ORDINATIO : THE VITRUVIAN CONCEPT AS A GENERATOR OF ARCHITECTURAL DESIGN

The article aims to investigate the role of the concept of ordinatio, listed by Vitruvius in De architectura treatise as one of the six fundamental components of the architectural design. By mapping occurrences of the concept through the text, the article proposes to contribute with a better comprehension of this concept which has been largely discussed in works regarding this Vitruvian treatise, due to the lack of clarity in which that its definition is presented in the original text regarding the operational and architectural points of view.

This assumption, though not detailed in this work, is based on studies linked to Vitruvius as an architect in the service of the Roman government, possibly belonging to the Ordo Apparitores 2 and identified as an Augustan intellectual, as described in the works of Pierre Gros and Elisa Romano. 3 Vitruvius is understood in this sense to be a professional whose duties and connections with power and with other professionals offered him access to specialist knowledge, and whose encyclopedic training enabled him to create an architectural design theory that should be consistent. 4 Considering that Vitruvius's text has no parallels in antiquity to enable a comparative study of its architectural theory, the primary and sole source for understanding Vitruvian theory is the text itself, and that its various translations can be considered as secondary sources due to the inherent characteristics of translation. This research therefore aims to contribute to the discussion about Vitruvian architectural theory strictly from the point of view of the text, taking it as the only source, even when dealing with ordinary concepts.
The research method for defining the theoretical concepts therefore consists firstly of mapping their appearance in the text, and secondly of analysing their usage in the various passages of the text in which they occur, since even those not directly related to architectural design theory can be traced in the search of Vitruvius's understanding of each particular concept. Graphical analysis also allows identification of the sequence in which the concepts are approached, their importance in a determined passage and the relations between them.

ordInatIo as the generator concept of desIgn
The purpose of this particular article, then, is to address the mapping and analyses involved in developing an understanding of ordinatio. Since the definition of ordinatio presented in the second chapter of Book II includes a major understanding of ordo in broad terms as well as of quantitas, membrum, numerus, modulus and symmetria, this work therefore seeks to analyse all occurrences of these roots in the first six books as found in the Harlenianus manuscript. These occurrences, compared with at least three different translations, involve a myriad of fragments of text which I believe can enhance understanding of ordinatio, as it will be described.
The analysis of the occurrences of the root ORD allows them to be classified into three types: a theoretical definition, the applicability of this in design terms and other acceptations of the root. From a total of 35 occurrences, the 15 most relevant for understanding the concept are concentrated in Books I, III and IV. The theoretical definition can be found in the second chapter of Book I, where three of the four occurrences of the root can also be found. While the applicability of the concept is concentrated in the 11 relevant occurrences in books III and IV, in which the design procedures of various types of temple are described. The other acceptations of the root can be found throughout the treatise and will be referenced when they contribute towards its understanding.
In the light of this somewhat imprecise definition, we can establish some preliminary conclusions. The first is that ordinatio includes the architect's work on the parts comprising the design. This procedure involves adapting elements according to a rule, which Vitruvius termed quantitas, to achieve a goal of symmetria. That said, we can also understand firstly that the design is something based on parts or membra, and secondly that these parts have an initial pre-defined configuration, since they have to be adapted to achieve symmetria.
Still in the second chapter, the term reappears in the sixth paragraph, 5 where Vitruvius defines the decor obtained by tradition and states that the appearance of a work would jar if elements of the Doric were transferred to the Ionic, since it includes foreign details to the consuetudinary order. It can therefore also be established that he sees the notion of ordo as something that has been constructed over time, based on architectural tradition. As something predetermined, or at least expected, ordinatio can thus be considered as a prior configuration or a pre-established arrangement.
Before moving on in this investigation of ordo in Books III and IV, it's needed to broaden understanding of the definition of ordinatio by expanding understanding of other terms in the definition, the first of which is quantitas. The root QUANTIT only appears five times in the treatise. In Book I the term is defined in the second chapter as the adoption of modules for measuring the elements, based on the members of the work itself. Returning to the considerations above, if a design is composed of elements that have in themselves some pre-established configuration and have to be adapted to comprise the design as a whole, the procedure of quantitas would therefore be an adjustment of the initial configuration of the elements by measuring and scaling according to a common modular unit, established based on the dimension of one of the elements making up the design. Further on, in Book III, the term appears as a modular quantification, 6 in Book IV as modular measurement, 7 and finally in Book V as related to the largeness of elements measured by interval. 8 So it can be concluded that the notion of quantitas is related to the sizing of elements, but a sizing governed by fixed intervals that relate to the concept of the module.
In attempt to understand this, the research moves on to some significant passages in the 13 occurrences of the root MODUL. The first of these is in Book III, where the author explains how to obtain the reference module for the design of a Eustyle temple based on a division of the front face according to the number of columns, taking one of the parts as the module for the whole design, corresponding to the diameter of the columns. 13 The theme of adopting a module generated from subdividing the frontal dimension of a temple is returned to in Book IV, in this case a Doric temple. 14 The other themes of architecture are addressed as the treatise continues and a less strict approach to a modular system can be seen as the solemnity of the buildings decreases. 15 We can therefore conclude from these passages that the establishment of modules is based on design constraints, such as the site, together with prior decisions at the outset of the design, such as definition of the genre of columns to be used, which is in turn related to the decor, or with the type of intercolumniation, which also has a relationship with decor.
constraints. Based on adoption of the modulus, all the design elements have to be measured based upon this reference interval, including its subdivisions, based on the notion of numerus.
Returning to the relevant occurrences of the root ORD, now in terms of the applicability of the concept, and seeking to validate the proposals listed above, we come to books III and IV. From the seven relevant occurrences in Book III, the first two reinforce the idea that ordinatio consists of a pre-established rule for each type of building, like a set of predetermined or expected formal relationships handed down from the ancients, 16 which we should respect because, as Vitruvius writes, "they ordered the members of the designs through proportion and symmetria to thus achieve harmony". 17 The other occurrences in Book III relate the root ORD to the alignment of elements. In four of these, the author associates ordines with columnarum 18 throughout Book III, meaning a line of columns or colonnade. In the third chapter Vitruvius associates ordines with matres, 19 meaning a row of matrons in a line, referring in this strange passage to their inability of passing arm in arm through the narrow intercolumniation. Both cases, albeit quite different, refer to the connection of ordo with arrangement according to alignment.
The relevant occurrences in Book IV are concentrated in chapters II and VIII, with the root ORD appearing three times in the latter. In these sections Vitruvius writes about 16 III, 1, 4. Ergo si ita natura conposuit corpus hominis, uti proportionibus membra ad summam figurationem eius respondeant, cum causa constituisse videntur antiqui, ut etiam in operum perfectionibus singulorum membrorum ad universam figurae speciem habeant commensus exactionem. Igitur cum in omnibus operibus ordines traderent, maxime in aedibus deorum, operum et laudes et culpae aeternae solent permanere. 17 III, 1, 9. Ergo si convenit ex articulis hominis numerum inventum esse et ex membris separatis ad universam corporis speciem ratae partis commensus fieri responsum, relinquitur, ut suscipiamus eos, qui etiam aedes deorum inmortalium constituentes ita membra operum ordinaverunt, ut proportionibus et symmetriis separatae atque universae convenientesque efficerentur eorum distributiones. 18  the permitted flexibility in relation to the geometric scheme in other types of temple. 20 Furthermore, the relationship between ordinatio, symmetria and dispositio can be seen when the author states that other types of temples can be ordinatae with the same symmetriis, yet forming different dispositiones. 21 In terms of the pre-definition that characterises the adoption of ordinatio, it is important to recall the commissioning and construction process for a public architectural work in ancient Rome. This process began with the nomination of a curator, specifying the commission in comparison with other existing works, as states Pierre Gros. 22 The curator was then charged with choosing an architect, who was responsible for developing the design according to the commission and therefore including the prior definitions and expected geometric scheme for the building, which might be adapted by the architect according to the site and other constrictions, but without his participation in the important initial decision. The building scheme was therefore something imposed on the architect, who was responsible for designing it accordingly, and his greatest challenge and highest reward, as Vitruvius tells in Book VI, was the establishment of the modular relationships between the parts, and not really the formal origination of the building. 23 Finally, we come to the last concept in the definition of ordinatio according to Vitruvius: symmetria. Although the study of this concept involves the analysis of a large number of occurrences -74 in the first six books -the following approach will be just enough to propose the understanding of symmetria as an attribute achieved by a work of architecture when complying with the procedure of quantitas on a base established by ordinatio.
This understanding appears quite clearly in the definition of the concept in Book I, where symmetria would be the dimensional correspondence between the design elements achieved through mathematical operations taking one part as the module for the scale of all the elements. 24 These operations are founded on geometry, as the author explains when addressing the necessary knowledges of the architect in the first chapter, stating that the difficult problems of symmetria are resolved by geometric theories and inventive methods. 25 As he does with ordinatio, Vitruvius tries to construct a reason for the pursuit of this attribute in architecture. This reason appears in Book II, founded on two premises: tradition, which comes from the accumulated experience of construction, bringing certainty to decisions previously unsure and vague; and nature, through which analogy with the human body provides a reference for the employment of symmetria. 26 Another important connection with the term symmetria relates to the notion of genre of columns. Vitruvius repeatedly relates the concept with the term genre throughout books III and IV, when he describes the symmetria of the Ionic genre, the symmetria of the Corinthian genre and the symmetria of the Doric genre, with 19 occurrences of the root SYMMETR concentrated in these passages. Completing the theme of temples in Book IV, Vitruvius uses the term a further seven times when addressing possible flexibility of the rules of symmetria, which can be altered and combined to form new proposals.
the existence of a different symmetria for each genre of columns. The third considers the dependence of the design's high quality on a greater number of modular dimensional relationships between the different elements achieved. And moreover, as the seriousness and public character of the design decrease, the rules of symmetria can be more flexible.

conclusIon
The proposal achieved from understanding ordinatio comes together as a preliminary geometric scheme that would act as a framework of possibilities from which the design would begin. This design would be a geometric scheme adopted from prior definitions, such as the expected configuration of the building, site constrictions, surroundings and the architectural language predetermined in the commissioning of the design, and therefore probably without the architect's decision. It is a primary procedure that geometrises the site, adapting pre-established building schemes, such as the six temple types listed by Vitruvius in the second chapter of Book III, 27 to the dimensions and features of the site and also establishing subdivisions of this initial geometry in the light of the genre of columns to be employed, to generate a kind of modular grid.
So, as a last proposal, the analysis of Vitruvius's descriptions of man's proportions laid out in Book III, allows comparison of ordinatio with the geometric system created for establishing the human figure based on geometry by the association of a square and a circle, 28 upon which one or more modular grids can be established using measured intervals taken from a component part of the body, such as the foot or palm. This scheme works both as a general system for localization of the parts, which supports the dispositio, and as modular dimensioning of the parts, to provide the basis for the achievement of symmetria. 27 III, 2, 1. Aedium autem principia sunt, e quibus constat figurarum aspectus; et primum in antis, quod graece naos en parastasin dicitur, deinde prostylos, amphiprostylos, peripteros, pseudodipteros, hypaethros (...). 28 III, 1, 3. Similiter vero sacrarum aedium membra ad universam totius magnitudinis summam ex partibus singulis convenientissimum debent habere commensus responsum. Item corporis centrum medium naturaliter est umbilicus. Namque si homo conlocatus fuerit supinus manibus et pedibus pansis circinique conlocantum centrum in umbilico eius, circumagendo rotundationem utrarumque manuum et pedum digiti linea tangentur. Non minus quemadmodum schema rotundationis in corpore efficitur, item quadrata designatio in eo invenietur. Nam si a pedibus imis ad summum caput mensum erit eaque mensura relata fuerit ad manus pansas, invenietur eadem latitudo uti altitudo, quemadmodum areae quae ad normam sunt quadratae.