ON THE FUNDAMENTAL TERMS OF VITRUVIUS’S ARCHITECTURAL THEORY

Vitruvius unfolds his theory of architecture in I, 2, 1-9. In these passages he maintains that architecture is distinguished from random building practice through a set of principles: ordinatio, in Greek taxis, dispositio, in Greek diathesis, eurythmia, symmetria, decor, distributio, in Greek oikonomia.1

There is, however considerable confusion surrounding these terms, and especially ordination, eurythmia and symmetria. «Vitruvius assembles terms of aesthetic criticism, without clearly distinguishing [them]» comments F. Granger.2 J.J. Pollitt adds: «[Vitruvius’s] distinction between taxis and symmetria for example is hazy and redundant».3 And P. Gros: «Malgré un discourse qui se veut intégralement cohérent, il apparaît très vite que les principes constitutifs de l’ art de bâtir, tel que cet auteur les définit dans son livre I, manquent souvent de précision et de pertinence».4 On the other hand, a number of scholars, just as dinstinguished as the aforementioned, have sought to overcome the apparent incoherence in Vitruvius’s theory. They, however, propose extremely complex interpretations of the terms appearing in I, 2 and their interraltions.5 But this is not Vitruvius’s style: his language may be quite confusing, but, usually, what he says is quite simple.

I fully agree with H. Geertmann who notes that «fenomeni propri del testo devono in primo luogo essere spiegati con l’ aiuto del testo stesso»,6 and this way is the way I am going to proceed.

The confusion surrounding the fundamental terms of Vitruvius’s architectural theory results, in my opinion, from the way the Roman master uses the word symmetria. I argue that Vitruvius attaches to it three related, but not identical meanings: a rather general one, a strict one in accordance with the definition he gives in I, 2, 4 and a literal one. All these meanings, however, are compatible with each other. The threefold meaning of symmetria, the frequent reference to it in De Architectura and the central role Vitruvius seems to have assigned to it in the definition of ordination lead to the assumption that it has a dominating importance in his theory of architecture.

«Le principe», writes P. Gros, «qui nous apparaît de ce point de vue le plus riche est celui de la symmetria. Placé en exergue dès les premières lignes du livre III, il constitue, parmi toutes les notions abstraites manipulées avec plus ou moins de bonheur par Vitruve, le seul invariant spécifique applicable à l’ activité archtecturale:7

and H. Knell notes : «Im Zentrum steht symmetria, die auf ordinatio and quantitas beruht, sowie disposito ermöglicht».8 I do not subscribe to this view. I do not think that the use of the word symmetria by Vitruvius implies that the author of De Architectura meant that symmetria is or should be the principle governing

1 Vitruvius, De Architectura, I, 2, 1: «Architectura autem constat ex ordinatione, quae graece taxis dicitur, et ex dispositione, hanc autem Graeci diathesin vocitant, et eurythmia et symmetria et decore et distributione, quae graece oeconomia dicitur= «Now architecture consists of order, which in Greek is called taxis, and of arrangement, which the Greeks name diathesis, and of eurythmia and symmetry and decor and distribution which in Greek is called oeconomia». All quotations of Latin text and translations are taken from the Loeb edition, ed. and trans. F. Granger (London 1931), unless otherwise indicated.

architecture. He never states such a thing and, in my opinion, he never lets us assume it.

I find it hard to believe that Vitruvius referred to the concepts of which «architectura constat»= «architecture consists» without any logical order or assessment of their relative importance. I am not convinced that he assigned what is regarded almost unanimously by modern scholars as the most important «component» of architecture (or even its goal) ─that is symmetria─ to fourth place. «And first, as order demands», he says at the end of Book II, «I will describe the temples of the immortal gods».9 Matters are dealt with in order of priority: this is what anyone would do who wished to address Caesar himself. Let us consider the definitions of the terms ordination and symmetria as translated by F. Granger (Loeb, 1931), M.H. Morgan (Harvard U.P., 1914) and Ph. Fleury (Les Belles Lettres, 1990).

Ordinatio est modica membrorum operas commoditas separatism universeque proportionis ad symmetriam comparatio. Haec componitur ex quantitate, quae graece posotes dicitur. Quantitas autem est modulorum ex ipsius operas sumptio e singulisque membrorum partibus universi operas conveniens effectus.

Order is the balanced adjustment of the details of the work separately, and, as to the whole, the arrangement of the proportion with a view to a symmetrical result. This is made up of Dimension, which in Greek is called posotes. Now Dimension is the taking of modules from the parts of the work: and the suitable effect of the whole work arising from the several subdivisions of the parts. (Granger)

Order gives due measure to the members of a work considered separately, and symmetrical agreement to the proportions of the whole. It is an adjustment according to quantity (in Greek posotes). By this I mean the selection of modules from the members of the work itself and, starting from these individual parts of members, constructing the whole work to correspond. (Morgan)

L’ ordonnance est l’ adaption convenable des mesures des membres de l’ ouvrage pris séparément et, pour l’ ensemble, l’ établishment de rapports aboutissant à la symétrie. Elle est constituée de la quantitas, qui se dit en grec posotes. La quantitas est le choix de modules à partir de «membres de» l’ ouvrage lui-même et une réalisation harmonieuse de l’ ensemble de l’ ouvrage à partir des différents parties de ses membres. (Fleury)

Item symmetria est ex ipsius operis membris conveniens consensus ex partibusque separatis ad universae figurae speciem ratae partis responsus.

Symmetry also is the appropriate harmony arising out of the details of the work itself ; the correspondence of each given detail among the separate details to the form of the design as a whole. (Granger)

Symmetry is a proper agreement between the members of the work itself, and relation between the different parts and the whole general scheme, in accordance with a certain part selected as standard. (Morgan)

De même la symétrie est l’ accord harmonieux des membres de l’ ouvrage même et la corrélation reposant sur une partie calculée entre les parties séparément et la configuration de l’ ensemble. (Fleury)

In the definition of Ordinatio Vitruvius uses two words with similar meaning (commoditas and modica)10 both deriving from modus, the Latin word for Greek metron (measure). This implies that Vitruvius does not speak of a state of balance11

between the members of a work: for this the word commoditas alone would be sufficient.12 Vitruvius is speaking probably of a design, an action by which the members of the work are adjusted to each other. This adjustment is described as modica, which I understand to mean that it is carried out with «a sense of metron», or «due measure». The rectus accommodatusque status is the result of the architect’s work. So I suggest that the first part of the definition of ordination be understood as follows: «Order is the balanced and measured adjustment of the members of the work considered separately…».

According to the Oxford Latin Dictionary the noun ordination had the following meanings: «1) the action of laying out in the correct relative positions, arrangement13

…2) the action of putting in order (something confused), organization», and «the ordering or regulating». And the verb ordino means: «1) to set out in order, arrange, …3) to make orderly or systematic, organize». It should be noted that Vitruvius defines disposiito and not ordination as the putting of things in the correct relative positions (more on this issue, below), so «putting in order» or «arrangement» seem to be the meanings that best convey Vitruvius’s use of the term ordination.

We may note that the Roman cultural environment of the late first century B.C. favoured the understanding of the world as a well-structured and ordered whole. Cicero concluded that «…thus all considerations from every viewpoint demonstrate that everything in our world is wonderfully ordered by divine intelligence and design for the welfare and preservation of all»14 ─ a view not far from that of Plato who asserted that «…God …took over all that was visible …He brought it into order (taxis) out of disorder (ataxia), deeming the former state is in all ways better than the latter».15 An architectural theory which favoured well-structured and ordered entities would have been welcomed in this environment.16

A well-structured and ordered whole presumes a rank order,17 and the establishment of this is implied in everyday language by the term «setting out in order»: the noun ordo has, according to the OLD, the significance of «…5) civil or social standing, rank, position.18 I will try to demonstrate that this is also the case with taxis, Greek for ordination, in Vitruvius’s architectural theory.

Although the word taxis in everyday language had mainly the meaning or arrangement,19 in many cases it implied a rank of order, a hierarchy. Anaximander spoke of the «order of time», which means «in due time», «in the course of time».20 The «order» that led Pythagoras to name the universe cosmos21 was by no means devoid of connotations of rank. The Atomists used the concept of taxis as a means of specifying a class of differences between the atoms. Aristotle summarized their views.22 «These differences (ie. between the atoms), the say, are … shape (schema), order (taxis) and position (thesis); because they hold that what is differs only in contour, intercontact and inclination ─ of these contour means shape, intercontact order, and inclination position. Thus eg. A differs from N in shape, AN differs from NA in order, and Z from N in position». In AN, A comes first and N follows, whereas in NA, N comes first and A follows. Even if the Atomists did not wish to imply differences of value between AN and NA this arrangement is prone to

become loaded with connotations: in common experience what comes first is of greater importance than that which follows.23 Plato’s God who brought order to the world of «visible» things established a rank order, too.24 If «order» implied the presence or the establishment of a rank order in everyday language as well as in philosophical views, why should it not be possible that Order signifies «rank order» in architectural theory?

Vitruvius uses the words compare and comparatio for an array of meanings, ranging from «preparation» to «provision» or «putting together» and «arrange».25

According to TTL comparatio has the significance both of …praeparatio and the Greek synkrisis (comparison) and antithesis (contradiction).26 A very accurate translation of comparatio in English is given by the OLD: «1) preparation, making ready, …4) combination, conjunction, 5) arrangement, settlement, but also 1) comparison or weighing of the relative merits or other values …3) relationship (of position)».27

In my opinion comparatio in the definition of ordination should be understood as carrying both meanings, that is «arrangement containing an element of comparison», or «arrangement according to relative importance», «arrangement according to an evaluation», in other words «creation of a hierarchy», «establishment of rank order», or, if Vitruvius attributed a less active character to it, simply «hierarchy», «rank order». It is legitimate to assume that Vitruvius is using comparatio here in this very specific meaning? Although comparatio in no other passage of De Architectura has a meaning related to comparison, I consider this assumption to be legitimate: when a word is used as term of an architectural theory, it may have a very specific meaning, as long as this meaning does not contradict the meaning this word has in everyday language.

On the other hand proportion can safely be understood as the relation of magnitudes, in this case of the members of the work. The definition of proportion given in De Architectura III, 1, 1 does not contradict this basic meaning: it rather focuses on the demand for a common measure ─ just as quantitas does. More on proportion, later. For the moment it is worth noting that proportionis occurs in the definition of ordination in the genitive singular. Why does Vitruvius not speak of «proportions» in the plural? Although our author is not very consistent in his use of grammatical number, I believe that in the present case we are dealing with a conscious choice on his part. He speaks of the relation (in the singular) of magnitudes (of the members) characteristic of the overall work: the relation (sing.) of magnitudes by which the entire work is structured.28

So comparatio proportionis could mean the creation of a hierarchy of magnitudes (of the members of the work). But even if we suppose that comparatio means simply «arrangement» it is the force of the genitive singular proportionis that leads to a similar interpretation: comparatio proportionis signifies the arrangement of the relation (not the relations) of magnitudes, or the attribution of (the proper) relative magnitudes (to the members of the work), whose purpose is to achieve symmetria (proportionis ad symmetriam comparatio).

But what is meant by ad symmetriam? This is the point that causes what I regard to be a major misunderstanding29 ─ and it is Vitruvius’s language which is misleading. I suggest that Vitruvius is here using the word symmetria in its literal meaning, that is a meaning related but not identical to the meaning it has in the definition given in I, 2, 4.

Symmetry, symmetria, implies that the elements of which the work is composed have a common measure by which they can be compared with each other. Let us

recall the basic definition of «symmetrical» magnitudes as given by Euclid.30

«Symmetrical magnitudes are those than can be measured by a common measure, and asymmetrical magnitudes are those for which no common measure can by found». In a broad, but still literal, sense two asymmetrical magnitudes cannot be compared to each other, insofar as no common measure exists, by which the comparison can be carried out. In a narrow sense, they can be compared, because a mathematical order of magnitudes can be established.31 But even in this case, if there is a common measure, then the comparison becomes more apparent, more «tangible», more obvious ─ it becomes an object of aesthetics. Furthermore, I have the feeling that symmetria in this context has the meaning it has in Philebos 25E and 64Eff: the incorporation of the metron in order to make two opposite things, two opposite concepts symphona, that is congruous, to fit to each other.32 Ad symmetriam then means: (articulation of the work according to a rank order, a hierarchy) striving to keep the members of the work comparable to each other, to keep the metron in the overall work.

De Architectura was written at a time, when hierarchy in social life resulted in huge differences in social status and in everyday life. By what means was the life and social status of imperator Caesar33 comparable to that of a slave? Any rank order tends to the «asymmetrical» in this sense. In architecture, one element may overshadow all the others, and render them unimportant, or irrelevant. This is what Vitruvius fears, and this is the danger about which he is trying to warn us. I therefore suggest that ordination should not be understood as an «arrangement of the proportion with a view to a symmetrical result» ─which places Order at the service of Symmetria─ but rather as:

«Order is the balanced and measured adjustment of the members of the work considered separately, and the creation of an hierarchy of magnitudes, to keep symmetry in the overall work», or, if we do not make use of the word «hierarchy»: «Order is the balanced and measured adjustment of the members of the work considered separately, and the establishment of such a relation of magnitudes, that symmetry is kept in the overall work».

In this context it makes perfect sense that «haec (ie. Ordination)34 componitur ex quantitate»= «Order is composed of Quantity», which I understand as: Order is shaped through Quantity. The hierarchy is created when the appropriate relative magnitude is attributed to each and every single member of the work.

Let me also suggest that Aristotle’s concept of taxis in Rhetoric 1414a ff. implies the attribution of right position and right length (that is the right magnitude) to the parts of a speech.35 It is not inconceivable that this understanding of taxis evolved in architectural theory into two separate notions: ordination, concerning the «quantitative» aspects ─the dimensions of the members─ and dispositio, concerning the «spatial» aspects ─the positions of the members─ of a work; more on dispositio, later.36

Quantitas is the «selection of modules from the work itself». I understand this to mean: «Quantity is the establishment of a common measure; this common measure should be selected from the members of the work». This obviously is intended to help bring about the coherence of a well-structured whole. Quantity is also the «e singulis membrorum partibus universi operas conveniens effectus». In my opinion, effectus has the meaning of «realization» or «construction».37 Conveniens38 which mainly means compatible, and consequently harmonious and suitable, probably has here the

meaning of harmonious. Conveniens effectus is the «harmonious» construction of the work, the construction of the whole in a way to make it «harmonious».

The «harmonious» character of the work derives from the proper, suitable determination of the basic relative magnitudes of the members and their parts, according to their importance, to their «rank». The analogy with the harmony of the world lies, in my understanding of Vitruvius, in selecting the basic relationship between the magnitudes of the parts in such a way as to create an hierarchically structured whole; this task can not be carried out by symmetria as defined in I, 2, 4. The analogy with the harmony of the world can not simply be based on the dozens of architectural relations that are inevitably to be found in a building and which are related to symmetria: symmetria is the conveniens consensus, the harmonious agreement between the members and between each member and the whole. Symmetry, consensus, in my opinion, describes a compatibility of the elements composing a work, based on common measure. This is, in my understanding, the difference between quantitas and symmetria. Both result in harmony, but through different paths; I can not imagine Vitruvius confusing two concepts outlined in the same chapter of his own treatise.

I, therefore, subscribe to the first part of Ph. Fleury’s aphorism,39 that «la quantitas pour Vitruve est la détermination du “combine grand”«, but not to its second part : «… c’ est l’ action de définir la symmetria pour un bâtiment donné ». This view leads to total chaos concerning the meaning of the notions quantitas and symmetria. Ordinatio, not symmetria is obviously meant in I, 2, 2, in the sentence following the definition of ordination: «haec componitur ex quantitate…». Order, not Symmetry is composed of Quantity. So, I translate:

Order is made up of Quantity which in Greek is called Posotes. Quantity is the selection of modules from the work itself and, starting from the individual parts of members, the construction of a harmonious whole.

The concept of proportio seems to complicate matters, and requires further consideration. Let us compare the way the term is used in De Architectura III, 1, 1:

Aedium composition constat ex symmetria, cuius rationem diligentissime architecti tenere debent. Ea autem paritur a proportione, quae graece analogia dicitur. Proportio est ratae parties membrorum in omni opera totiusque commodulato, ex qua ratio efficitur symmetriarum. Namque non potest aedis ulla sine symmetria atque proportione rationem habere compositionis.

The design of a temple depends on symmetry, the principles of which must be most carefully observed by the architect. They are due to Proportion, in Greek analogia. Proportion is a correspondence among the measures of the members of an entire work, and of the whole to a certain part selected as standard. From this symmetry results. Without Symmetry and Proportion there can be no Reason in the design of any temple.40

I would suggest that Vitruvius’s proportion corresponds closely to the definition of symmetria given by Euclid. Proportion is simply the arithmetical relations existing in a work, the relations between magnitudes, which are formed on the basis of a module. When these are such that we have consensus, when we have symmetria, and only then do we have Reason in temple building, or if ratio is

intended in a less specific sense, only then do we have a proper plan in temple building. Proportion is the simple commensurability (commodulatio), whereas symmetria possesses a qualitative aspect. This Symmetry possesses something in the «mean» and the «blending» of things opposed to each other described by Plato in the Philebos 64Eff. I take issue with Pierre Gross, who writes: «Vitruve fournit une traduction satisfaisante (of symmetria) avec le terme commodulatio, désigne effectivement la commensurabilité de toutes les composantes s’ une œvre complexe fondée sur le recours à une unité modulaire».41 This is only partly true, for Vitruvius clearly states in the above-mentioned passage that proportion, not symmetria, is: «…ratae parties membrorum in omni opera totiusque commodulatio».

Symmetria, that is consensus, is found primarily in the arithmetical relationships observed in the human body ─ a topic discussed by Vitruvius in III,k 1, 2-3. This whole passage can be understood as an answer to the question: when can we say that a set of arithmetical relations is congruous, so that it results in a concensus? The answer given is: when the arithmetical relations are «similar» to those found in the human body, for Vitruvius says that, «the other limbs (of the human body) also have their proportionate measurements… In like fashion the members of the temples ought to have dimensions of their several parts corresponding by a common measure to the general sum of their whole magnitude».42 It goes without saying that not only symmetria, but also taxis, is inherent in the human body, for it is a clear, well-structured whole.

Vitruvius refers often to the «symmetry» of a building. I suggest that this «symmetry» is a general way of speaking of the proportion and of the relation of magnitudes in a building ─ P. Gross probably has those cases in mind when he identifies commodulatio with symmetria. Vitruvius speaks of the symmetries of Doric doors in IV, 6, 1 and of the symmetries of columns in IV, 8, 2; symmetry appears along with proportion in IV, 8, 3 and we have buildings «laid out with other symmetries» in IV, 8, 4, all passages in which this generic meaning of symmetria fits best. On the other hand passages in which symmetria is to be understood as having the meaning Vitruvius attaches to it in the definition given in I, 2, 4, I can only see here the author telling us how to achieve consensus, or how Symmetry should be achieved in certain building types. He does not necessarily imply that Symmetry must be our major objective when designing a building. We should remember how Vitruvius concludes his reference to the symmetry of the human body in III, 1, 9:

Ergo si convenit ex articulis hominis numerum inventum esse …relinquitur, ut suscipiamus eos, qui etiam aedes deorum inmortalium constituentes ita membra operum ordinaverunt, ut proportionibus et symmetriis separatae atque universae convenientes que efficerentur eorum distributiones.

Therefore, if it is agreed that number is found from the articulation of the human body… it remains that we take up those who in planning the temples of the immortal gods have so fixed the rank order of the members of the work (they have attributed the appropriate relative magnitudes to the members of the work), that by the help of proportion and symmetry their several and general distributions are rendered congruous.43

This reading understands ordino as having a meaning similar to that of ordination, that is the establishment of a rank order, which is realized by the attribution of the appropriate magnitude to the members of the work. Once more Symmetry is

subordinate to Order, not vice-versa. Its function is to render congruous a setting outlined by Order.

I would suggest that Order in this sense is one of the main issues of the De Architectura, although its author explicitly refers to it only in a few passages. He describes various buildings and their structural parts without saying «this is how the proper Order will be achieved». Such is the case with distributio and dispositio too. But it should be noted that by prescribing the proportions of the members Vitruvious prescribes their relative magnitudes, and by that their rank order, even if this is not made explicit to the reader. When, for example, he describes the peripteral temple as one which has 6 by 11 columns he speaks of Order: the relation of magnitudes between the columns and the pediments is, more or less, set.44 And in his accounts of the three architectural orders a major step is taken towards the attribution of the proper relative magnitudes, and bestowing the proper Order on the building itself. Here the passage in IV, praef., 2 is relevant:

Ex tribus generibus quae subtilissimas haberent proportionibus modulorum quantitates ionici generic moribus docui.

Of the three orders which, through proportional magnitudes, furnish the most subtle Quantities, I have set forth the Ionic order as it has been formed by tradition.45

Vitruvius summarizes his treatment of the Ionic order through the concept of Quantity, which is a component of ordination, not through that of symmetria. I understand the property of Order to be inherent not only to the Ionic, but also to the Doric and the Corinthian orders. The column shafts have an appropriate magnitude in relation to their capitals, the architrave to the column capitals, the pediment to the architrave.

Turning now to consider the definition of the term dispositio. If ordinatio is realized by the attribution of the appropriate magnitude to the members of the work, dispositio, it seems, assigns the members of the work to their appropriate relative position:

Dispositio autem est rerum apta conlocatio elegansque compositionibus effectus operis cum qualitate.46

This has been variously translated as follows:

Arrangement, however, is the fit assemblage of details, and, arising from this assemblage, the elegant effect of the work and its dimensions, along with a certain quality of character. (Granger)

Arrangement includes the putting of things in their proper places and the elegance of effect that is due to adjustments appropriate to the character of the work. (Morgan)

La disposition est la mise en place correcte des élements et, grâce à ces arrangements, la réalisation élegante d’ un ouvrage où apparaît la gualité. (Fleury)

Quality, is intended, in my view, in a Stoic sense.47 Poiotes, the Greek for qualitas, was the second «category» of Stoic ontological definition, which made

the substratum, the shapeless and unidentifiable matter, a specific object.48

Understood thus, qualitas in this passage becomes equivalent to what we mean today by «identity».

Such a reading of qualitas is matched by an interpretation of elegans as «particular» or «outstanding» (praestans, egregious).49 As already noted effectus therefore has the meaning of «realization». Elegans effectus is the process of choosing the appropriate elements and appointing them to the appropriate place. It is the action by which a building is born out of the chaos of «raw material» in disorder. It is the shaping of a building out of a random juxtaposition of architectural elements. It is the articulation of a spatially ordered whole.50

The articulation is carried out through the composition of the members. Compositionibus appears in the plural. Although, as already noted, Vitruvius is not very consistent in his use of grammatical number, I believe that in this case h is referring to a single building. So by compositionibus I understand «composite assemblage», «assemblage of the members in such a way as to make them belong to many entities at the same time»: A column must be considered as a member of a colonnade, but as a member of the column/architrave/pediment entity as well.

Elegans and effectus encompass compositionibus and become inherently linked. The interpretations proposed for elegans and qualitas may explain why these two words appear in what would otherwise be the least expected place: in the definition of dispositio rather than that of eurythmia or symmetria.

In sum, I suggest the following translation for the definition of dispositio:

Arrangement is the proper placement of architectural elements and, through their composite assemblage, the shaping of the work’s identity.

It makes perfect sense that the sentence following this definition reads:»species dispositionis … sunt hae: ichnographia, orthographia, scaenographia». I understand this to mean: «Arrangement is apparent through ground-plan, elevation and perspective.51 Dispositio becomes manifest through these three ways of «depicting the work to be» that is by the right placement of the elements of a work in a well-structured whole.52 The neat arrangement of various rooms round the peristyle of a palaestra53 is to be seen in the ground plan (Greek ichnographia); the elegant distribution of columns and antae in a stage wall54 is to be seen in the elevation (Greek orthographia); the pleasing arrangement of a T-shaped basilica room55 is to be seen in the «perspective» (Greek scaenographia).56 Both ichnographia and orthographia must be carried out modice, which in my understanding, means, here too, with «due measure» (Granger: «competent», Morgan:: «proper», Fleury: «à l’ échelle»).

Le me now offer some remarks on Vitruvius’ definition of eurythmia, the third in sequence of the terms mentioned in I, 2, coming just before that of symmetria.

Eurythmia est venusta species commodusque in conpositionibus membrorum aspectus. Haec efficitur, cum membra operis convenientia sunt altitudinis ad latitudinem, latitudinis ad longitudinem, et ad summam omnia respondent suae symmetriae.

Proportion implies a graceful semblance; the suitable display of details in their context. This is attained when the details of the work are of a height suitable to their

breadth, of a breadth suitable to their length; in a word, when everything has a symmetrical correspondence. (Granger)

Eurythmy is beauty and fitness in the adjustments of the members. This is found when the members of a work are of a height suitable to their breadth, of a breadth suited to their length and in a word, when they all correspond summetrically. (Morgan)

L’ eurythmie est l’ apparence gracieuse et l’ aspect bien proportionné que réside dans la composition des membres. Elle se réalise quand les membres de l’ ouvrage ont une hauter en rapport avec la largeur, une largeur en rapport avec la longueur, et au total quand toutes les parties correspondent à la symétrie que leur a été fixé. (Fleury)

The meaning of the word eurythmia in the Classical tradition has been discussed exhaustively. H. Brunn claimed there was in eurythmia a «Milderung» of symmetria.57

For C.Watzinger it represented the visual effect of dispositio,58 and for F. Schlikker the «gracefulness» of a work.59 The major issue remains the real meaning of rhythmos: is it «shape» or «form», or «rhythm» in the modern sense of the word ─ that is, does eurythmia mean «the quality of being well shaped, well formed», as J.J. Pollitt60 puts it, or «having a pleasant rhythm, or rhythmical movement». Ancient sources indicate the former interpretation as more probable, without excluding, however, the latter: E. Petersen made a major contribution on this issue showing that thythmoi were the «positions» of the body during the dance.61

Eurythmia is in the first instance, for Vitruvius, venusta species: as mentioned above, species has the meaning of «visual appearance», «form» and «shape». Venusta species can probably be identified with the attribution of the «quality of being well shaped» to the members of a work. If I have it right, Vitruvius assigns appearance to third place, after magnitude and position: the members should have the right magnitude, the right position, and a pleasing appearance.

Vitruvius does not speak of each single member; eurythmia resides «in compositionibus membrorum», that is what we have called the «composite assemblage» of the members.62 This is underlined by the second term needed to be fulfilled in order for eurythmia to be achieved: commodus aspectus, the balanced appearance, the «fitting aspect» of the members. So I translate the essential definition as:

Eurythmy is a beautiful aspect and a balanced appearance of the members in their composite assemblage.

In order for a work to be distinguished by Eurythmy its members should have a pleasing appearance when perceived as parts of a group; they should possess the quality of being well-shaped as constituents of a set. Vitruvius asks: Has a column the appropriate entasis in order to look strong enough to hold the entablature and the pediment? Are the columns thick enough for the colonnade to have a balanced appearance? He does not ask: Is the column beautiful per se? In this context both notions of eurythmia apply: for a set of related objects to have a «beautiful aspect» and a «balanced appearance» almost means that they are to be «distinguished by a pleasant rhythm».

«Eurythmia efficitur cum…= Eurythmy is achieved when…», I understand: «The pre-requisite of eurythmia is…», or:

This is achieved, when the members of the work are of a height suitable to their breadth, of a breadth suitable to their length; an in a word, when they all correspond symmetrically.

«Symmetros est eurythmiae qualitas» points out Vitruvius in I, 2, 4, which I understand as follows: «In order for eurythmia to be achieved, and in order for the members to have a pleasing appearance when perceived as parts of composite assemblages, those members should be symmetrical». In other words there must be a harmonious agreement between the members of the work based on the adoption of a common measure. Symmetry serves Eurythmia, just as it serves Order.

We are faced with the task of establishing «objective» criteria in a field dominated by «taste», i.e. subjectivism. It is obvious that Vitruvius, a Roman military engineer, does not feel familiar enough with a so-called «artistic» approach to Architecture. He tries to determine rationally how a pleasing appearance is produced and he introduces the notion of sets of members, for which the laws resulting in the «beauty» of a set of objects may be clearly described; this is not the case with the laws resulting in the «beauty» of a single object. So, Vitruvius’s eurythmia seems to depend rather on reason, than on impulses.

Let us consider Vitruvius’s arguments for the need for refinements (or optical corrections), in III, 3, 11 and IV, 4, 3. He writes in III, 3, 11: «The angle columns also must be made thicker by the fiftieth part of their diameter, because they are cut into by the air and appear more slender to the spectator».63 Here we can discern the theory, according to which vision is based on «emanations» (aporroai) of the objects that we see (just like something we smell). The corner columns, being more exposed to the air than the others, are subject to greater losses of «emanations», and therefore appear thinner than the others. In developing his argument, Vitruvius does not have recourse to observations relating to the «psychology» of the observer. He bases the need for refinements of «objective laws of nature».

It is in the sphere of optical corrections that we have one of the few ancient references to eurythmia as a concept relating to architecture.64 The reference is by Philo Mech (4, 4) who notes that «(members) of equal thickness and constructed perpendicular appeared to be of unequal thickness and not perpendicular… because the eyes deceive us… So, by a process of trial and error, adding to masses and again subtracting from them, and establishing tapers and trying out every possible means, architectural forms are produced which are suited to the vision and appear eurythma.65

Although his goal is similar to Vitruvius’ (viz. the production of well-shaped forms), Philo seems to place emphasis on the «psychological» element, the «subjective» element ─since he does not give any «scientific» explanation of these phenomena─ to the detriment of the «objective».

A modicum of subjectivity may be felt in Vitruvius’s reference to eurythmia in VI, 2, 5 ─and only there─ where he urges the architect to adjust the symmetries of private buildings. The adjustments, however, aim at fitting the buildings into the given sites; they should result in proportionis ad decorum apparatio, that is they must be made with «regard to appropriateness of proportion». In other words, they must be justified and obey commonly held aesthetic and social conventions. So, I cannot fully subscribe to J. J. Pollitts’ view that Vitruvius’s eurythmia was a «pleasing quality which arose from the alteration and adjustment of concrete forms and it was something which had to be understood subjectively, than demonstrated objectively».66

On the contrary, I feel that Vitruvius, against the current of his time, wanted architecture to serve the Beautiful only when this necessarily implied that it also served Reason.

The important role of Eurythmy in Vitruvius’s architectural theory is, in my view, well established. We should bear in mind the definition of eurythmia, if we want to understand the definition of symmetria without loading it with meanings the Roman architect never intended. Morgan’s translation is excellent; nevertheless I would substitute «harmonious» for «proper» in order to emphasize the concept of conveniens consensus. 67

Symmetry is a harmonious agreement between the members of the work itself and

relation between the different parts and the whole general scheme, in accordance with a certain part selected as standard.

On the concept and definition of decor there is little that needs to be said. As J. J. Pollitt puts it: «As applied to architecture by Vitruvius, decor is the principle by which one judges whether the form of a building is appropriate to its function and location and whether the details of the building are appropriate to its total form».68

Decor autem est emendatus operis aspectus probates rebus conpositi cum auctoritate. Is perficitur statione, quod graece thematismo dicitur, seu consuetudine aut natura.

Décor demands the faultless ensemble of a work composed, in accordance with precedent, of approved details. It obeys convention, which in Greek is called thematismos, or custom or nature. (Granger)

Propriety is that perfection of style which comes when a work is authoritatively constructed on approved principles. It arises from prescription (Greek thematismo), from usage, or from nature. (Morgan)

La convenance est l’ aspect soigné d’ un ouvrage réalisé avec qualité au moyen d’ éléments éprouvés. On l’ obtient en suivant une règle, qui se dit en grec thematismo, l’ habitude ou la nature. (Fleury)

Elaborating on decor which perficitur … statione Vitruvius tries to show that there is direct correspondence between the gods and architectural orders; this is the only manifestation of decor realized by statione. I interpret statione as: «by taking into account the status» of a person or of a God.69 I do not understand the term as following some rules or prescriptions but the acknowledgement of somebeing’s unchallenged status and the response to it. I suggest as a translation:

Propriety is the faultless appearance of a building composed of approved elements on established principles. It arises when account is taken of status ─ in Greek thematismos, custom and nature.

The concept of distributio, the sixth and last term mentioned by Vitruvius, is the least contentious, dealing as it does with economical use of site and materials and effective and reasonable cost management.

Distributio autem est copiarum locique commode dispensation parcaque in operibus sumptus ratione temperatio.

Distribution or Economy, however, is the suitable disposal of supplies and the site, and the thrifty and wise control of expense in the works. (Granger)

Economy denotes the proper management of materials and site, as well as a thrifty balancing of cost and common sense in the construction of the works. (Morgan)

La distribution est la répartition convenable des resources et du terrain et, dans les ouvrages, un sage équilibre des dépenses grâce au calcul. (Fleury)

To sum up : Architectura constat ex ordinatione… Architecture consists of Order… and not, as C. Faventinus claims, architecturae partes sunt… (the parts of architecture are…). What transforms simple building practice into architecture is ordination, dispositio, eurythmia, symmetria, decor and distributio.

Ordinatio, Order, is the first principle mentioned by Vitruvius, so we may conclude that it is regarded as the most important one. Its objective is the creation of a hierarchy, the establishment of a rank order among the elements constituting the work, by attributing the proper magnitude to each one of them. This attribution is called posotes, Quantity. Dispositio, Arrangement, is the second principle mentioned. It deals with the right placement of the elements, their right grouping, by which the work acquires its unique identity. It is apparent in the ground-plan, in elevations, in perspectival views. Eurythmia, Eurythmy is the third principle; it is the attribution of the quality of being well formed to each one of the members, in such a way that the members may be perceived as forming groups distinguished by balanced appearance. Symmetria, the fourth principle, describes the internal harmony of the work, achieved when there is consensus between members formed on the basis of a module, and between members and the whole, that is when the proportions are congruous. Decor, the fifth principle, deals with the «appropriate» articulation, the «authoritative» construction of the work on principles respecting religion, nature and social conventions. Distributio, finally, aims at achieving the best result with the means one has at one’s disposal.

So, according to my argument, although the «components of architecture» are equal in value from one point of view, the order in which they are mentioned is not fortuitous. In the designing of technical works, Vitruvius places greatest emphasis on Reason in general, and secondarily on proportions, or arithmetical relations. I believe that it is in Order that «pure» Reason, free of all material constraints, is primarily manifested: rank order is the cornerstone of well-structured wholes, governed by Reason. Dispositio, the arrangement of the elements of the work, depends to a great extent on Reason, too, since it is closely related to the constitution of well-structured entities. Eurythmia, since it involves sets of elements, is close enough to pure Reason, since well-structured entities are by definition beautiful. Symmetria is distinct from pure Reason, since it depends on the notion of consensus applied to mathematical relations of purely technical character. Decor is much more dependent on practical constraints, than on pure Reason, since it is the «proper» articulation of the work, which takes into account natural, social and historical factors. At the bottom of the scale is Distributio, which is no more than a «reasonable» economic response to Necessity.

Let us conclude with the proposed translation for all six definitions given by Vitruvius:

Order is the balanced and measured adjustment of the members of the work considered separately, and the creation of a hierarchy of magnitudes, to keep symmetry in the overall work. Order is made up of Quantity, which in Greek is called Posotes. Quantity is the selection of modules from the members of the work itself and, starting from the individual parts of members, the construction of a harmonious whole.

Arrangement is the proper placement of architectural elements and, through their composite assemblage, the shaping of the work’s identity. Arrangement is apparent through ground plan, elevation and perspective.

Eurythmy is a beautiful aspect and a balanced appearance of the members in their composite assemblage. This is achieved, when the members of the work are of a height suitable to their breadth, of a breadth suitable to their length; and in a work, when they all correspond symmetrically.

Symmetry is a harmonious agreement between the members of the work itself and relation between the different parts and the whole general scheme, in accordance with a certain part selected as standard.

Propriety is the faultless appearance of a building composed of approved elements on established principles. It arises when account is taken of status ─in Greek thematismos─ custom and nature.

Economy is the suitable disposal of supplies and the site, and the thrifty and wise control of expense in the works.

Vitruvius created a properly constituted, clearly articulated system of values that needed to be present in a technical work for it to cross the borders from handicraft, from techne in the ancient sense of the word, to become Architecture.

NOTES1 Vitruvius, De Architectura, I, 2, 1: «Architectura autem constat ex ordinatione,

quae graece taxis dicitur, et ex dispositione, hanc autem Graeci diathesin vocitant, et eurythmia et symmetria et decore et distributione, quae graece oeconomia dicitur= «Now architecture consists of order, which in Greek is called taxis, and of arrangement, which the Greeks name diathesis, and of eurythmia and symmetry and decor and distribution which in Greek is called oeconomia». All quotations of Latin text and translations are taken from the Loeb edition, ed. and trans. F. Granger (London 1931), unless otherwise indicated.

2 Vitruvius, De Architectura, Loeb edn. Vol. 1, 24, n. 1.3 J.J. Pollitt, The Ancient view of Greek Art (New Haven and London 1974) 67.4 P. Gros, «Les fondements philosophiques de l’ harmonie architecturale selon

Vitruve», JTLA 14 (1989) 13ff.5 E.G., J. A. Jolles, Vitruvs Aesthetik, Ph. D.Thesis (Freiburg 1905), C.Watzinger,

«Vitruvstudien», RhM 64 (1919), 202 ff., F. Schlikker, Hellenistische Vorstellungen von der Schönheit des Bauwerk nach Vitruv, Ph.D. thesis (Berlin 1940) 70ff., R. L. Scranton, «Vitruvius’ Arts of Architecture», Hesperia 43 (1974) 494 ff., E. Frézouls, «Vitruve et le dessin d’ architecture», Le dessin d’ architecture dans les sociétés antiques. Actes du colloque de Strasbourg, 26-28. 1. 1984 (Strasbourg 1985) 213 ff., H. Knell, Vitruvs Architekturtheorie. Versuch einer Interpretation (Darmstadt 1985).

6 H. Geertmann, «Teoria e attualità della progettistica architettonica di Vitruvio», Le projet de Vitruve (Roma 1994) 7ff.

7 Gros, loc. cit. (n. 4 above).8 H. Knell, Vitruvs Architekturtheorie (n. 5 above) 34.9 Vitruvius, De Architectura, II, 10, 3: «Et primum de deorum immortalium

aedibus sacris et de earum symmetriis et propotionibus, uti ordo postulat, insequenti perscribam».

10 According to the Thesaurus Linguae Latinae, commoditas has the significance of «…rectus accommodatusque status alicuius rei». TLL quotes Vitrurius’s definition of Order. Again, modica has the significance of Greek metrion; mediocrus, temperatus, conveniens are its synonyms. C. Fensterbusch, Zehn Bücher über Architektur (Karlsrhue 1964) n. 42, identifies commoditas with the Greek symmetria. P. Gros, Introduction to book III, Les Belles Lettres, p. XXX, concludes that commoditas/commodulatio and proportio are the equivalents of approximations of symmetria.

11 I agree with F. Granger in understanding commoditas as implying the notion of balance, and specifically as «balanced adjustment».

12 Most scholars agree on the «active» character of commoditas in the definition of ordination. So Granger understands «balanced adjustment» and Morgan «gives the measure».

13 OLD lists the reference to Vitruvius’ definition of ordination in I, 2, 1 under this meaning.

14 Cicero N.D. II, 132: «…sic undique omni ratione concluditur mente consilioque divino omnia in hoc mundo ad salutem omnium conservationemque admirabiliter administrari» (ed. H. Rackham, Loeb 1933). Vitruvius was a great admirer of Cicero, see De Architectura IX, praef., 17.

15 Plato, Timaeus, 30A (trans. R. G. Bury, Loeb 1929).16 Aristotle introduced the concept of art imitating nature, a concept which has

retained its validity ever since. Vitruvius urges us to respect nature and to learn from nature, and sees in good architecture an imitation ─in a broad sense─ of nature, eg. In II, 1, 6; III, 1, 9; V, 2, 2. If nature is ordered, so should edifices be. This attitude is obviously influenced by Stoic philosophy, too. By «according to nature» (Greek kata physin) the Stoics connoted a well-structured order of values, see SVF III, 140-146. Also Cicero De Fin. III, 20: «…selection… tum ad extremum xonstans consentaneaque naturae, in qua primum inesse incipit et intellegi quid sit quod vere bonum posit dici= …finally, choice fully nationalized and in harmony with nature; it is at this final stage that the Good properly so called first emerges and comes to be understood in its true nature» (ed. & trans. H. Rackham, Loeb 1914).

17 The image of the world as a whole structured according to a strict rank order is vividly expressed in Cicero’s N.D.; cf. also the pyramis bonorum in. Cic. De Fin. III, 20-23.

18 OLD lists among others the reference to Cic. De Off., I, 151 under this meaning.19 See LSJ, sv. Taxis.20 Diels, Vors. 2, 1, 15.21 Diels, Vors. 4, 21, 15 quotes Aetius in wiritng: «Pythagoras named the universe

cosmon because of the order prevailing». The word cosmos means initially a well ordered entity, eg. Troops, hair, etc., see LSJ, sv. kosmos.

22 Arist. Metaph., 985 b. I quote this passage as translated by H. Trendennick (Loeb 1933), except for taxis which I translate as «order» instead of Trendennick’s «arrangement».

23 For the rank order associated with the concept of Greek protos and Latin primus see LSJ and OLD, respectively.

24 Cf. the aforementioned passage, Timaeus 30A (above, n. 15). Plato’s cosmos is an ordered whole; rank order is present everywhere in Plato’s world, in nature as well as in society; eg. «first (in rank) and as elder among the gods, the earth was created…» (Timaeus 40C).

25 In I, 5, 8 it means the putting together of various materials: ex his comparationibus… perfectus habeatur… murus. In II, 7, 1, provision: eximuntur copiae (of stones) et comparantur. In II, 7, 3, composition of a material: ita spissis comparationibus solidata. In V, 6, 1 spatial arrangement: comparationes basilicarum.

26 TLL lists the reference to De Architectura I, 2, 1 under «comparison» and «contradiction».

27 OLD lists the reference to Cic. N.D. II, 51 under «relationship of position»: «cum solis et lunae et quinque errantium ad eandem inter se comparationem confectis…= when the sun, the moon and five planets… have returned to the same position relative to one another…».

28 Cf. M. H. Morgan’s translation: «Order gives the due measure…».29 Scholars unanimously agree that the purpose of ordination is to achieve

symmetria in the sense symmetria is meant by Vitruvius in the definition given in I, 2, 4. Even H. Geertmann, who denies symmetry’s central role asks himself: «perché questa operazione della ordination?», and he replies: «per ottenere in un edificio, dice Vitruvio, la situazione o proprietà della symmetria», «Teoria e attualita…» (see n. 6 above).

30 Euclid, Elements 10, definition 1. 31 v2 is of lesser magnitude than 2, although 2 is not x (x being a natural number)

times v2.32 «The class of the equal and double and everything which puts an end to the

differences between opposites and makes them commensurable (symmetra) and harmonious (symphona) by the introduction of number» (Plato, Philebos 25E), «metriotes and symmetria are everywhere identified with beauty and virtue» (Plato, Philebos 64E, trans. H. N. Fowler, Loeb 1925).

33 Vitruvius, De Architectura I, 1, 1, for the dedication of the treatise to imperator Caesar.

34 From a grammatical point of view it is not clear whether haec refers to ordination or symmetria, but the structure of this passage suggests to me that haec is substituted for the word at the beginning of the preceding sentence, that is ordination, not the word at the end of the preceding sentence, that is symmetria. In the latter case Vitruvius would probably have added a word, eg. Item, as he does a couple of sentences later, in I, 2, 4: «item symmetria est».

35 Quite a few scholars have pointed to the relationship between architecture (and especially Order) and rhetoric, among them P. Gros in his comments of Vitruvius book III, where he gives extensive bibliography on this subject. Geertmann, «Teoria e attualita…» (n. 6 above), noted: «Egli comincia con la ordination, la taxis, base di tutto anche nella retorica». See also L. Callebat, «Rhétorique et architecture dans le ‘de Architectura’ de Vitruve», Le projet de Vitruve (Roma 1994) 31ff.

36 In this context Cicero’s use, in N.D. II, 51, of the word comparatio to signify the relationship of position reveals similarities to Vitruvius’s use of comparatio in the definition of ordination.

37 According to OLD effectus has the meaning of «1) the making, creation (of something organic), 2) the carrying out (of a purpose, task etc.), 3) that which is

achieved». In this case meaning 1) or 2) probably fits best. In any case, the «effect» is the result of the architect’s work. Granger understands effectus as «effect», Fleury and Ferri (Vitruvio (dai libri I-VIII), recensione del testo, traduzione e note, Roma 1960) as «execution» or «realization», Morgan as «effect» (in the definition of dispositio) and «construction» (in the definition of Quantity).

38 The Greek equivalent of con-venio is probably syn-baino, which among others means «to be compatible», «to agree», see LSJ, cv. symbainein.

39 Note 2. 2. 2 of book I.40 Translation up to «standard» by M. H. Morgan. Granger translates the last

sentence: «for without symmetry and proportion no temple can have a regular plan».41 P. Gros, loc. Cit. (above, n. 4).42 Vitruvius, De Architectura III, 1, 2-3: «…reliqua quoque membra suas habent

commensus proportiones… similiter vero sacrarum aedium membra ad universam totius magnitudinis summam ex paribus singulis convenientissimum debent habere commensus responsum».

43 F. Granger translates : «Therefore, if it is agreed that number is found from the articulation of the body… it remains that we take up those who in planning the temples so ordained the parts of the work that, by the help of proportion and symmetry, their several and general distribution is rendered congruous».

44 Vitruvius, De Architectura III, 2, 5: «The peripteral will be that which shall have six columns in the front and six at the back, and on either side eleven, counting in the angle columns».

45 This is my translation of this passage. It is not clear whether we should translate together proportionibus modularum or modularum quantitates.The word modulus is often used by Vitruvius in a generic way to indicate the dimensions of a building, so De Architectura, IV, 1, 8: «subtilitateque iudiciorum progressi et gracilioribus modulis delectati septem crassitudinis diametros… con-stituerunt= having made progress in refinement and delicacy of feeling, and finding pleasure in more slender pro-portions, they have established seven diameters…» (trans. M. H. Morgan); III, 5, 9: «oculi species… incertam modul-orum renuntiat sensibus quantitatem= the eye… conveys to the mind only a confused estimate of the dimensions» (trans. M. H. Morgan). So what is meant here is either «proportional magnitudes= (members) whose magnitude have proportional relationships to each other» or «quantities of magnitudes= (members) given the appropriate relative magnitude».

46 Vitruvius, De Architectura, I, 2, 2,.47 Vitruvius is quite eclectic in his views, but in a great many cases he is influenced

by Stoic philosophy, e.g. in his view on the creation of civilization in II, 1, 1-7, and in his ethical considerations in VI, praef 5; VII, praef 1-8.

48 The four categories of Stoic ontological definition are substratum, quality, state and relative state, each of them comprising the preceding ones.

49 According to TLL some of the latiore sensu meanings of elegans are praestans, egregious, perfectus, and when referring to man-made objects bene compositus etc. According to OLD elegans has the significance of «1) careful in choosing, fastidious, peculiar» etc.

50 Vitruvius uses the word elegans in 16 cases and elegantia in a further 6. In quite a few instances it has the meaning of «well formed», «well composed» eg. I. 6, 1: «oppidum Mytilenae magnificenter est aedificatum et eleganter= the town of Mytilene is magnificently built and well formed…»; V, pr. 1: «verborum elegans dispositio= the nice arrangement of words».

51 Granger translates: «The kinds of the Arrangement are…», Morgan: «Its forms of expression are…», Fleury: «Les aspects de la disposition… sont…».

52 Species has the meaning of «aspect» or «visual appearance» and not of a «subdivision of class» in all five passages in which it is used in book I: I, 1, 4; I, 2, 3; I, 2, 4; I, 2, 5; I, 3.2. According to OLD species has the meaning of «1) something presented to view, a spectacle, sight… 3) visual appearance, look, aspect… 5) outward appearance… 10) a subdivision of class or kind, a sort, species». According to LSJ the equivalent Greek word eidos has the following meanings: «1) form… 2) material shape… 3) shape, form, expression» etc.

53 A topic discussed in V, 11, 1-11.54 Discussed in V, 6, 6.55 Discussed in V, 1, 9-10.56 I do not understand «perspective» as a single vanishing point perspective, but as

a «primitive» method of determining the diminution of magnitudes depending on the distance of the depicted objects from the viewer; see P. Lephas, «On Vitruvius’s concept of scaenographia», Quaderni ticinesi di numismatica e antichità classiche 25 (1998) 261 ff.

57 H. Brunn, Geschichte der Griechischen Künstler (2nd edn. Stuttgart 1889) 98ff.58 C. Watzinger, «Vitruvstudien» RhM 64 (1909) 202ff.59 F. Schlikker, Hellenistische Vorstellungen von der Schönheit des Bauwerks nach

Vitruv (n. 5 above), 70 ff.60 J. J. Pollitt, The ancient view…, 153 ff. Pollitt gives a very accurate translation of

Vitruvius’s eurythmia: «Eurythmia is a beautiful appearance and a fitting aspect of the parts in compositions», The ancient view…, 145.

61 E. Petersen, «Rythmus», AbhGott, N.F. 16 (1916-17) 1 ff.62 See above, in my interpretation of the term dispositio.63 Translated by F. Granger.64 An other passage, attributed to Geminus (or Damianus?), which appears in

Heron’s Def. 135 may be referring to paintings, probably stage paintings, and not to buildings: it points that architects, «when drawing buildings, must make the columns thicker in the middle, so as to create a work that is eurythmon with regard to the way in which we perceive it». Since the possible dates of this passage range over a period of 400 years (see P. Schuhl, Platon et l’ art de son temps (Paris 1933) 74 ff.), it can really be of little help in the present discussion.

65 Translated from «So…» up to «appear» by J. J. Pollitt, the Ancient View of Greek Art (1974), 144. Philo explains the process of refinement of architectural forms through history.

66 J. J. Pollitt, loc. cit., 148.67 See above on proportio and symmetria. Vitruvius’s definition of Symmetry in

Latin, along with translation by F. Granger, M. H. Morgan and Ph. Fleury, is quoted above in this paper just after the definition and respective translations of Order. The French translation of symmetria in the Belles Lettres edition is, in my view, also excellent.

68 J. J. Pollitt, The Ancient View of Greek Art (1974), 69.69 Vitruvius, De Architectura, I, 2, 5. «Status» should be understood latiore sensu.

Vitruvius asserts that «the construction of temples of the Ionic order to Juno, Diana, Father Bacchus and the other gods of that kind, will be in keeping with the middle position (habita erit ratio mediocritatis) which they hold» (trans. M. H. Morgan).

BIBLIOGRAPHY

J. von Arnim, Stoicorum Veterum Fragmenta (Leipzig 1903).

H. Brunn, Geschichte der Griechischen Künstler (2nd edn Stuttgart 1889).

L. Callebat, «Rhétorique et architecture dans le ‘de Architectura’ de Vitruv», Le project de Vitruve (Roma 1994) 31 ff.

E. Frézouls, «Vitruve et le dessin d’ architecture», Le dessin d’ architecture dans les sociétés antiques, Actes du colloque de Strasbourg, 26-28. 1. 1984 (Strasbourg 1985) 213 ff.

H. Geertmann, «Teoria et attualità della progettistica architettonica di Vitruvio», Le projet de Vitruve (Roma 1994) 7ff.

P. Gros, «Les fondements philosophiques de l’ harmonie architecturale selon Vitruve», JTLA 14 (1989) 13 ff.

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Ancient authors

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Cicero, De fin., ed. trans. H. Rackham (Loeb 1914).

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Vitruvius, De Architectura,. trans. M. H. Morgan (Harvard U.P. 1914).

Vitruvius, De Architectura, ed. trans. Ph. Fleury (Les Belles Lettres 1990).