The Vis Saint Gilles Quarrée or the Caracol de Emperadores Cuadrado: a Model Frequently Encountered in Spanish-French

Architectural Treatises from the Modern Period

Alberto Sanjurjo To satisfy curious spirits I will propose the design of a spiral staircase as that of Saint Gilles, which may be raised on a perfect square, or rather, oblong, that is to say, longer than wider, and on whatever other form or figure one may wish.

(L´Orme 1567, f.127)

With these words, Philibert de L´Orme begins his explanation of the vis quarrée. This deals with a spiral staircase on a square or polygonal plan, which is covered and supported by a barrel vault which both turns and rises. This type of staircase which first appears in Le premier tome de L´Architecture (1567) by Philibert de L´Orme and in El libro de Trazas de Cortes de Piedra (between 1575 and 1590) by Alonso de Vandelvira, is frequently found in the stone-cutting treatises prepared in Spain and France during the Modern Period (XVI-XVIII). (fig.1) My paper examines this model from formal, geometric and constructive criteria and sets out to discover why, despite widespread diffusion in texts, it was put into practice on very few occasions.

Figure 1. Drawing of the vis Saint Gilles quarrée (L’Orme 1567, f.127v)

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CONCERNING A DEFINITION In his own definition, De L´Orme relates the vis quarrée to the vis Saint Gilles, as do the majority of French authors. This is the first important difference from Spanish texts. Vandelvira, in the explanation of his model known as Caracol de emperadores cuadrado, makes no mention of the Spanish version of the vis Saint Gilles: the vía de San Gil. (ETSAM R31,f.55v) We should remember that the vis Saint Gilles is one of the most complex elements of the so called art du trait or art of stonework. In essence, we are dealing with a spiral staircase on a circular plan, covered by a barrel vault which is used as support. This model to be found in the majority of texts devoted to stone-cutting in Spain and France, takes its name from a staircase in the Abbey of Saint Gilles in the French Languedoc. For centuries, due to its perfection and difficulty, this spiral staircase was a place of pilgrimage for stonemasons and would become the archetype of a model which was portrayed profusely in treatises up until the nineteenth century. This model appears in Spanish texts under the name of vía de San Gil (Vandelvira, (ETSAM R31), Martínez de Aranda (SHM Aranda) y Portor (BNE Ms 9114)). Vandelvira, the only one of these three authors who describes a square vaulted spiral staircase, defines it as an arch which inclines (splaying in the language of Vandelvira) between a tower and a turret (ETSAM R31, f.55v). It is curious how in Vandelvira’s own description, no reference is made to the design of the staircase. This is perhaps because the elements which define the model are the warped supporting plan of the vault and the vault itself. Indeed, Vandelvira proposes a possible constructive solution with a ramp as in the tower of the cathedral, La Giralda, in Sevilla (ETSAM R31 f. 55v). (fig.2)

But Vandelvira is not the only Spanish sixteenth century author who describes a spiral staircase with a square vaulted plan. In about 1560, a manuscript known as Libro de arquitectura was written by an architect from Córdoba, Hernán Ruiz II, also known as el Joven. In its last pages (ETSAM R39, f.148-152) this manuscript contains a number of drawings, without any accompanying written explanation, in which we are shown the stairs of a square tower with vaulted flights. It is possible that these drawings are a collection of designs intended for the staircase of the tower of one of the many interventions of Hernán Ruiz II in the Andalusian Renaissance. Here we are shown the original approach of this architect which we will develop later. In the definition of de L’Orme, a significant detail is that of the possibility of implementing this staircase from different polygonal base plans: square, rectangular, hexagonal, octagonal and even triangular. A relationship is established with the appearance of stairs of this type in France, between the end of the 15th and the beginning of the sixteenth century, linked to the figure of Martin Chambiges (Perouse 1982, p.145). Although these treatises give no more than a secondary part to stairs which have a polygonal plan (they are only mentioned by de L’Orme and Frezier and never developed graphically) constructed examples of stairs of this type are more numerous than those on a square plan.

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Figure 2. Caracol de emperadores cuadrado in Vandelvira’s manuscript (ETSAM R31 f.55v)

ANALYSIS OF SOURCES The primary sources used in this paper come from a set of collections of elements and models of stone-cutting and architectural treatises produced in Spain and France during the sixteenth century through to the eighteenth century. The first phase, set within the sixteenth century and the first years of the seventeenth century, is characterized by the existence in Spain of hand-written manuscripts of stonework bonding details, prepared for professional use and, in general, not intended for printing. These are composed of a collection of drawings, classified by subject, and accompanied by concise written explanations. These cartillas were passed among groups of stonemasons who copied, lent, and in some cases

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even bequeathed them to members of their family or to fellow workers. The manuscripts of Hernan Ruiz II, Alonso de Vandelvira and Ginés Martínez de Aranda are of particular note in this period. (Bonet 1989) The treatise writings of the coupe des pierres in France in the sixteenth century have different formal characteristics from those of Spain. Architecture by de L’Orme is the first printed treatise produced in France. This is a general Architectural treatise intended to disseminate knowledge and Books III and IV are given over to the Art du trait. While in France the first texts concerning stone-cutting are printed and enjoy a wide circulation, those in Spain are handwritten and become known only in professional circles. This is not to say that the development of treatise writing about stone-cutting in Spain in the sixteenth century was inferior to that in France, but rather the opposite. The number and variety of elements and models gathered in the treatises of Vandelvira and Martínez de Aranda compared with those of De L’Orme, highlight the magnificent level of Spanish stonework. (Rabasa 2000, p.220) The mutual influence between Spain and France in the sixteenth century has been reflected upon by various authors in recent years. If the influence of Architecture by De L’Orme is evident in subsequent French treatises, this direct influence is not so clear in Spanish treatises. The most widely held theory at present is that defended by Perouse de Montclos who even says that these two states could be considered as one entity due to the similarities and connections between them. A vine of Languedoc stock would have nurtured the art of stonework on both sides of the Pyrenees, and in conjunction with considerable mobility between stonemasons, would have made similar developments in stone construction possible in places as far apart geographically as Andalusia and the north of France. (Perouse 1982, p.200) In the seventeenth century, a break is found in the evolution of Spanish-French treatise writing. In France this is the century when treatises devoted to stone-cutting are produced; in only three years, three treatises is published: Desargues, Jousse and Derand. Le Secret d’architecture by Jousse is the first printed treatise wholly devoted to stone-cutting, but its editorial success came to be obscured by the appearance, one year later, of the great French treatise of the seventeenth century: Architecture del voutes by Father Derand. The diffusion of this treatise is unprecedented in the treatise writings of stone-cutting. In Spain, in this century as in the sixteenth century, the major contributions still manifest themselves in handwritten treatises. (fig.3) In the seventeenth century national arena, the principal document on the art of stonework is the work of Joseph Gelabert. In Spain, the eighteenth century is characterized by the production of compendia or general treatise on mathematics which included the occasional volume devoted to the art of stone-cutting elements. From among these compendia, that produced by Father Tomás Vicente Tosca will stand out. This shows a strong influence from the text of Milliet-Dechales (1674). (fig.4) Another text of mathematical compilation which devotes a volume to Civil Architecture is that of the academician

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D. Benito Bails. This is an eclectic work, to say the least, literally copied from numerous authors, offering, in some cases, contradictory examples which reflect the different mentalities and cultures of the authors copied and summarizes Stéréotomie by Frezier. There is not even one original contribution and the author’s eagerness to summarize causes him to include texts lacking connecting themes which might lead to general conclusions. The text which presents greater interest from the point of view of stonework in the eighteenth century is, once more, a handwritten text, Cuaderno de Arquitectura by Juan de Pontor y Castro (BNE Ms 9114). Its interest lies, on the one hand, in the composition of the manuscript itself and, on the other hand, in the attachment to a particular school. Regarding the composition of the manuscript, Gómez Martínez proposes the theory that we would have before us a notebook, of drawings of elements of stone-cutting from the sixteenth century which reaches the hands of Juan de Portor, who completes it, filling the spaces left for the silent drawings with their explanations and contributes new designs which are typical of the eighteenth century, some of these being copied from Tosca (1998, p.38-39). Regarding the link with a particular school, Gómez Martínez, perhaps influenced by Gómez Moreno (1949, p.14) y Barbe-Coquelin de Lisle (1977, p.31-32), maintaining the attachment of the original text to a later school of Vandelviresco origin. José Calvo (1999, tI, p.113), however, maintains a clearer and more obvious link with Cristóbal de Rojas and Ginés Martínez de Aranda.

Figure 3. Vis Saint Gilles quarré (Derand 1643, p.414)

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Figure 4. Front page and drawing De helice Aegidii quadrata (Milliet-Dechales 1674, p.686)

In France in the eighteenth century, the two most complete treatises are produced, from the point of view of the analyses and especially regarding graphic representation. Traité de la Coupe des Pierres by Jean Baptiste de la Rue, 1728, does not contribute important new features to the French seventeenth century treatises. But its main interest lies in the graphic field. This meticulous edition is enriched by the splendid engravings with which the text is illustrated. Among these, we find bonding diagrams drawn in orthogonal projection, in plan and elevation, accompanied by numerous explanatory drawings in oblique perspective. (Sakarovitch 1998, p. 143) (fig.5) The other great French treatise from the eighteenth century is the Traité de Stereotomie by the engineer Frezier. It may be said that with this treatise we reach the culmination of stereotomic knowledge in the eighteenth century. It is organized in three volumes. In the first, he presents an almost mathematical study of the surfaces, influenced by the work of Desargues. In the other two remaining volumes he analyzes a great variety of models, mixing theoretic and especially geometric description with criticism of the tradition embodied in the treatises of Derand and De la Rue. We put the finishing touches to our journey with an indication of the decline of stone-cutting treatise writing in Spain. Our final work of reference is, once more, the translation of a French text.

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Fausto Martínez de la Torre will, in 1795, publish a translation of a French text of professor Simonin from the year 1792. This brief survey of Spanish-French treatise writing on the art of stonework in the Modern Period, highlights the connections, as regards equality, which stem from a common Romanesque trunk, carried out in the sixteenth century, leading up to a dependence which begins in the seventeenth century and culminates in the eighteenth century with the manifest influence of French treatise writing on that of Spain.

Figure 5. Vis Saint Gilles quarrée (La Rue 1728, p.141) DESIGN AND GEOMETRY OF THE VIS SAINT GILLES QUARRÉE The design process for square spiral staircases is, in general terms, the same in all the treatises analyzed. First a plan is drawn of the exterior and interior squares which contain the stairs. The majority of authors take advantage of a double axis of symmetry in order to draw only one part of

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the stair. Except for the drawing of Vandelvira and one of those of Hernán Ruiz which show the full plan, other authors draw three-quarters (De L’Orme), half (Derand, Millet-Dechales and De la Rue) or even one quarter (Frezier) of the stair well. Once the external walls and the central buttress have been drawn, the generating arch of the vault is laid out, designated cintre by French authors and which Frezier very correctly describes as “primitive centering” (1754 tIII, p.223). (fig.6) This same term is that used by Rondelet (1804, p.326). The primitive centering is converted in each head joint, according to the angle which its plan forms with the axis of the vault, into different extended centerings (cintre rallongée) which we will describe later.

Figure 6. Vis Saint Gilles quarrée (Frezier 1754, tIII,p.230) It is important to emphasize that the generating arch or primitive centering need not constitute part of the constructed vault. Vandelvira makes this very clear. In his description, the semicircular arch

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which generates the surface of the vault does not coincide with any of head joints. The arch is, therefore, a theoretical instrument for generating a vault. For this reason, we find Frezier’s description of centering as primitive to be particularly interesting. The next step is to divide the arch into an unequal number of equal parts. These voussoirs will also define the number of courses that the vault will have. Almost all authors, with the exception of Rondelet, agree by drawing five voussoirs per arch. And now, the points of intrados and extrados, of division between voussoires, are projected on to the horizontal diameter of the centering. In stonework language this is known as “to plumb” which will allow us to determine the projections of the bed joints. For each of these points, straight parallel lines in plan view is drawn to the faces of the wall and central buttress. These straight lines will turn around the central buttress, en retour as the French say. It is important to point out that according to Frezier, these straight lines which are the horizontal projections of the bed joints are only parallel in this projection. In vertical projection it can be clearly seen how the straight lines that define the lower intersection of the bed joints, are at the same time rulings of the intrados surface of the vault. Once the projections of the bed joints are drawn in plan view, the face of the exterior wall and the interior buttress is divided in equal parts. The aim of this operation is to determine the points by which the arrises of the steps are drawn, joining with the centre of the buttress the real essence of spiral staircases. Having drawn the steps, the result is similar to the spiral staircase except for the shape of the faces of the stair-well and the buttress itself of the stair. An important difference between the solution proposed by De L’Orme and all the others lies in the design of the steps. De L’Orme divides each flight of steps in equal angles, while the other authors do so in segments or equal parts. By dividing in equal parts, the treads of the steps seem to have different dimensions. Perhaps for this reason, De L’Orme opts for dividing the layout of the steps into equal angles, as is the case in spiral staircases of circular design. The problem is situated in the line of springing of the vault on the faces of the walls. If we take for granted that the latter must be parallel to the pitch of the stairs, we find that such a line will not be straight, because by maintaining the pitch of the flights of steps with different segments of partition, the resulting line joining them is a curve. Later treatise writers must have realised this, since it is one of the unanimous points in describing this type of staircase: all draw as straight the lines of springing of a vault on the faces, due to the distribution of the steps being proportional and not gradual. Now is the moment, as Vandelvira states, to remove the centering from each arch. We have already mentioned that the arches formed in each joint are different. The construction method, as Perouse says, is by trial and error, although we disagree with him that the arch lacks geometric construction (1982, p.88). Following the same line of argument as Perouse, Palacios says “[…] since the cylindrical surface of the vault twists, these sections will no longer be conventional ellipses which are produced by cutting any cylindrical surface by means of a plane oblique to its axis” (1990,

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p.127). We should say, with regard to this, that the arches defined by this method, are ellipses. Frezier is the first author to reflect this in his treatise. The constructional process for the arches is similar in all treatises, and Frezier describes it thus:

Upon the parts IK, FB, NL of these lines (diameters of the centerings) elliptic centerings is drawn, i.e. plumbed from the primitive centering, p2, p3, p4, p5, which is taken perpendicularly on the diameters: NL, FK, IK, on the points on which they are cut by the parallels of the projections of the bed joints.

(Frezier 1754, tIII, p219.) This method, frequently used in stonework, is the same as that used to draw the curve intersection between two barrel vaults. Here we have a construction by which an ellipse is drawn by points which are obtained from the rabattement of the directrix of the generating cylinder of the vault. (fig.7)

Figure 7. Junction between two cylinders for a domical vault (Torija 1661, f.19r)

Afterwards, each centering or arch is placed with its diameter always horizontal, at different heights according to the pitch of the stair. The drawing of this pitch on the faces of the wall and buttress will help us with this. The elliptic centerings are the directrixes of a scroll ruled surface which has the intersections of the bed joints with the intrados surface of the vault as rulings. No author described this surface geometrically until Frezier did so: “Concerning vaults composed of cylindroid surfaces and inclined horizon”, (1754, tIII, p.216) as Palacios translates in the second edition of his book.

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Most authors in their geometric analysis, merely advice that the vis Saint Gilles quarrée can be considered as a mixture of groin vault and domical vault, scroll and inclined. De la Rue explains his very clearly:

[…] these intersections (when one barrel vault joins with another) from the wall to the keystone share the domical vault and from the keystone to the buttress have a groin vault: the keystone has both. The voussoires of the flights of steps of a spiral staircase can be compared, from one angle to another, as from B to C, with those of an inclined oblique vault by both faces […]

(De la Rue 1728, p.140) The meeting between the sections of a vault produce intersections, one part being convex and the other concave, which remind us of those produced between two barrel vaults. Nevertheless, the differences between cylindrical barrel vaults and cylindroids are such that they require a detailed explanation. (fig.8)

Figure 8. Above. Inclined barrel vault with vertical plan diagonal sections.

Below. Cylindroid vault as that of the vis Saint Gilles quarrée. Frezier devotes the first part of his arguments to describe these differences between regular cylindrical barrel vaults and the vaults and the vaults of the vis Saint Gilles quarrée. The main difference is that in a cylindrical barrel vault the springings form an inclined or horizontal plane, depending on the axis of the vault. In a vis Saint Gilles quarrée the springings are not in the same plane. We obtain what Palacios designates plano alabeado de imposta. This scroll plane may be

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defined as a scroll ruled surface with director plane which has the horizontal diameters of the centerings as directrixes, and the springings or projections of the bed joints as rulings. This director plane, triaxial ruled surface is a hyperbolic paraboloid. Juan de Portor y Castro describes in his Cuaderno de Arquitectura a stair represented under the title of: “square scroll staircase horizontal to the landings with straight courses” (BNE Ms 9114, f.28r) which presents, as plane of support, a scroll ruled surface equal to that which serves as scroll springing plane in the vis Saint Gilles quarrée. (fig.9)

Figure 9. Square scroll staircase horizontal to the landings with straight courses in the teatrise of Portor y Castro (BNE Ms 9114,f.28r)

The intrados surface of the vault is, as we have already mentioned, a scroll ruled surface known as cylindroid. This surface has a director plane parallel to the vertical planes which define the faces of

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the wall and the central buttress. In order to draw rulings of the surface, planes parallel to the director must be made. The intersections of these planes with the directrixes, which are the centerings, will give us the points by which we can draw the rulings. These rulings are the intersections of the bed joints of the vault with its intrados surface.

Frezier, when he explains the way of laying out a scroll surface, gives the example of the vis Saint Gilles quarrée, explains the general carving procedure and gives advice on how to obtain greater accuracy: (fig.10)

[…] always resting the ruler on the two opposing arches, this is moved, little by little, parallel to the sides, forming a concave or convex surface, […] in addition to obtain the best situation as regards accuracy, the opposing arches is divided in the same number of equal parts and the ruler is placed on the corresponding parts

(Frezier 1754, t II, p 40)

Figure 10. Drawing of scroll surfaces (Frezier 1754, tII,p.42)

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THE PROCESS OF STONE-CARVING The vault of the vis Saint Gilles quarrée shows two types of voussoirs: those corresponding to straight flights and those located at the intersection of a flight of steps. Unlike the vis Saint Gilles ronde, in which all the voussoirs are equal by courses, in the square plan spiral staircase we come across different straight flight voussoirs, depending on the number of division in each flight. In general, the division between voussoir is produced by vertical planes which line up with the arrises of the steps. Following from the number of steps per flight, we will have the same number of divisions between the voussoirs which, as we have already commented, will not match each other because each of the centerings used to form them are also different. The method employed for carving, by almost all authors, for the two types of voussoirs -straight flight and intersection-, is known as squaring method or equarrisament. We should note that the squaring method consists of carving a voussoir from a prismatic block, removing wedges of material to obtain the definitive piece. Projections on horizontal and vertical planes are used instead of true size templates as in the alternative method by panneaux or, rather, the direct method as named by Rabasa (2000, p. 154). Taking the plan of a stair, in which the projections of the head and bed joints are defined, as a starting point, we draw a template with the form of the horizontal projection of the intrados surface of the voussoir which is going to be carved. In the language of Spanish sixteenth century stonemasons these are designated plantas por cara or panneaux de doyle in French. We will call this an intrados template, but it should be made clear that these templates represent the horizontal projection of the intrados of the voussoir and not its real size. Once the intrados template has been defined, a prism is rough-hewn from a block of stone which has this template as its base and its height is the size obtained from the section of the stair. To achieve this we will make use of a drawing showing the arch and its divisions in their real size. A template is shaped from the form of the head joint of the voussoir to be carved. Thus we have two types of template: that of the intrados, that of the head. Vandelvira explains clearly the process used to obtain the height of the prism: The voussoir must be put as a square and to this we must add the part which is proportional to the height of the flight of the stair which corresponds, normally one step (ETSAM R31, f.56r). This operation has to be done on a separate drawing. The head of the voussoir, including its extrados, is inscribed in a rectangle. This construction is very common in the drawings of stonework models made with the squaring method. Hernán Ruiz used it also in the drawings of his proposals for square plan spiral staircases. (fig.11)

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Figure 11. Drawing of two voussoirs of the vis Saint Gilles quarrée.

What are these aids that the French authors use ? De la Rue gives them the name of Panneaux de rampe or ramp templates. They are a projection, on a vertical plane, of the pitch of the intersection lines of the beds with the intrados of the vault. Frezier explains this very clearly:

[…] the arrises of these rampant joints is drawn by flat vertical surfaces raised on the horizontal projections of the bed joints. […] these can be easily drawn without knowing more than the inclination with the horizon […].

(Frezier 1754, t.III, p.220) To draw these arrises, Frezier also resorts to this type of template and makes it clear that they do not define the real size of the surface. Rondelet, who was not considered important until now as a writer of stone cutting treatises, is the author who is most critical with his predecessors. He will make some interesting comments concerning methods commonly accepted and described in treatises. His criticism is based in the analysis of the solidness and constructive logic of the French texts of stone-cutting. (fig.12) In the same line, it is important to point out his commentary on the head joints in the drawing of the vis Saint Gilles quarrée. Rondelet criticizes the fact that all previous authors arrange the head joints

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according to the direction of the steps and that this causes acute angles in plan and elevation, which are contrary to constructive solidity (1804, p.328). A proposal, in which he places the head joints in vertical planes perpendicular to the axis of the vault, accompanies this critique. This solution posed at the beginning of the nineteenth century agrees with one of those studied by Hernán Ruiz, el Joven, in the last pages of his treatise – probably from the second half of the sixteenth century.

Figure 12. Vis Saint Gilles quarrée. (Rondelet 1804, pl.LIII) Hernán Ruiz draws square plan spiral staircases, in which a possible solution based on the squaring method can be discerned. The voussoirs fall within squares and, in elevation, the springing lines and joint projections are drawn, taking us back to the solution proposed by Vandelvira. But what is really innovatory is the setting out of two solutions for the arrangement of the head joints of the voussoirs. In one of these, the radical head joints are resolved, lining up with the arrises of the steps, and in the other, these joints are arranged perpendicular to the axis of the vault, as Rondelet will do almost two centuries later. (fig.13) It would seem that Hernán Ruiz, in the sixteenth century, had the same way of looking at things as Rondelet. Another important detail is found in folio 152v. When drawing the pitches of the bed joints of different voussoirs Hernán Ruiz draws a template with sides, corresponding with the head joints, that are perpendicular to the pitch of the bed joint. This template, within a rectangle, gives us more information about Hernán Ruiz’s method: it is without doubt the squaring method. But the original part is in the head joints. Hernán Ruiz places these joints perpendicular to the pitch of the vault. No treatise neither in Spanish nor French does so for this type of stair nor for its sister, the vis

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de Saint Gilles ronde, until Monge and Rondelet, at the end of the eighteenth and the beginning of the nineteenth century respectively. It is true that the constructed examples of vis Saint Gilles, generally, present the head joints perpendicular to pitch of the half helix, but this common sense practice in stonework is not reflected in treatises until the end of the eighteenth century. (fig.14)

Figure 13. sketches by Hernán Ruiz el Joven for a square plan vaulted spiral staircase. Left. With head joints perpendicular to the wall. Right. With head joints according to the direction of the steps.

(ETSAM R39, f.149v-150r) Rondelet, by propounding the head joints in planes perpendicular to the projection of the axis of the vault, recognises the difficulty of the drawing of perpendicular sections. These sections is rampant arches, difficult to draw. Perhaps for his reason, we might understand better Hernán Ruiz’s hesitant approach. It must be noted that, despite Rondelet’s constant plea for constructive solidity and having pointed this out at the time of analysing the vis Saint Gilles ronde, he ends up drawing in his model of vis Saint Gilles quarrée, the head joints vertical. VIS SAINT GILLES: QUARREE VERSUS RONDE With the exception of the Spanish manuscripts, which maintain a clear differentiation, the vis Saint Gilles quarrée comes accompanied by its sister la vis Saint Gilles ronde, in the treatises. Frezier explains, skilfully, a theory by which one could consider la vis ronde as the limit to which a polygonal plan vis tends when the number of its sides is made infinite:

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If the curve of double curvature of the springings of the vis of Saint Gilles ronde is substituted by a succession of straight lines inscribed in each helix of the springing of the tower and the buttress, being equal in number, and equal to each other in each springing and in each rotation of these different helices; instead of a cylindroid body which rotates there would be various portions of cylindroids some finishing in others, rotating and rising in a polygonal base tower which could have as many sides as one wanted; it could be triangular, square, pentagonal, hexagonal, etc. in such a way that if the number of these sides becomes infinite, the vis is transformed into the case of the vis de Saint Gilles ronde

(Frezier 1754, t. II ps 217-218)

Figure 14. Drawing by Hernán Ruiz el Joven for a square plan spiral staircase. Despite this forced geometric relationship described by Frezier, it is important to stress that the vaults of this type of stairs belong to different families. We have seen how the polygonal plan vis is formed by portions of cylindroids, that is to say, scroll ruled surfaces of director plane, while the round plan vis is formed by a surface of helicoidal revolution in which the ruling is a circumference.

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But it is in the construction where we find a clear relationship between these polygonal plan stairs and that of the vis Saint Gilles ronde. At the beginning of this paper we made reference to a group of stairs linked to the figure of Martin Chambiges. These stairs are mainly built in direct relationship with a circular plan vis. Thus, in the left wing of the transept of Sens Cathedral, we find an octagonal plan staircase of vis Saint Gilles which changes into a circular vis. In the towers of the façade of Troyes Cathedral we find this connection once more. In the lower part of the left tower there is hexagonal plan vis Saint Gilles staircase joined by a scroll vault to a circular plan staircase in the upper part. In the right tower the game is the opposite, vis Saint Gilles ronde in the lower part and polygonal in the upper part. In Saint Merri Church in Paris we find a stair which has a pentagonal plan in the lower part and hexagonal in the upper part. And in Saint Gervais Church in Paris we find two stairs in both wings of the transept which have a hexagonal plan vis Saint Gilles and change into a circular plan in the upper part. (Perouse 1982, p.284-316) (fig.15)

Figure 15. Hexagonal plan vis Saint Gilles, from the right wing of the transept of Saint Gervais Church in Paris. Photographs by the author.

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This evident connection between vaulted spiral staircases of different types, together with the very few constructed examples of such staircases in Spain and France makes us think of the polygonal and round vis Saint Gilles as stair cases of prestige. They were intended and constructed, not as an answer to a formal or functional problem, but rather to show the great mastery of their authors. The few vaulted polygonal plan spiral staircases actually achieved are pentagonal, hexagonal and octagonal. D’Aviler in his Dictionnaire d’architecture civile et hidraulique sets the small staircases in the Luxembourg Palace in Paris as a constructed model of the vis Saint Gilles quarrée (1755, p.166). Searching for signs of the existence of these stairs, we come across the description that Sauval (1724, t.III, p8) gives of a scroll stair whose design, he says, is very clever. These stairs, no longer in existence, have been an object of reflection for Perouse, who has no doubt in claiming that these stairs are for D’Aviler archetypal. Why has this model, developed in the majority of Spanish-French treatises from the Modern Period, hardly ever been constructed? Rondelet puts forward an answer to this question: this is a stair which is very difficult to execute and rather unnecessary from a functional point of view. For Rondelet, the appearance of the intrados surface of the vault is somewhat unpleasant and the radial arrangement of the steps in a square stair-well not very functional and even dangerous at the angles. In my opinion, this forms part of a small catalogue of stereotomie models intended to lend prestige to its author. A prestige for a prestigious master. REFERENCES Manuscripts Escuela Técnica Superior de Arquitectura de Madrid (ETSAM) library R31, known as Libro de trazas de cortes de Piedras, attributed to Alonso de Vandelvira. R39, known as Libro de arquitectura, attributed to Hernán Ruiz el Joven. Biblioteca Nacional de España (BNE) Ms 9114, known as Cuaderno de arquitectura, attributed to Juan de Portor y Castro. Servicio Histórico Militar (SHM) Manuscript Known Cerramientos y trazas de montea, attributed to Ginés Martínez de Aranda. Printed Works Barbé-Coquelin de Lisle, G, 1977, “Introducción” in Tratado de Arquitectura de Alonso de Vandelvira, Albacete, Caja de Ahorros de Albacete.

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Bonet Correa, A, 1989, “Los tratados de montea y cortes de piedra españoles en los siglos XVI, XVII y XVIII”, Academia, pp.29-62. Calvo López, J, 1999, “Cerramientos y Trazas de Montea de Ginés Martínez de Aranda”, unpublished PhD thesis, Universidad Politécnica de Madrid. D’Aviler, A.C., Dictionnaire d’architecture civile et hidraulique , Paris, 1755. Derand,F , 1643, L´Architecture des voûtes, Paris, Sébastien Cramoisy. Frézier, A.F, 1737-1739, La theoríe et la practique de la coupe des pierres et de bois pour la construction des voutes… ou traité de stéréotomie à l’usage de l’Architecture. 3 vols. Estraburgo and Paris. Second edition 1754-1769. Gómez Martínez, Javier, 1998, El gótico español en la edad moderna: bóvedas de crucería, Valladolid, Universidad de Valladolid. Gómez-Moreno, Manuel, 1949, El libro Español de Arquitectura, Madrid, Instituto de España. L´Orme, Philibert de, 1567, Premier tome de l´Architecture, Paris, Federic Morel. La Rue, J.B, 1728, Traitè de la Coupe des Pierres. Paris. Imprimirie Royale. Martínez de la Torre, F, 1795, Tratado elemental de cortes de cantería o arte de la montea escrito en francés por Mr. Simonin profesor de matemáticas. Madrid. Milliet-Dechales, C, 1674, Cursus seu mundus mthematicus, Tractatus XIV, “De lapidum sectione”, Lyon, Anissonm. Palacios, J.C, 1990, Trazas y Cortes de Cantería en el Renacimiento Español, Madrid, Ministerio de Cultura. Pérouse de Montclos, J.M, 1982, L´architecture a la francaise. Du milieu du XV a la fin du XVIII siecle. Picard. Rabasa Díaz, E, 2000, Forma y Construcción en Piedra. De la cantería medieval a la estereotomía del siglo XIX, Akal. Rondelet, J, 1804, Traité théorique et pratique de L´art de bâtir. second tome. Paris. Chez l’auteur, enclos du Pantheón.

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Sakarovitch, J, 1998, Épures d’architecture. De la coupe des pierres à la géométrie descriptive. XVIe-XIXe siècles, Birkhäuser. Sauval, H, 1724, Histoire et recherches des antiquites de la ville de Paris, Paris, Charles Motete-Jacques Chardon. Torija, J, 1661, Breve tratado de bovedas, Madrid, Pablo del Val.

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