‘Mixed’ mathematics in engineering education in Spain: Pedro Lucuce's course at the Barcelona Royal Military Academy of Mathematics in the eighteenth century
2011; Taylor & Francis; Volume: 3; Issue: 3 Linguagem: Inglês
10.1080/19378629.2011.618188
ISSN1940-8374
AutoresMaría Rosa Massa Esteve, Antoni Roca-Rosell, Carles Puig-Pla,
Tópico(s)Historical Philosophy and Science
ResumoAbstract Engineering in Spain developed as a scientific profession during the nineteenth century. Nevertheless, the idea of combining theory and practice was forged in the eighteenth century as a result of several influences. The example of the Royal Military Academy of Mathematics of Barcelona established in 1720 seems particularly interesting from this point of view insofar as its main goal was to supply knowledge in mathematics to young and experienced officers in three main military fields: engineering, artillery and the navy. In 1739, an Ordinance of the Royal Academy established a general course of mathematics to train military engineers. This course was prepared by its director Pedro Lucuce and it centred on 'mixed' mathematics, i.e. those domains useful in warfare and engineering. It became a pillar of the academy's curriculum. By analysing the course content, the authors hope to shed light on a number of aspects relating to this training and to test the hypothesis that Lucuce's programme should be understood as falling within the tradition of the mathematical courses, launched in the seventeenth century. Keywords: Lucuce's courseRoyal Military Academy of Mathematics of Barcelonamixed mathematicsphysico-mathematicsmathematical courseseighteenth centurySpanish engineeringengineering education Acknowledgements The authors would like to thank Antónia Conde, Ana Cardoso de Matos, M. Paula Diogo, Victor Navarro-Brotons and Mònica Blanco from their contributions and ideas on engineering and mathematical education in Portugal and Spain. The authors are also grateful to Irina Gouzévitch and Peter Jones for their help and comments. Notes 1This research work is being carried out in the broader context of the study of scientific institutions and the reception of new scientific ideas in Catalonia, specifically the project: "Engineering and Scientific Culture in Catalonia and Spain (1720–2000)" (HUM2007-62222/HIST) and its continuation "Engineering, Mathematics, and Society in Catalonia and Spain XVII–XX centuries" HAR2010-17461/HIST. Also the Acción Integrada with the Portuguese team directed by M.P. Diogo, HP2008-0012. 2There is scant information about Mateo Calabro. It is said that he was born in Messina, Italy. It seems that he travelled in America, where he came to understand the importance of mathematics. He was chosen by Verboom (see footnote 26), as the first teacher of mathematics and director of the Academy of Barcelona. He thought that the course of mathematics of the academy should embrace more subjects than Verboom had planned. Probably because of his disagreements with Verboom, he left the Barcelona Academy in 1738 and moved to Valencia where he tried to set up another academy of mathematics. There, however, he encountered the opposition of the Valencian mathematicians. See Capel, Sánchez and Moncada, De Palas a Minerva and Navarro-Brotons, Tradició i canvi científic. 3Pedro de Lucuce studied Canon Law at the University of Oviedo, but he left this career to join the army in 1711, during the War of Spanish Succession. After the war he was incorporated in a regiment in Madrid where he had the opportunity to study mathematics for his own initiative. In 1730, he was elected simultaneously member of the Corps of Military Engineers and of the Corps of Artillery. He chose the engineering corps and in 1736 he joined the Academy of Mathematics of Barcelona. 4The main references are: Riera, "L'Acadèmia de Matemàtiques"; Capel, Sánchez, and Moncada, De Palas a Minerva; Alcaide and Capel, "El curso decosmografía"; Muñoz Corbalán, L'Acadèmia; Capel, "Construcción del Estado"; Roca-Rosell et al., "The Military Academy"; Galland, Les Ingenieurs militaires espagnols; and De Mora Charles and Massa Esteve, "On Pedro de Lucuce's Mathematical Course". 5On this academy, see Navarro Loidi, Las Ciencias Matemáticas. 6Capel, Sánchez, and Moncada, De Palas a Minerva, 255–345. 7On Almadén, see Sánchez Gómez, "Minería y metalurgia," 239–49; and Gouzévitch and Gouzévitch, "Agustin Betancourt and Mining Technologies," 14–7. 8On Betancourt, see Chatzis, Gouzévitch and Gouzévitch, "Agustin de Betancourt". 9See Lusa Monforte, "La creación"; Lusa Monforte and Roca-Rosell, "Historia de la Ingeniería Industrial"; and Roca-Rosell et al., "Industrial Engineering". 10See Lafuente and Sellés, El Observatorio and Sellés, "Navegación e Hidrografía," 527 passim. 11Lafuente and Peset, "Las academias militares" and Lafuente and Peset, "Militarización". 12See Roberts, Schaffer, and Dear, The Mindful Hand. 13Tartaglia describes what he refers to as the "vulgar", that is to say, the mathematics most people know, which includes arithmetic, geometry, music, astronomy, astrology, cosmography, geography, corography, perspective, specularia, the science of weights, architecture and many others. He also recognizes as usual the Quadrivium formed by arithmetic, geometry, music and astronomy. He then goes on to point out that Luca Pacioli, in his classification, modifies the Quadrivium by adding perspective, and states that therefore it would consist of five parts, or three parts if music were removed. Tartaglia also cites Pierre d'Ailly's classification, which concludes that music, astronomy and perspective belong to mixed mathematics. Tartaglia, Euclide Megarense, Introduction. 14Tartaglia, Euclide Megarense and Brown, "The Evolution of the Term" "Mixed Mathematics". 15In France, military schools began to proliferate thanks to the initiative of Richelieu, and in Spain, we can cite the schools of artillery created in the sixteenth and seventeenth century. See Hahn, "L'enseignement scientifique" and Vicente Maroto, "Las escuelas". 16Massa Esteve, "Symbolic Language". 17Hérigone, Cursus Mathematicus. 18Dechales was a Jesuit missionary in Turkey. For 4 years he gave public courses on mathematics at the College of Clermont in Paris. Before teaching in Lyon and in Chambery, he worked in Marseille, where he taught the arts of navigation and military engineering and practical applications of the mathematics to the sciences. From Marseille he moved to Turin where he was named professor of mathematics at the University. He died there at the age of 57. For more information, see Schaaf, "Dechales," 621–2. 19It was republished in 1690, after the death of its author, with various new annexes to bring the contents up to date. 20For more information on Tosca's Compendio, see Navarro-Brotons, Tradició i canvi científic. 21Dear, "Art, Nature, Metaphor," 168–79. 22Bernard Forest de Bélidor was born in Catalonia in 1698, because his father belonged to the French army fighting in the Nine Years' War (1688–1697). He joined the army and, given his knowledge of mathematics, he became a teacher at the new school of Artillery of La Fère (1720). In 1722, he became a member of the Académie des Sciences of Paris and in 1726, the Royal Society of London. 24Bélidor, Nouveau Cours, Préface. 23The 1757 edition of the Nouveau Cours is completely renewed. 25Bélidor, La Science. See Vérin, La Gloire des ingénieurs, chapter VI and Gouzévitch and Verin, Sobre la institución y el desarrollo de la ingeniería 26Jorge Próspero de Verboom was born in Brussels in 1667. He was educated in the Academy of Brussels directed by Sebastián Fernández Medrano. In 1692, he succeeded his father as an important engineer in the Low Countries. It seems that he met the French engineer Sebastien de Vauban. In 1709, he was in charge of the creation of the Spanish Corps of Military Engineers, approved in 1711. He died in 1744. 27Verboom, Jorge Próspero, "Project pour une Académie, ou Ecole, ou se doit démontrer les Mathematiques, Fortifications, et Dessein, dans les parties qui conviennent de sçavoir à un officier de Guerre, et particulièrement pour ceux qui souhaitent d'entrer dans le Corps des Ingénieurs," 1712, cited and explained in Estudio histórico, 13. 28In the Utrecht Treaty (1713), the Low Countries were definitely separate from the Spanish Crown. 29It was definitely finished in 1750. 30Verboom, Jorge Próspero (?), "Discurso y Proyecto," f. 42r, 43r, 46r–47v. Some authors doubt the authorship of this text, but we think that it can be attributed to Verboom. 31Fernández Duran to Verboom, Madrid, March 28, 1715, Guerra Moderna, leg. 2994, Archivo General de Simancas (AGS). 32The Barcelona Academy of Mathematics had seven directors: Mateo Calabro (1720–1738); Pedro de Lucuce y Ponce (1738–1779); Claudio Martel (1756–1760); Juan Caballero y Arigorri (1779–1784); Miguel Sánchez Taramas (1784–1789); Félix Arriete (1790–1793) and Domingo Belestá y Pared (1794–1802). See Capel, Sánchez, and Moncada, De Palas a Minerva. 33Reproduced in Muñoz Corbalán, L'Acadèmia, 399–402. 34Capel, Sánchez, and Moncada, De Palas a Minerva. 35There is a facsimile of the treaty of fortification, from a copy conserved in the University of Salamanca. Calabro, Tratado de Fortificación. 36Verboom, "Proyecto o Idea," 17. 37Ibid., 18. 38Ibid., 44. 39Probably referring to the Port Royal Logic. 40Lucuce, "Formulario," 8 June; "Formulario," 29 June; and "Formulario," 6 July. 41The debate appears in the letter: Pedro de Lucuce to the Duque de Montemar, Barcelona, June 14, 1737, Guerra Moderna, leg. 2994, AGS. 43 Ordenanza, 1. 42There is a printed version of the ordinance: Ordenanza. 44Ibid., 1. 45Ibid., 8. 46In the early 1750s, Jorge Juan, the Spanish scientist and naval officer, played an important role in the acquisition of mathematical tools and books for military schools in Barcelona and Cadiz. 47Carrillo de Albornoz, "Els plans" and Capel, Sánchez, and Moncada, De Palas a Minerva. 48On Cabrer, see Estudio histórico, vol. 2; Capel et al., Los Ingenieros militares en España, 97–9; and several mentions in Capel, Sánchez, and Moncada, De Palas a Minerva. On Zarco, see Estudio histórico, vol. 2; there is a biography written by his family, a copy of which is conserved in the Biblioteca Central Militar, Madrid, "Noticia biográfica". 49For the purposes of our analysis we are using the copy made by Zarco, which includes all the figures. In the same library there are around three more copies. In the Library of the Corps of Artillery and in the Association of Architects at Madrid, there are also incomplete copies. Capel, Sánchez, and Moncada, De Palas a Minerva, 368. There is another incomplete copy in the Military Library of Barcelona. Thanks to Alcaide and Capel, there is a copy of the book on cosmography belonging to a private collection in the Library of the University of Barcelona. There is a copy of the book on geometry in the Library of the Ateneu Barcelonès of Barcelona. In the Biblioteca de Catalunya there are copies of the treatises of geometry, statics and fortification. 50This treatise is not included in the copies of Zarco and Cabrer. There is only one copy in the Library of the Colegio de Arquitectos in Madrid. See Rabanal Yus, "El tratado de arquitectura," 179–85. 52Ibid., Introduction f. 3v. 51Lucuce, Curso Mathematico, Introducción f. 9 [vol. 1]. 54Lucuce, Curso Mathematico, Introduction. 53Dear, "Art, Nature, Metaphor," 168. 55Lucuce, Curso Mathematico, Introduction. This part is almost identical to Tosca's introduction in his Compendio Mathematico. 56Navarro Brotons, Tradició i Canvi científic. 57Verboom, "Proyecto o Idea," 44. 58Verboom explains that the basis of this course should be the first six books of Euclid as they were explained by the Messieurs of Port Royal in their new Elements of Geometry. In fact Antoine Arnaud and others argued that the elements should be explained following the ideas stated in the Logique de Port-Royal. For more information, see Gardies, Pascal, entre Eudoxe et Cantor, 85–108. 59 Monografía sobre el área del cono oblícuo, publicada el 1755 por la Academia Militar de Mathematicas de Barcelona. AGS, Section Guerra Moderna, bundle 3778. It was quoted by Cuesta Dutari, Historia de la invención del análisis infinitesimal, 155–87. 60These authors of the monograph about the oblique cone should refer to the work Analyse démontré ou la méthode de résoudre les problèmes des mathématiques et d'apprendre facilement ces sciences, Paris, 1708, by Charles René Reyneau. 61The authors should refer to the work Analyse des infiniments petits. Comprenant le calcul intégral dans toute son étendue, Paris, 1735, by Edmund Stone, m. 1768. 62The authors should refer to Elementa Matheseo Universae (1713–1715) by Christian Wolff (Breslau, 1679–Halle, 1754). 63 Monografía sobre el área del cono … , 2. 64Galindo, El conocimiento constructivo and Galindo, "La ciencia de los Ingenieros". Muller, Tratado de fortificación. 65Lucuce, Principios de Fortificación. 66See Montaner i Martorell, La Modernització de l'utillatge mental, 117–222. 67March, Nociones Militares. 68Lluch, Las Españas. 69Nieto-Galan and Roca-Rosell, "Scientific Education". 70See Capel, Sánchez, and Moncada, De Palas a Minerva and Muñoz Corbalan, L'Acadèmia. 71During the eighteenth century, only 15% of the members of the Corps of Engineers had been students of the Academy of Barcelona. Capel, Sánchez, and Moncada, De Palas a Minerva, 272–6. 72Lluch, "Troballes," 1997. 73Record on students. Guerra Moderna, leg. 3030, AGS. 74Montaner i Pascual, La Modernització de l'utillatge mental; Arranz i Herrero, Mestres d'obres; Arranz i Herrero, La Menestralia; Rosell, La construcció en l'arquitectura; and Rosell, "Arquitectura i construcció". 75The Renart collection is described in Biblioteca de Catalunya, Inventari del fons Renart, Barcelona 2005: http://www.bcn.cat/fons/inventaris/arxiu/Renart_Ajuda_cerca.pdf (accessed September 2011). 76Leg. XXVIII, Fons Renart, Biblioteca de Catalunya. Partially reproduced in Rosell, La construcció en l'arquitectura. 77Galindo, El conocimiento constructivo, 175–81. 78There is a list of the books belonging to the library of the academy. See Riera, "L'Acadèmia de Matemàtiques," 102–22.
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