1. Introduction: the catenary arch in Spain in the nineteenth and twentieth century

Catenary arches are one of the main features of Art Nouveau architecture in Spain. Their shape is based on the modern theory of masonry arches. This theory was developed during the nineteenth century and claimed the work of Antoni Gaudí (1852–1926) as its main exponent [1]. Architect Cèsar Martinell i Brunet (1888–1973) built the so-called wine cathedrals (1918–1924) which were built by the Commonwealth of Catalonia (1907–1925).

These buildings in the nineteenth-century style named as Noucentisme may be regarded as the last ig cluster of constructions featuring Catalan masonry [2]. The catenary arches designed and built by Cèsar Martinell belong to the Catalan modernist architecture Antoni Gaudí i Cornet (1852–1926). Thus, in a hanging chain, any inward pulling force is matched by an equal outward pushing force. Martinell knew Gaudi's work and inherited his techniques. This is evidenced by his many writings on Gaudí [3], whom he met during a visit to the Sagrada Familia church in 1915, when Martinell was about to complete his studies at the Barcelona School of

Architecture. From then on, Martinell joined an exclusive group of disciples who learned a way of doing architecture aside from university teachings [4].

awareness about the shape of the catenary was applied by Christopher Wren (1632–1723) in the dome of San Pablo (1675), with the collaboration of Robert

Scientific Knowledge of Spanish Military Engineers in the Seventeenth Century

title "Solutio problematis funicaularii" [14] and also by Chistiaan Huygens

(1629–1695) with the title "Dynastae Zulichemii, solutio problematis funicularii" [15]. The mathematic equation of the catenary would be formulated some years later by David Gregory (1659–1708) and published in the Philosophical Transactions of the Royal Society (1697). Gregory affirms that the catenary is the real shape of an arch, because if these can sustain themselves, it is because a catenary can be drawn in its section [16]. James Stirling (1692–1770), in the Lineae Tertii Ordinis Neutonianae (1717), compiled the ideas of the English school building a catenary with hanging spheres, to simulate the behavior of a constructive element [17]. This solution inspired the analysis by Giovanni Poleni (1683–1761) in the Memorie Istoriche della Gran Cupola del Tempio Vaticano (1748) [18], who developed a methodology similar to Stirling's, to understand the breaking of the vault of the San Pietro

In Spain, the development and application of this theory take place in the context of the Mathematics Academy of Barcelona (1720). The work of Bernard Forest de Bélidor (1698–1761) is the main reference of the curve of equilibrium theory. In La science des ingénieurs dans la conduite des travaux de fortification et architecture civile (1729), Book II, Chap. III, Prop. V, Bélidor sets out the curve that must be given to a vault, so all its parts weigh the same and stand in equilibrium [20], and as a result its curve will have the shape of a catenary. And so he determines, for military constructions, up to five types of different vaults: rounded, tiers-point pointed, elliptical drawn as a segmental arch, the flat ones, and the derived forms of the catenary [21]. In addition, the work De la poussée des voûtes, (1729), by Pierre Couplet (+1743), mentions the chaînette, the hanging chain, as the best of all shapes for the construction of vaults. He also says that to build this vault, every part of the hanging rope has to be loaded with the proportional weight of the

construction, so the resultant curve will be the one to be used [22].

2. The libraries of the military engineers of the eighteenth century

On 13 January 1710, King Philip V appointed Jorge Prosper Verboom

Calabro was appointed head of the Mathematics Academy of Barcelona

(1665–1744) as engineer in chief. Verboom was a disciple of Sebastián Fernández de Medrano. Together with Alejandro de Retz (c. 1660–c. 1732), chief engineer of the Catalan region, Verboom was the link with the former academy in Brussels. Mateo

(1720–1738), and he had profound disagreements with Jorge Prosper Verboom with regard to the training program. Therefore, in 1738 Verboom offered the head position of the academy to Pedro de Lucuze y Ponce (1692–1779), who held that position until his death. Among other duties, the academy had to build a collection of scientific works which would be used as reference texts for military training. This bibliographic interest led Vicente García de la Huerta (1734–1787) to publish Bibliotheca Militar Española (1760), a collection of the most important military

Simon Stevin (1548–1620), in De Beghinselen der Weeghconst (1586), had previously proven the law of equilibrium of a body on an inclined plane. There we can see a hanging cable which has the shape of a catenary [12]. Despite the evidence provided by the figure, there was not any mathematical approach to catenaries. That is why Jakob Bernoulli (1654–1705), in Acta Eruditorum (1690), issued a challenge to the mathematical community to solve this problem [13]. The solution was published in Acta Eruditorum (1691) by Johann Bernoulli (1667–1748) with the

Hooke in the design [11].

DOI: http://dx.doi.org/10.5772/intechopen.87060

Basilica [19].

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For Martinell, Gaudí was a much more interesting lesson of life and architecture than most of the teachings given at university. Gaudí's words became architectural when the very statement of the scientific truth and the procedures he himself invented were able to explain problems and geometric concepts which remained unclear in the classrooms of the school of architecture. Antoni Gaudí's theory of structures relies on the strength of geometry, in particular on the strength of the parabolic and catenary shapes. The construction technique used by Cèsar Martinell stems from the methods applied by Gaudí to calculate the geometric shapes of vaults and arches [5] (Figure 1). Other architects have written about this view; see, for instance, the lecture entitled La fábrica de ladrillo en la construcción catalana (1900), by Josep Domènech i Estapà (1858–1917). In this lecture it is claimed that the parabolic and catenary shapes are the lines of equilibrium in a system of evenly distributed loads, where the parabolic shape relates to the horizontal projection and the catenary shape relates to the arch length [6].

Otherwise, these concepts were introduced in the formation of architects through the Escuela Especial de Arquitectura de Madrid (1844). The work Traite Theorique et Pratique de L'art de bâtir (1802–1817) by Jean-Baptiste Rondelet (1742–1829) exposes the methodology to lay out catenary arches by means of the theory of the chain and another complicated procedure [7]. In addition, a treatise by John Millington (1779–1868) was also used in architecture schools. It was translated as Elementos de Arquitectura (1848) and contained Hooke's theory and the layout of the catenary [8]. Juan Torras i Guardiola (1827–1910) developed the scientific basis for the calculation of these structures in the Barcelona School of Architecture (1875) [9].
