The geometric layout of the southern Gothic apse of the cathedral of Tortosa
DOI:
https://doi.org/10.3989/ic.6442Keywords:
Tortosa Cathedral, geometric systems, heptagon, neoplatonism, proportion, sacred geometryAbstract
The statistical analysis of the results of the new surveys carried out with Terrestrial Laser Scanner (TLS) in the southern Gothic cathedral of Tortosa (1383), have shown that the metrological layout of its tetradecagonal apse has a methodological accuracy of [±1,502%]. Analytically, it is determined that, within the range of precision, the total width of the ambulatory is 150 palms, and that the radial chapels have a dimension of 24 palms, which is 3 canes, a tonal ratio (9:8) with respect to the measurement of the aisle of 27 palms. The keystone is located at 100 spans, and its final section has a ratio (3:2) between the width of the ambulatory, 150 spans, and its height. In conclusion, we can observe a proportional conjunction between the medieval order and the Gothic masonry. The proportions of Tortosa cathedral are part of the Timaeus tradition, which was well known to its promoters, different from that of the northern Gothic masters, with section models ad triangulum (1:√3/2) and ad quadratum (1:1) defined in the debates in Milan Cathedral.
Downloads
References
(1) Bork, R. (2022). A geometrical perspective on Otto von Simson's Gothic Cathedral. Nexus Netw J, 24, 397-421. https://doi.org/10.1007/s00004-022-00591-2
(2) Viollet-le-Duc, E. E. (1845-1868). Dictionnaire raisonné de l'architecture française du XIe au XVIe siècle. vol. 10 Paris: B. Bance, A. Morel, V2, 372-375.
(3) Lasteyrie, de R. (1926). L'Architecture Religieuse en France. A L'Epoque Gothique. Paris: Auguste Picard, 351.
(4) Beltrami, L. (1887ª). Per la facciata del Duomo di Milano. Parte Prima. Le Linee Fondamentali. Milano: Tip. A. Colombo & A. Cordani, 16-36.
(5) Viollet-le-Duc, E. E. (1863). Entretiens sur l'architecture, vol. 1 Paris: A. Morel et Cie Éditeurs, 394.
(6) Lund, J. F. M. (1921). Ad Quadratum: a study of the geometrical bases of classical and medieval religious architecture. London: B.T. Batsford, 1-4.
(7) Moessel. E. (1926). Die proportion in antike und mittelalter. München: C.H. Beck, 69-108.
(8) Ghyka, M. C. (1931). Le nombre d'or, rites et rythmes pythagoriciens dans le développement de la pensée occidentale. Tome I, Les Rythmes. Paris: Librairie Gallimard, 81-122.
(9) Verga, C. (1980). Il Duomo di Milano da Bramante-Cesariano a Stornaloco. Crema: Tip. Donarini e Locatello, 25, Figura 9.
(10) Mathonière. J.M. (2003). L'Ancien compagnonnage germanique des tailleurs de Pierre. Fragments d'histoire du Compagnonnage, Musée du Compagnonnage. Tours, 5: 86-90.
(11) Sebregondi, G. C.; Schofield, R. (2016). First principles: Gabriele Stornaloco and Milan Cathedral. Architectural History, 56: 63-132. https://doi.org/10.1017/arh.2016.3
(12) Beaujouan, G. (1963). Calcul d'expert, en 1391, sur le chantier du Dôme de MilanIn: Le Moyen Age. Brussels: Livraire Jubilaire, 555-563.
(13) Laguno, E. (1829). Noticia de los Arquitectos y Arquitectura de España desde su restauración. 4 vols. Madrid : Imprenta Real. 1, 261-27.
(14) Cornford, F. Mc. (1937). Plato's cosmology. The Timaeus of Plato. London: Kegan Paul,Trech, Trubner &Co, 66 -71.
(15) Lluis i Ginovart, J; López-Piquer M.& Urbano-Lorente, J. (2018). Transfer of Mathematical Knowledge for Building Medieval Cathedrals. Nexus Network Journal, 20, 153-172. https://doi.org/10.1007/s00004-017-0359-3
(16) Zaragozá A.; Ibáñez, J. (2014). Hacia una historia de la arquitectura en la Corona de Aragón entre los siglos XIV y XV a partir de los testeros de los templos. Ábsides construidos, ábsides proyectados e ideales y ábsides sublimes. Artigrama. 29: 261-303. https://doi.org/10.26754/ojs_artigrama/artigrama.2014298078
(17) Lluis i Ginovart, J; Costa-Jover, A; Coll-Pla, S. (2015). Placing the keystone of the vault over the presbytery in Tortosa Cathedral, Spain (1428-40), Construction History. 30 (1),1-21, (Figura 3.b).
(18) Lluis i Ginovart J; Costa-Jover, A; Coll-Pla, S. (2014). The reconstruction of a Romanesque palimpsest using non-destructive techniques. Informes de la Construción, 66: 536, e045. https://doi.org/10.3989/ic.13.184
(19) Barney, S. A. (et alli) (2006). The Etymologies of Isidore of Seville. New York: Cambridge University Press, 377. https://doi.org/10.1017/CBO9780511482113
(20) Clementis VIII. (1595). Pontificale Romanum Clementis VIII Pont. Max. iussu restitutum atque editum. Romae: apud Iacobum Lunam: impensis Leonardi Parasoli & Sociorum., 281-296.
(21) Puig i Cadafalch, J. (1923). El problema de la transformació de la catedral del nord importada a Catalunya: contribució a l'estudi de l'arquitectura gótica meridional. Miscel·lània Partas de la Riba. Barcelona: Institut d'Estudis Catalans 65-87.
(22) Font i Carreras, A. (1891). Barcelona Cathedral. Slight considerations on its architectural beauty. Barcelona: Imprenta y Litografía en Henrich y Cª, 9-14).
(23) Sebastián, S. (1994). Symbolic Message of Medieval Art. Architecture, Liturgy and Iconography. Madrid: Ediciones Encuentro, 352-355).
(24) Canal. J. (1832). España sagrada: tomo XLV, tratado LXXXVIII. Madrid: En la Imprenta de Don José del Collado.
(25) Alsina, C (et. al.).(1990). Pesos, mides i mesures dels Països catalans. Barcelona: Curial, 37-38).)
(26) Riu, M. (1996). Pesos, mides i mesures a la Catalunya del segle XIII. Anuario de Estudios Medievales, 26 (2): 825-837. https://doi.org/10.3989/aem.1996.v26.i2.669
(27) Bovelles, Ch. (1542). Livre singulier et utile, touchant l'art praticque de geometrie, compose nouvellement en françoys, par maistre Charles de Bouvelles. Paris: Regnaud Chaudière et Claude, 5v.
(28) Durero, A. 1525. Underweysung der Messung, mit dem Zirckel und Richtscheyt: in Linien Ebnen vo gantzen Corporen. Nürenberg: Hieronymum Formschneyder, 26r-27v.
(29) Kepler, J. (1619). Ioannis Keppleri Harmonices mundi libri V. Lincii Austriae, sumptibus Godofredi Tampachii bibl. Francof.: excudebat Ioannes Plancu, 32-40. https://doi.org/10.5479/sil.135810.39088002800316
(30) Gauss, C. F. (1801). Disquisitiones Arithmeticae. Auctore D. Carolo Federico Gauss. Lipsiae: In Commissis apud Gerh. Fleischer Jun, 454-463) https://doi.org/10.5479/sil.324926.39088000932822
(31) Aghayani-Chavoshi, (2010). Ketâb al-nejârat (On what is indispensable to artisans in geometric constructions) Tehran: Written Heritage Research Centre & Institut Français de Recherche Iran, Y47B-,Y47C, Y47D
(32) Raynaud, D. (2012). Abū al-Wafā' Latinus. A study of method. Historia Mathematica, 39: 34-83. https://doi.org/10.1016/j.hm.2011.09.001
(33) Heideloff, C.A. (1844). Die Bauhütte des Mittelalters in kurzgefasste geschichtliche Darstellung mit Urkunden und andern Beilagen, so wie einer Abhandlung über den Spitzbogen in der Architektur der Alten. Nuremberg: Berlag von Johann Adam Stein, 96-97)
(34) Roritzer, M. (1999). Das Büchlein von der Fialen Gerechtigheit (fak. Regensburg 1486) und Die Geometria Deutsch (fak. Regensburg un 1487/88). Regensburg: Hürtgenwald Guido Pressler, 56-60.
(35) Schoene, H. (1903). Heronis Alexandrini opera quae supersunt omnia. Vol III: Rationes dimetiendi et commentatio dioptrica. Leipzig : Teubner, 55-59.
(36) Friedlein, G. 1867. De institutione arithmetica libri duo. De institutione Musica libri quinque. In: Aedibus BG (ed) Accedit geometria quae fertur Boetii. Leipzig: Teubneri, 420-421.
(37) Lundy, M. (1998). Sacred Geometry. New York: Wooden Books/Walker & Company, 36-37.
(38) Finlay, A. H. (1959). Zig-Zag Paths. The Mathematical Gazette, 43:199. https://doi.org/10.1017/S0025557200237303
(39) Lluis i Ginovart, J.; Fortuny-Anguera, G.;,Agustí Costa Jover, A. ; Sola-Morales Serra, P.(2013). Gothic Construction and the Traça of a Heptagonal Apse: The Problem of the Heptagon. Nexus Network Journal, 15: 325-348. https://doi.org/10.1007/s00004-013-0152-x
(40) Lluis i Ginovart, J; Lluis-Teruel, C. (2023). Incommensurability, the Heptagon of Ignacio Muñoz (1684), and Kepler's Heresy. The Mathematical Intelligencer, 45, 108-117. https://doi.org/10.1007/s00283-022-10247-1
(41) Heath, T. L., ed. (1908). The Thirteen Books of Euclid's Elements. 3 vols. Cambridge: University Press. vol. 2, 88-111.
(42) Lluis-Teruel, C.; Lluis i Ginovart, J. (2023). El heptágono de fray Ignacio Muñoz y su Manifiesto Geométrico (1684). EGA Expresión Gráfica Arquitectónica, 47, 122-135. https://doi.org/10.4995/ega.2023.16289
(43) Nuere E. (2001).Nuevo tratado de la carpinteria de lo blanco. Madrid: Ediciones Munilla-Leira, 68.
(44) Ascani, V. (1991) "I disegni architettonici attribuiti ad Antonio de Vicenzo. Caracteristiche Tecniche e Ruolo Degli 'appunti grafici' nnella prassi progettuale tardogotica", Arte Medievale. Periodico internazionale di critica dell'arte medievale. II Serie, V. 1, 105-115
(45) Vitruvio, M. P. (1521). Di Lucio Vitruvio Pollione de Architectura libri dece traducti di latino in Vulgare affigurati: Comentati & con mirando ordine insigniti. Como: Gotardo da Ponte, 15r- 15v.
(46) Bubnov, N. (1899). Gerberti postea Silvestri II papae opera mathematica (972- 1003). Berlin: Friedländer, 43-45.
(47) Ackerman, J.S. (1949). "Ars Sine Scientia Nihil Est" Gothic Theory of Architecture at the Cathedral of Milan, The Art Bulletin, 31(2), 84-11. https://doi.org/10.2307/3047224
(48) Pardillos, M.T. (2000). The book of numbers attributed to Saint Isidore, bishop of Seville. Emblemata, 6, 285-304.
(49) Alberti, L.B. (1485). De re aedificatoria. Florence: Niccolò di Lorenzo Alemanno, fol 20 r-21 v.
(50) Saluzzo, C. 1841. Trattato Architettura Civile e Militare di Francesco di Giorigio Martini achitectto senese del secolo XV obra per prima volta publicato. Torino, Tav. III, Figura 5.
(51) Pelerin, J. (1505). De artificiali perspectiva. Viator. Tulli: Petri Iacobi, Illustr., carta [XVII] verso.
(52) Ryff, W. H. (1547). Der furnembsten, notwendigsten, der gantzen Architectur angehörigen mathematischen vnd mechanischen Künst eygentlicher Bericht: vnd vast klare, verstendliche Vnterrichtung, zu rechtem Verstandt der Lehr Vitruuij, in drey furneme Bücher abgetheilet: als, Der newen Perspectiua ... der Geometrischen Büxenmeisterey, vnd Geometrischen Messung. Nürnberg: Johann Petreius, fol. 22 v-23 r.
(53) Vitruvius, M. P. (1548). Der furnembsten notwendigsten der gantzen Architectur angehörigen mathematischen und mechanischen Künst eygentlicher Bericht und verstendliche Unterrichtung. Johan Petreius. Nürnberg, Propo. XXII-XXIII.
(54) De l'Orme, P. (1567). Le premier tome de l'architecture. París: Frédéric Morel, 235 r.
(55) Nava, A. (1854). Memorie e documenti storici intorno all'origine, alle vicende ed ai riti del Duomo di Milano Publicato per cura del Conte Ambrogio Nava. Milano: Tipografia de Borroni e Scotti, 26 bis.
(56) Mella, E. A (1863). Elementi di architettura gotica da documenti antichi. Litogª. Corbetta edite prope ,Tav XIX, Figura3)
(57) Mongeri, G. (1887). Per la facciata del Duomo di Milano. 1887. Memorie e Commenti. Milano. Prem. Tipo-Litografia degli Ingegneri', 36 bis Vol. XXXV, Tav. II.
(58) Beltrami, L. 1887b. Per la facciata del Duomo di Milano. Parte Terza. La Teoria. Milano: Tip. A. Colombo & A. Cordani.
(59) Boito, C. 1889. Il Duomo di Milano e i disegni per la sua facciata. Milano: Tipografía di Luigi Marchi, 121.
(60) Beltrami, L. (1900). Il coronamento nella fronte del duomo di Milano in base ad antichi disegni in parte inediti :con prefazione in risposta al voto di sette architetti. Milano: Tipografia Umberto Allegretit, 46.
(61) Lassus, J.B. 1858. Album de Villard de Honnecourt. Architecte du XIIIe siècle. Paris: Imprimerie impériale, 113-120, Plancha 27).
(62) Frank, P. (1945).The secret of the medieval masons. The Art Bulletin, 27: 36-75, 59. https://doi.org/10.2307/3046979
(63) Valentini, G. (1990). Il Duomo di Milano. Una disputa medievale sul modelo del tempio. Milano: Nuovo Edizioni Duomo, 70.
(64) Lluis i Ginovart, J., Costa-Jover, A., Fortuny i Anguera, G. (2015). Elementos auxiliares de construcción en la arquitectura gótica. El pilar «major» de la catedral de Tortosa.Informes de la Construcción, 67, 537, e057. https://doi.org/10.3989/ic.13.059
(65) Aurelius Augustine. 1876. The City of God, Volume II. Translated by the Rev. Marcus Dods, M.A. Edinburgh:T. & T. Clark, 357.
(66) Lluis-Teruel, C. (2019). El quadrivium y la catedral gótica, Módulo Arquitectura CUC, 22, 1, 195-218. https://doi.org/10.17981/mod.arq.cuc.22.1.2019.08
(67) Lluis i Ginovart, J., Costa-Jover, A., Coll-Pla, S. (2016). La determinación del concepto de homogeneidad versus resistencia en los pilares de una catedral gótica mediante técnicas no invasivas. Informes de la Construcción, 68, 543, e155. https://doi.org/10.3989/ic.15.119
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Consejo Superior de Investigaciones Científicas (CSIC)
This work is licensed under a Creative Commons Attribution 4.0 International License.
© CSIC. Manuscripts published in both the print and online versions of this journal are the property of the Consejo Superior de Investigaciones Científicas, and quoting this source is a requirement for any partial or full reproduction.
All contents of this electronic edition, except where otherwise noted, are distributed under a Creative Commons Attribution 4.0 International (CC BY 4.0) licence. You may read the basic information and the legal text of the licence. The indication of the CC BY 4.0 licence must be expressly stated in this way when necessary.
Self-archiving in repositories, personal webpages or similar, of any version other than the final version of the work produced by the publisher, is not allowed.
