. The cosmic richness of the latter has with very few exceptions passed unnoticed, and the same is true of its aesthetics. For example, the excellent French historian of urban planning Pierre Lavedan (Lavedan and Hugueney 1966: 362– 363) retains only the obvious, the salubrity factor, in Vitruvius’s urban proposal and the resulting orientation of the streets; as for aesthetics, he finds it only in the rules of proportion and symmetria for individual buildings. Fleury himself writes (1990: CIII) that aesthetic considerations are totally absent from the Vitruvian city — and the interests of Caesar and Octavian in the renovation of Rome ignored — and he tries to justify this presumed lack by stating that the description of the city is in an abridged form, and the intended readers of the work were not architects, but clients. There have been some attempts to define Vitruvius’s urban aesthetics, but they do not refer to his proposed city. In an unpublished paper, Gros, based on the description Vitruvius gives (II.VIII: 11 and 13) of the site and arrangement of the city of Halicarnassus, concludes that this allows us to form an idea of how Vitruvius conceives the beautiful urban landscape (see Fleury 1990: XCIV, n. 60). And Fleury (1990: 151, n. 5) adds to the brief catalogue of scholarship on Vitruvius’s conception of urban beauty by referring to the opinion of Vitruvius (I.VI.1) that the town of Mytilene on the island of Lesvos is built with magnificence and elegance. We may, however, have a more concrete and deeper grasp of Vitruvius’s urban aesthetics by a contextual work on his urban proposal. As we saw, his city is implicitly or explicitly connected to a square. The square had two major and interrelated qualities. First, it was considered as one of the fundamental geometrical figures and a constituent of the cube. Second, it had attracted attention that the ratio of any two sides of a square is equal to one, the first integral number. The importance of these qualities makes it plausible that they are consciously incorporated in Vitruvius’s urban square. If this is so, his proposal must be integrally related to proportion and to the aesthetics of the square. The square is also the unitary, generative and constantly repeated element of the city.13 The possibility that this square is semantized with an aesthetic code increases further from its inscription within a circle. For the Pythagoreans, beauty derives from simplicity, regularity, and order. This frequently implies reference to a center and uniformity around it, a pattern, which attains perfection with the circle and the sphere (Schlikker 1940: 67). For Vitruvius also, not only is the circle as such perfect, but the combination of the circle and the square marks his aesthetics of the body.

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In fact, the geometrical complex of the windrose-cum-city is almost the same as the geometry accompanying the human body (cf. Gros 1990: 172, n. 2). The geometry of the windrose is based on a center, the combination of a circle and a square, the perpendicular axes of the former and of the latter, and radii (identified with the semi-axes). These same elements, in a less rigid geometrical form, accompany the human body: the navel as center, the circle and the square, the perpendicular axes of the circle formed by the diagonally spread members, which also correspond to radii, and the perpendicular axes of the square, formed by the height of the body and the outstretched hands (though the four parts of these axes are not all equal). With the windrose Vitruvius gives a specific geometrical relation between the two figures of circle and square,14 as he did not do in their encounter when delimiting the extremities of man. We get the impression that the windrose allowed Vitruvius to formulate a perfect geometrical complex, to which he also assimilates the body, although the constraints of the latter forced him to a looser conceptualization. The aesthetic perfection surrounding the urban competes with that of the body. The above inscription of the urban leading to a coherent combination of two perfect geometrical figures crowns, to use Gros’s observation on the circle, its meaning as a totality incorporating symmetria and reveals its beauty. But there is even more symmetria in the windrose. Vitruvius (III.I: 5–9), wanting to found the units of measurement on nature, makes reference to the perfect number of the Greeks, the number ten; this number he considers perfect because it follows from the number of the fingers of the two hands. Let us recall here that ten was the perfect number for the Pythagoreans (called also ‘‘memory’’) and is also the number of the books of Vitruvius’s own work. Concerning this last point, Alexander Kessissoglu argues that Vitruvius in the organization of his work followed the Pythagoreans, who used to divide the elaboration of a subject into ten parts, and when they could not attain this number with the pertinent material they did so with borrowings from adjacent subjects. The latter would be the case, according to Kessissoglu, with Vitruvius, since of his ten books only the first seven concern architecture in the narrow sense, as Vitruvius himself testifies (Kessissoglu 1993: 100, 101–102, 114). But, on the other hand, Vitruvius is explicit that architecture is composed of three parts: building (see Books I–VII), horology (Book IX) and mechanics (Book X) — see I.III.1. Of course, horology and mechanics mainly concern engineers, but as we saw there was no strict division in antiquity between engineers and architects. Now, Book VIII revolves around hydrology and hydraulics. A limited part of it, concerning aqueducts and similar matters, is related to building, but its major part, a trea-

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tise on water, is in fact very loosely related to it (Callebat 1973: VII–X; see also Fleury 1990: 121–122, n. 1). Given the above, Kessissoglu’s view on the number of books is sound, but his argument concerning the artificial completion of this number in Vitruvius’s work is rather weak. On the matter of the perfection of the number ten, Vitruvius also mentions Plato and contrasts his view with that of the ‘‘Mathematicians’’ — the neo-Pythagoreans and the Euclideans as distinguished from the Pythagoreans — for whom the perfect number was six (see also Gros 1976: 689–700, 1990: 73, n. 1 and 2001: 18). Both numbers influenced his windrose, as I shall argue immediately below. Vitruvius goes on to present different numerical qualities of six; one of these is that if one-third of six is added to this number we get eight. According to Gros (1990: 74, n. 5), Vitruvius may here be misunderstanding the Greeks, mistaking numbers for relations; he points out, however, that Vitruvius’s source was reliable. Six would be perfect also because it is found in the human body: the foot is one-sixth of the height, and the cubit consists of six palms or twentyfour fingers (III.1: 5–7). Vitruvius knew that six was the foundation of the principle, which he attributes to the Pythagoreans, that a text should be no more than three cubes long, because the number of 216 lines of the cube corresponds to the volume of a cube with an edge having a length of six ð216 ¼ 6 3 Þ; this cube was called by the Pythagoreans sjairik´ov , (spherical), because 216 ends with six, and apokatastatik´ov, because, since each edge of it equals six units, it shows everywhere the same perfection (see Kessissoglu 1993: 103). Later, as Vitruvius explains, the ancestors combined these two perfect numbers into one ‘‘most perfect’’ number, sixteen. It originates from the foot, because the foot equals sixteen fingers (III.1.8).15 We see that the foot is the common locus of the perfection of six and sixteen. The body, through the unit (and sub-units) of measurement it provides and the proportions within and between its parts and between them and the whole, which are related to this unit, delivers the perfect numbers and articulates the system of measurement and symmetria (cf. III.1.9; see also Gros 1990: 65, n. 7). We should recall here the Etruscan division of the celestial circle into sixteen parts. On this basis, the number sixteen would not only be derived from the body, but also from the universe. We may conclude that Vitruvius’s eight-part and octagonal windrose was considered by him to be related to the most perfect number, sixteen, both because of the numerical relation between eight and sixteen (16:2 ¼ 8), and because he arrives at its form through a notional sixteen-sided polygon. Thus, the windrose seems to incorporate sixteen in an indirect manner, and it also probably incorporates indirectly the number six, in the form of the , ep´itritov (6 þ 1/3
6 ¼ 8).

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Thus, we conclude that the Vitruvian windrose is founded on perfect numbers, just as are the body and the universe. As in the case of the body, it articulates them with a geometry including a unit of measurement and symmetria. The unit is the radius of the circle. The symmetria is that there are eight parts (delimited on each side by the unit), all parts are equal and each part is an eighth of the whole. The special value of the number eighth for Vitruvius is not only attested by the windrose. Speaking about the tracing of the volute of the Ionic capital (III.V.6), Vitruvius uses the term tetrans. According to Gros (1990: 162, n. 4), it refers to each of the four equal segments of two perpendicular axes dividing a circle or a square into four equal parts. In this interpretation, Gros follows Burkhardt Wesenberg (1983: 135–137). He compares, after him, this passage with X.VI.1, which concerns one of the machines for raising water. A wooden beam is rounded by a compass. At the two extremities, the circumference will be divided by a compass into eight sectors through tetrantes and octantes. According to Wesenberg, the four octants are the segments of two perpendicular axes at a 45-degree angle to two initial perpendicular axes, which form the four tetrantes. Callebat and Fleury (1986: 155, n. 4) accept the interpretation that these terms indicate arcs of a circle. In either case, the existence of these terms shows the marked character, for Vitruvius, of divisions in four and then eight parts. Vitruvius was undoubtedly conscious of the relation between the geometrical complexes of the city and the body. A building, for him, follows the same rules as the body, being regulated by the laws of the universe. A theatre must follow acoustic principles and these are related to the music of the universe (see also Brown 1963: 105). Would it ever be possible that the city, built space just as the building (see also Knell 1985: 37), should not follow the same imperatives? This geometrical homology between the urban-in-context (the windrose), the body-in-context (the circle and the square), and the cosmic, in the context of which the two first obey the laws of the third (cf. Gros 2001: 18), is to be compared to the homology in substance between site and organism deriving from the structure of the cosmic elements. To conclude, the Vitruvian city is isomorphic to the structure of an anthropomorphic code and depends on two major symbolic codes: a cosmic and a (quasi-) aesthetic code (see also Lagopoulos 2000). An important recent text by Gros investigates precisely the relationship established by Vitruvius between the body on the one hand, and the cosmic and the aesthetic on the other. Gros argues that Vitruvius relates the body to two purely abstract geometrical figures considered as perfect (an operation he opposes to the reality of the living, three-dimensional body), which follow from and complement the numerical symmetria; the concep-

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tion of these figures as perfect would be due to the influence of texts of Platonic inspiration. Just as the architectural work before its material manifestation seems to take shape, for Vitruvius, in architectural drawings incorporating abstract ideas, so the abstract geometry of the body follows from the speculative domain. According to Gros, Vitruvius in order to legitimize architecture has recourse to the Platonic creator and cosmogony. The cosmic elements are symbolized in Timaeus by regular polyhedrons, among which are the cube (earth) and the dodecahedron (universe), the closest to the sphere. For Gros, in the Platonic tradition the phases of the polyhedrons are considered as standing for the whole of the latter, and the square was assimilated to the earth and the circle to the sky. Thus, if the number six for Vitruvius relates the body to the cube, allowing in this manner for the transition from numbers to geometry, the same relationship is also achieved by the square, while the circle relates the body to the sphere: the perfect man partakes of both the earth and the sky. This conception, which for Gros represents the high point of Vitruvius’s speculation, shows the coherence that exists in the work of Vitruvius between the body and the cosmic and aesthetic dimensions (Gros 2001: 15, 17–21). It seems to me that, with very few exceptions, almost all modern scholars who have discussed the Vitruvian city read too narrowly the account of Vitruvius, concentrating exclusively on the text (I. VI) or on its narrow context (I: IV–VII), at the expense of the wider context, and on the literal at the expense of the symbolic, i.e., connotation. In fact, there are two consecutive contexts for the city plan of Vitruvius: the narrow one, which is the rest of his planning theory, and the wider, his whole work. The combination of the lack of the wider context with a literal reading leads to a reading imprisoned in Vitruvius’s denotative urban discourse and the conclusion that his proposed city responds to practical preoccupations concerning first salubrity and then defense. Such a reading is guided by rational thought, the rediscovery of the Renaissance. But modern rational thought is a tool wide open to Eurocentric extrapolations and interpretations. Among the very few exceptions to the rationalist interpretation of Vitruvius, in addition to the above-mentioned article by Gros, is an excellent article by Paolo Marconi (1972). Marconi observes that during the Renaissance, particularly in the architectural treatises of the quattrocento, cosmography influenced the form of the city. He shows the intense interest of the Renaissance in the figure of the homo ad circulum, representing man as a microcosm, and argues that it o¤ered the model for the circular city extending around a sacred navel. It is this man-asmicrocosm, according to Marconi, which inspired the four-part cities,

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organized around a cross and having a marked center. This figure is also behind the cosmogram composed of two crosses with a common center, turned by 45 degrees to each other and accompanied by the squares of which they are the diagonals. A square inscribed diagonally within a circle, its diagonals forming a cross, is a cosmogram, and the same holds for the city plans incorporating a sixteen-part division of the horizon. In the above context Marconi analyzes the urban proposals of Alberti, Filarete, Martini and Fra Giocondo, to whom I also made reference earlier. He also discusses the case of Cesare Cesariano. For Marconi, Cesariano establishes a close connection between the homo ad circulum (combined with the homo ad quadratum), who has his navel as center and articulates a two-cross and two-square composition inscribed within a circle, and cosmograms based on Vitruvius’s first Book; it is from there that Cesariano’s radial city emanates, with its eight main sectors, sixteen sub-sectors and twenty-four directions. Marconi argues that these ideas, figures, and city plans are derived from Vitruvius’s views. In fact, on the one hand he takes the position that the man-as-microcosm theory of classical antiquity, also present in Plato’s Timaeus, passed into the Middle Ages and then the Renaissance, and observes that Vitruvius’s version was influential during the latter. On the other, he points out that the idea of the relation between cosmography — itself inseparable from the man-as-microcosm concept — and the city, as well as the plan of the city, were inherited by the Middle Ages and the Renaissance from Vitruvius. I cannot but agree with Marconi that the influence of Vitruvius on Renaissance urban planning was major. And in fact his ideas, figures and city plan were a major — but not the only — source of inspiration for the Renaissance. Marconi finds a continuity between the sacred center of the Rome of Romulus, its mundus, which was the umbilicus urbis, and the navel of Vitruvius’s figure of the homo ad circulum; he also identifies the circle surrounding homo with the horizon, without however extending on this argument. Concerning the comparable figure of the windrose, Marconi stresses in its construction the circle, the pattern of the inscribed square and the divisions of the windrose into eight and sixteen parts. He considers that the square within a circle is the preeminent cosmological diagram of the first Book and that the importance given to the orientation of the city parallels that given to the relation between the city and cosmography. The comparison between the homo ad circulum and the windrose leads Marconi to conclude that Vitruvius applies to the city the theory of the microcosm. What I feel is missing from Marconi’s argumentation is the systematic evidence from Vitruvius’s work that would support it. This is what I have

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attempted with the present essay. I have tried, through a semiotic analysis, to articulate the text of Vitruvius on the city plan with its contexts and his concern for the symbolic level. My conclusion is that behind Vitruvius’s urban text and his literal urban discourse there is a subtext — or rather a super-text — a worldview, as Gros puts it (2001: 22), and a connotative discourse; and behind the codes of salubrity and defense there are the connotative cosmic and aesthetic codes and a connection to the anthropomorphic code. These codes are closely related to each other and unified by the laws of the universe and the sacredness attached to it. Their shared quality of symmetria o¤ers Vitruvius an ontological anchoring for building and the city (see also Grassi 1962: 163). Thus, the above codes are not simple additions to, nor peripheral extensions or decorations of, the urban text. They are, in Vitruvius’s discourse, the hidden prime movers of the urban, and structure the nucleus of his (borrowed) ideology on built space.

Notes *

I should like to express my warm thanks to Professor Pierre Gros, who had the patience to read my text carefully more than once and whose penetrating observations were of great help to me. 1. This study represents a much-expanded version of a paper delivered at the 1998 Urbino colloquium of the International Association for the Semiotics of Space (see Lagopoulos 2000). 2. Lise Bek (1985) develops interesting ideas on the actualization of eurythmia in Roman architecture and urban planning. According to Bek, eurythmia was a principle already used in the Hellenistic period for temples and in urban planning, where it took the form of the panoramic view. However, the form that eurythmia was given in the work of Vitruvius (or maybe earlier) was that of the stricter ‘‘view planning.’’ The latter may be observed and is predominant in domestic architecture, and derives from the use of ‘‘optical axiality,’’ that is, the determination of a visual axis depending on the viewer. For Bek, the descriptions of the Roman authors — from which she drew her above conclusion — refer to the visual impression created by a building in its environment, a garden, the interior of a building or the sight from inside outwards, an impression accompanied by semantic oppositions. She believes that this approach is similar to the conception with which these buildings were realized. View planning was a purely aesthetic principle referring to the ‘‘elevation’’ (by which she means the visual image) and was not restricted to isolated buildings, but also extended to building complexes, more specifically the forum. Bek opposes this emphasis on the viewer to the interest in the strict geometrical organization of the ground plan, related to symmetria. According to her, in the monumental architecture of the imperial period the two coexist, but optical axiality tends to coincide with the geometrical axis of the ground plan. Bek reminds us that Vitruvius states that in the temples, erected for the eternal gods, symmetria must be observed as

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closely as possible. She rightly thinks that eurythmia did not influence the Roman city plan; according to her, the latter was a sacred ground ruled by symmetria (which is true, but for the Greek city) as Vitruvius defines it, through the partition into streets, squares and insulae. The building complexes in the cityscape, ruled by eurythmia, should be considered as a visualization of the city plan, and thus the harmony of symmetria would be perceptible to the viewer; view planning would correspond to the visual expression of the sacredness of the city. Thus, the city would be situated mid-way between the sacred temple ruled by symmetria and profane domestic architecture ruled by eurythmia, being both the sacred ground of eternity and the setting for daily life. 3. Friedrich Wilhelm Schlikker (1940: 74–77) believes that eurythmia cannot be identified with the visual correction of symmetria and that such correction is just one case of eurythmia. However, Vitruvius seems to generally hold this view; Schlikker apparently extrapolates (see also 1940: 70–71) from the Peripatetics to Vitruvius. 4. In a perceptive article, Gros (1976: for example, 672, 673, 675, 685, 690–692, 693–694, 695) reminds us that Vitruvius uses simple numerical relations — and these in fact correspond to the original meaning of symmetria. However, Gros shows that some of them are simplifications corresponding to an earlier use of irrational numbers. He attributes the tendency to use irrational numbers as numerical relations to Vitruvius’s lack of familiarity with irrational numbers, which are related to geometrical constructions. According to Schlikker (1940: 66), this latter relation was discovered in Greece at the end of the fifth century BC and this aspect of geometry opposes it to symmetria. But, following him, during the next century relations including irrational numbers were integrated into symmetria. Herman Geertman disagrees with the conclusion of Gros concerning Vitruvius’s unfamiliarity with irrational numbers. Geertman agrees with Gros that in the three cases he comments upon — which refer to elements of columns — Vitruvius translates geometrical procedures to numerical relations and concedes that the latter occasionally show a lack of comprehension of geometrical construction. Discussing generally the use of geometry in architecture by the Greeks and the Romans, Geertman makes a distinction between the direct application of geometrical figures, that is, the initial tracing of a building by using a geometrical figure, and a conception in terms of geometrical figures which is, however, materialized with numerical means. He relates the numerical approach to geometry to persons like Plato and Eudoxus and he argues that in architecture the numerical system is found together with the geometrical system in five houses from Pompeii and three temples in Asia Minor, all from the third century BC. He concludes that the use of a numerical system derived from geometry was then current practice; the numerical equivalents of geometrical proportions would be derived on the basis of fixed rules. Now, according to Geertman, Vitruvius considered geometry too complex to use as a guide and felt that numerical relations o¤er a clearer picture. Geertman concedes that, compared to the above Hellenistic system, the numerical relations Vitruvius formulates present gaps and fail to represent adequately the original geometrical system, depriving it of its structure. He believes, nevertheless, that the same comparison shows that Vitruvius’s relations are derived from geometry. In this case, Vitruvius would not himself perform forced simplifications of a pure Hellenistic geometrical system, but he would be following Hellenistic numerical constructions; he did not introduce a new system, but oversimplified traditional knowledge. Geertman also concludes that Vitruvius was familiar with the architectural systems based on the direct application of geometry (Geertman 1984a: 33, 52 and 1984b: 54, 57–58).

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6.

7.

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Despite his very thorough study of ancient architecture, I do not think that Geertman’s disagreement with Gros is convincing. We can infer from Gros that Vitruvius was aware of the issue of geometry and the irrational numbers, but what Gros argues is that he was not in a position to handle it. Gros complements this position with another one: Vitruvius would believe that only numerical relations deliver the pure laws of architecture (Gros 1988: 55–56). While Geertman compares the numerical relations presented by Vitruvius to his convincingly inferred Hellenistic system and concludes that they do not correspond well to the original geometrical system, he nevertheless believes that Vitruvius was familiar with the latter. But even if Vitruvius’s sources included such a system — and we do not know in this case to what degree a geometrical system might have been present in those sources — his data, with the drawbacks that Geertman himself notes, do not allow us to conclude that, beyond the numerical system, Vitruvius had mastered geometry and irrational numbers. Knell’s representation of what he considers to be Vitruvius’s holistic conception places symmetria in the center and sees eurythmia as the integrator of the system. Between these two, one group evolves from symmetria to ordering and disposition, on the grounds that symmetria refers to the former and makes possible the latter; and another group evolves from the same starting point to appropriateness, through its relation to symmetria, and distribution, which he understands as part of appropriateness. As for Scranton, he starts from Watzinger’s observation about the division of the six concepts into two groups, the one referring to activities and the other to qualities, and proposes the sequence symmetria, eurythmia, and appropriateness, followed by disposition, ordering, and distribution. In his excellent study on ancient Greek and Roman winds, Karl Nielsen argues that from the first century BC we find in antiquity two competing windrose systems: the twelve-part windrose of Timosthenes, the admiral of Ptolemy II Philadelphus, and the eight-part windrose of an unknown author. The first is a developed form of Aristotles’s windrose and fully geometrical, that is, divided in equal parts, without introducing irregularities due to the points of the solstices. The second is equally geometrical, derived from the equal division of four quadrants and thus related to a regular octagon. It is this second, Hellenistic, windrose, which was borrowed by Vitruvius (Nielsen 1945: 41–42, 46–49, 74–75). The twenty-four winds are for Vitruvius produced by the eight main winds, through their variations in the very large space where they blow, caused by changes in direction and leaps. Based on Vitruvius’s description of the twenty-four winds and his logic concerning the eight winds, there is no doubt that the former are arranged symmetrically as to the two main axes N-S and E-W. Fleury (1990: 171–172, n. 1) rightly suggests the chord as the radius. He also indicates that the sixteenth of the circumference is defined geometrically through three successive divisions: that of the circumference through two perpendicular diameters, that of one of its four equal parts by tracing the bisector of the right angle, and that of one of the eighths thus arrived at by tracing the bisector of the angle corresponding to it. Fleury (1990: XCVI–XCVII and 126, n. 6) deduces that Vitruvius inclines towards an orientation of the site to the east. On the other hand, Vitruvius recommends the avoidance of the orientation towards the course of the sun for granaries, which must be oriented to the north or northeast (VI.VI.4), and the use of the orientation to the north for covered cellars. Also, the openings of bedrooms and libraries must be orientated to the rising sun, baths and winter apartments to the winter sunset, picture galleries and apartments that need a steady light to the north (I.II.7). Another one is that the walls should be oriented towards the north or northeast.

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10. The principle of this proposal is entirely convincing, however, not all arguments in favor of the grid plan are equally well founded. H. von Hesberg (1989: 135), for example, maintains that Vitruvius’s observation concerning the breaking of the winds on the angles of the buildings suggests streets crossing at right angles. But there is no necessary relation between the breaking of the winds on the angles and the grid plan. If Vitruvius’s proposes a grid plan — and he does — then there is such a breaking, but the sole fact of breaking does not necessarily lead to a grid, since a radial-concentric plan may have the same result (as is clear from Hugh Plommer’s proposal presented below). 11. The valorization of the right is general in the Roman tradition. Thus, for example, according to Vitruvius (III.IV.4) the number of steps leading up to the temples must be odd, so that, as we start ascending with the right foot, the same foot will also be set on top (for this access dextro pede, see also Fleury 1990: 93, n. 11.1; Gros 1990: 135, n. 2). 12. Music has in common with astronomy the discussion of the harmony of stars and musical chords (I.I.16). 13. The aesthetic quality of the ratio 1:1 is attested in a quite di¤erent context. In III.V.11, Vitruvius writes that the projection of the cornice, dentil included, must be equal to the height from the frieze to the top of the cymatium of the cornice. He then generalizes this prescription by writing that all projections are more graceful when they project as much as their height. Gros (1990: 187, n. 5) notes that this rule is for Vitruvius one of the essential conditions of beauty, and beauty in this case is visual harmony founded on a simple rational fact. 14. The same inscription of a square within a circle, this time the eye of the volute of the Ionic capital, allows the tracing of the rest of the volute (III.V.6; see also Gros 1990: 160–164, n. 3 and 4). The same inscription also leads to the determination of the hollow of the flutes of the Doric columns (IV.III.9). 15. Knell (1985: 66) observes that it is naive to add the two perfect numbers. He notes, however, that this operation shows the importance of the numerical system based on the foot for architecture.

References Bek, Lise. 1985. ‘‘Venusta species’’: A Hellenistic rhetorical concept as the aesthetic principle in Roman townscape. Analecta Romana Instituti Danici 14. 139–148. Bollack, Jean. 1965. Empedocle, vol. 1. Introduction a` l’ancienne physique. Paris: Minuit. Brown, Frank E. 1963. Vitruvius and the liberal art of architecture. Bucknell Review 11(4). 99–107. Callebat, Louis (ed.). 1973. Vitruve, De l’architecture: Livre VIII. Paris: Les Belles Lettres. Callebat, Louis & Philippe Fleury (eds.). 1986. Vitruve, De l’architecture: Livre X. Paris: Les Belles Lettres. Choay, Franc¸oise. 1980. La re`gle et le mode`le: Sur la the´orie de l’architecture et de l’urbanisme. Paris: Seuil. Falus, R. 1979. Sur la the´orie de module de Vitruve. Acta Archaeologica 31(1/2). 249–270. Fleury, Philippe (ed.). 1990. Vitruve, De l’architecture: Livre I. Paris: Les Belles Lettres. Fre´zouls, Edmond. 1968. Sur la conception de l’art chez Vitruve. In Jan Burian & Ladislav Vidman (eds.), Antiquitas graeco-romana ac tempora nostra (Acta Congressus Internatio-

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Alexandros Ph. Lagopoulos (b. 1939) is Professor Emeritus at Aristotle University of Thessaloniki [email protected]. His research interests include urban planning, social semiotics, anthropology of space, and semiotic spatial models of precapitalist and contemporary societies. His publications include The City and the sign: An introduction to urban semiotics (co-edited with Mark Gottdiener, 1986); Meaning and geography: The social conception of the region in Northern Greece (with Karin Boklund-Lagopoulou, 1992); Urbanisme et se´miotique dans les socie´te´s pre´industrielles (1995); Heaven on Earth: Sanctification rituals of the Greek traditional settlement and their origin (in Greek, 2002).