The Values of Illustration in the Economic Society of Asturias and Its Reflection in Mathematics Education at the Royal Asturian Institute of Nautical Studies and Mineralogy during the Last Quarter of the 18th Century

Abstract

The Economic Society of Friends of the Country of Asturias, Spain, was an instrument of enlightened reformism which operated in a region with serious economic backwardness. It was born in 1780 at the initiative of Campomanes and responds to the Matritense model, meaning that it focused on economic development and popular education. It is known that Jovellanos directly participated in the establishment of the Royal Institute of Nautical Studies and Mineralogy of Gijón. In this work, the historical method of research in education was used with the objective of determining the sociogenesis of the kind of technical mathematics that was taught in this Institute. The results show the role of the Asturian Economic Society in the creation of the Institute and we also analysed the teaching and curriculum of mathematics that was taught there, and if it was in line with the internal debates of the discipline in that historical moment. The limitations of the Jovellanista model of the Technical Training School for Sailors and Miners created in Gijón are made clear, although the attempt to start it up in such a peripheral place is no less remarkable.

1. Introduction

There is no consensus among historians on the limits of the Enlightenment in Spain. The Enlightenment period often refers to the “esprit français” prevailing in Spain, and its ideologues are identified with “enlightened despotism”; some researchers reduce the Enlightenment to the time of Carlos III, Carlos IV, and Godoy; even Sarrailh [1] and Herr [2] chronologically simplify Spanish reformism to the time of Carlos III. They also refer to this period as the Century of the Lights, although, as Richard Herr observed, these lights, in truth, “bore little resemblance to the lumières of their northern neighbour” [2] (p. 165). It is true that with the entry of the Bourbons with Calos III, King of Spain in the period 1759–1788, and after the War of Succession, reformist ideas based on the essential axes of the Enlightenment were consolidated: the strengthening of the Crown, economic interventionism, and the promotion of culture and regalism [3] (p. 447).

Culture was promoted through the creation of French style cultural institutions: the National Library (1711), the Academy of Language (1714), the Academy of History (1738), etc. The Sociedades Económicas de Amigos del País [Economic Societies of Friends of the Country] were also created throughout Spain, driven by Campomanes, who was a Prosecutor of the Council of Castile and who tried to mobilise the local ruling classes of the nobility and the incipient bourgeoisie by the promulgation of a series of regulations which tended to reward commercial, artisanal, and industrial activity.

The Economic Societies of Friends of the Country were a fundamental instrument of Carlos III’s reformist policy and a vehicle for enlightenment ideas in terms of the objectives they pursued and the activities they carried out.

Numerous studies have focused on analysing the birth, development and influence of the Economic Societies of Friends of the Country (see [4,5,6,7,8]) and the bibliography referring to specific Societies in each region or city is also very extensive; these are generally studies of an institutional nature, often with similar functioning and activities. The Asturias Society is one of the least known, especially due to the scarce documentation preserved, since the Acts prior to 1791 disappeared very quickly due to the spoliation carried out in 1808 by the French in the War of Independence, as some of the studies of the Economic Society of Friends of the Country of Asturias indicate(see [9,10,11,12,13]).

Campomanes’s initiative to create the Economic Societies, as well as his objectives and proposals for their operation, spread throughout the country following the official model of the Matritense, as we will see in this work, which was different from the model of the Bascongada, created by Xavier María de Munibe e Idiáquez, Count of Peñaflorida, in 1763, which was the first Society of this kind created in Spain. The creative fever of the Economic Societies of Friends of the Country dates from 1774–1784, and it aimed to outline a complex and ambitious socio-economic model that encompassed all economic sectors, but prioritised industry. Figure 1 below is a portrait of Campomanes, the driving force behind the creation of the Sociedades Económicas de Amigos del País.

The Asturian Society of Friends of the Country promoted the creation of the Royal Institute of Nautical and Mineralogy of Gijón where technical Mathematics for Miners and Sailors were taught. It was founded by Jovellanos. Gaspar Melchor de Jovellanos was an enlightened figure born in Gijón (Asturias), a writer, jurist and politician who was particularly committed to the economic and cultural development of his country.

In this article we will study this mathematics as a special type of knowledge that can only be studied within its institutional context. This is what is called disciplinary code, constituted by the set of ideas, values, assumptions, regulations and practical routines that are often translated into legitimizing discourses and public languages about the educational value of the discipline, and that guide the professional practice of teachers. The disciplinary code is a social creation that has a process of construction and not of creation. Our specific concern will be to carry out a social, scientific and academic contextualization.

2. Materials and Methods

This work is part of the research in history of mathematics education. The historical method of research in education [14] has been used here, which follows the phases: Heuristic, Critical, Hermeneutic and Exposition.

This paper presents a descriptive and ex post facto research, focused on the analysis of ancient texts from the perspective of the history of mathematics and mathematics education. We will reconstruct the socio-historical reality of the teaching of mathematics in Jovellanos’s Institute, which was founded with the support of the Economic Society of Friends of the Country of Asturias. This research conforms to the explanation of the sociogenesis of a school discipline proposed by López-Esteban [15] for the teaching of Arithmetic and Algebra in teacher training.

The analysis technique used was content analysis, a technique widely used in research of the history of mathematics and mathematics education [16,17]. We considered the socio-political situation, the Societies, the Institution, and the internal debates of the discipline for the analysis of the study plan for the training of sailors and miners that was followed in Jovellanos’s Royal Asturian Institute of Nautical Studies and Mineralogy at the end of the 18th century.

The analysis instrument used in this work was developed from the works cited above and is shown in the form included in

Table 1. Form for the analysis of mathematical and mathematics education content.

Criteria	Items
General data	Name of publication
	Date of publication
	Number of pages dedicated to mathematics or mathematics education/number of pages of the document
	Author (s) (if indicated)
Categories of analysis	Mathematical content: arithmetic, algebraic, geometric, calculus… Context: mathematical, commercial, technical, educational…
	Up-to-date relevance of the contents: do the contents only present classic knowledge or are the latest discoveries on the subject included.
	Connections: have other editions been published; has the author published other works on mathematics…
	Other mentions of mathematics and mathematics education, further content…

. This was validated by means of a triangulation of experts on research methods in education, history of mathematics, and mathematics education.

The sources used to reconstruct the life of the Society and the Institute are, above all, documents from these institutions which are preserved in the ARIDEA (Archive of the Royal Institute of Asturian Studies) and in the Virtual Library of the Principality of Asturias, as well as Jovellanos’s diaries and complete works from the AHA (Historical Archive of Asturias), the AHN (National Historical Archive), and Campomanes Archive (AC), and also studies on the Economic Societies of Friends of the Country and, especially, on the Asturian Society, in order to obtain a panoramic and global vision of Asturian society at that time in history.

3. Results

The result of this research will be the explanation of the sociogenesis of technical mathematics which was taught as a school discipline at the Royal Asturian Institute of Nautical Studies and Mineralogy. To this end, we will analyse the Societies of Friends of the Country in Spain and the Society that was constituted in Asturias, which supported the creation of the Institute; we will also analyse the teaching and curriculum of mathematics that was taught there, and whether it was up to date with the internal debates of the discipline at that historical moment.

3.1. The Economic Societies of Friends of the Country in Spain in the 18th Century

The Basque Economic Society was the first to be created in December 1764 at the request of the Count of Peñaflorida. Jesús Astiagarraga [18] explains how a group of nineteen noble regional politicians founded the Basque Society in Azcoitia, drafted its first statutes and adopted the name “Amigos del País” [Friends of the Country], as well as the motto: “Irurac bat”, “Tres en una” [Three in one], in allusion to the three sections of each of the Basque provinces. Its goals, defined in its statutes, focused on promoting agriculture, industry, commerce, arts, and sciences.

Economic groups interested in social aspects, such as the care of the poor, or with agrarian and technical interests, which brought together intellectuals, businessmen and educated landowners, had emerged in different European countries during the first half of the 18th century [19] (pp. 92–134). The first known initiatives appeared in the Anglo-Saxon sphere. In 1723, The Honourable Society of Improvers in the Knowledge of Agriculture in Scotland was founded in Edinburgh and so was the Dublin Society for improving Husbandry, Agriculture, and the other useful Arts and Sciences in 1731. These pioneering experiments spread throughout Europe, from the French Societés royals d’agriculture, starting with the Société Royals d’agriculture de la Géralité de Paris (founded in 1761) to the Ökonomische Gesellschaft zu Bern founded in 1762, or those of Graz and Leipzig, both of who were born in 1764. Studies such as those by Daniel Roche (see [20,21,22]) on the French provincial academies made it possible to overcome a vision of the Enlightenment limited to the most brilliant Parisian circles, to extend its radius of action to the wealthy and educated groups in the provinces. It should also be noted that between 1781 and 1810 a dozen Societies were created in different parts of the Spanish Empire: the first was founded in Manila, the most important ones were those of Havana and Guatemala, and those of Santiago de Cuba, Lima, Quito, Nueva Granada, Santa Fe de Bogota and Caracas also stood out [23].

We will now examine what these Societies were like in Spain. The Basque Economic Society founded the Seminary of Vergara, a training centre for professional and technological development where Basque youths lived alongside students and teachers from the rest of Spain and Europe.

Ten years after the foundation of the Basque Economic Society, the starting point for the spread of the Societies in Spain was November 1774, with the publication of Discurso sobre el fomento de la industria popular [speech about the promotion of popular industry] [24] by Campomanes, in which a plan was drawn up to create Economic Societies throughout the kingdom and the main ideas for their organisation and objectives were outlined. According to Sarrailh [1] (p. 252), its origin must be found in Carlos III’s desire to promote a “cultura nacional con carácter utilitario” [national culture with a utilitarian character]. The speech, in a wide edition of 30,000 copies, was distributed to corregidor jurisdictions, municipalities, audiences, chancelleries, and bishoprics, and the authorities were urged to promote the founding of these Societies [11]. Petitions to found these Societies in various cities and provinces would soon reach the Council of Castile. Campomanes aimed his initiative to create these institutions at the nobility, clergy, and wealthy classes. Studies of specific Societies provide an insight into their social composition and, although a broad social spectrum among their members cannot be denied, it is obvious that all Societies include the most representative members of the local nobility and clergy.

The geographical distribution of the Economic Societies was not uniform, according to the study carried out by Inmaculada Arias de Saavedra [25]. While in Asturias, Aragon, Cantabria, Galicia, La Rioja, Mallorca, Murcia, and Valencia a single Society of regional scope was predominant, in other areas, the foundations multiplied, reaching a total number of almost eighty, which received royal approval before 1808 [17].

All the Economic Societies of Friends of the Country had quite similar organisations. In general, they conformed to Campomanes’s guidelines, as set out in the statutes of the Matritense Society of Friends of the Country, an organization that soon became the rector of the Societies of the kingdom, supervising the approval of the others’ statutes [6]. They included an indeterminate number of full members (with no special requirements other than residence in the host city and payment of dues), who performed ordinary tasks, as well as honorary members and members of merit (residing outside the city). There were also added members, which included farmers, manufacturers and craftsmen, with advisory tasks, but with a secondary position with respect to the full members. For their government, they usually elected the posts of Director, Secretary, Censor, Accountant and Treasurer, all elective, with variable duration, although re-elections were possible. To carry out their tasks, they were grouped into Commissions, depending on subject matter. There were three commissions in the Matritense, the Commissions of Agriculture, Industry, and Arts, and this became the most widespread model.

The Economic Societies were born with a double mission: to spread useful teachings and to rationalise the economy [8]. In order to achieve these missions, the actions carried out by these Societies went in three main directions: (a) Charity, as they fought unemployment, poverty, public begging and idleness, with the creation of asylums or hospices to provide shelter and work for destitute and unemployed families; (b) Teaching, by which they sought to banish ignorance and routine, and to teach adults, but especially the young, with the basic elements of instruction and religion, the principles of a useful profession that would enable them to stand on their own feet; and (c) The promotion of production in all fields of human activity: agriculture, then by far the most important, arts and crafts, industry, commerce. Through experiments and prizes, they tried to develop the branches that they considered most useful to the needs of each region. The teaching activity of the Friends of the Country focused on two sectors [26]:

• That of the “patriotic schools”, especially weaving schools and first letters schools.
• That of special teachings, where the Societies acted as centres for the spread of Enlightenment culture. Some of them had a clear artisanal focus, such as the schools of drawing and mathematics, since they were specialised in practical subjects applicable to industry, shipbuilding, architecture, etc. With these teachings, the Societies tried to introduce substantial modifications, which represented an unquestionable innovation and progress in comparison to previously prevalent models.

3.2. The Society of Friends of the Country of Asturias

The Economic Society of Friends of the Country of Asturias was founded on 15 April 1780 at the request of the Count of Campomanes, and its Statutes were confirmed and authorised by Royal Decree of 7 March 1781. The work of Mª Ángeles Faya Díaz [13] classifies the activities of the Economic Society of Friends of the Country of Asturias, relating them to the socio-economic context of the region, into three main groups: the promotion of agriculture, the advancement of industry, fishing and commerce, and teaching and social assistance.

The Statutes of the Asturian Society indicate that the most important Commissions are “la de los protectores de oficios, la de curadores de las escuelas patrióticas y de los mendígos de que está inundada esta Ciudad” [that of the protectors of professions, that of the guardians of patriotic schools and that of the beggars with whom this City is inundated] [27] (p. 39).

In addition to weekly meetings of the ordinary Board on Mondays at half past ten [27] (p. 13), extraordinary meetings were held, as well as annual public meetings, to which local authorities were invited and where achievements were publicly announced, prizes were awarded, etc. The Asturian Society generally followed the Matritense’s organisational model. Figure 2 shows the cover of the Estatutos de la Sociedad Económica de Asturias.

The Statutes of the Asturian Society, in their preamble, quote the speech Extracto de los fundamentales principios que han motivado el establecimiento de la Sociedad Económica [Extract of the fundamental principles that have motivated the establishment of the Economic Society], written in 1780 by D. Joaquín José Queipo de Llano, Count of Toreno and major ensign of the General Board of the Principality of Asturias. The Extracto tries to justify the creation of the Economic Society by expressing the enormous benefit that the Economic Society would bring and by specifying the Society’s goals. The aim was “desterrar la ociosidad, y la mendiguez, destinando los niños á las Artes, y las niñas á todo género de hilados con que adelanten las fábricas sus texidos, se aumente la Agricultura, Comercio y artes y la industria popular tenga sus efectos” [to banish idleness and beggars, by destining boys to the arts, and girls to all kinds of weaving, so that the factories will advance their textiles, so that agriculture, commerce and the arts will increase, and so that popular industry will have its effects] [27] (p. 4). In the Statutes, the first chapter indicates that its objective is “conferir; y producir las memorias para mejorar la industria popular y los oficios, los secretos de las artes, las máquinas para facilitar las maniobras a y auxiliar la enseñanza. El fomento de la agricultura, plantíos, cría de ganados, pesca, comercio navegación, minerales, y mármoles será otra de sus principales ocupaciones como tan importantes á este país, tratando por menor los ramos subalternos relativos á la labranza, plantíos, y cría” [to confer; and to produce memories to improve the popular industry and the commerces, the secrets of the arts, the machines to facilitate manoeuvres and to help the teaching. The promotion of agriculture, plantations, cattle breeding, fishing, commerce, navigation, minerals, and marbles will be others of its main occupations as being so important to this country, dealing in the minor branches related to tillage, plantations, and animal breeding].

The Asturias Society, like many others, devoted much of its budget to giving prizes and rewards, a controversial way of boosting the economy. In fact, it was a symbolic form of aid, given the little funding it had. The conservation in the ARIDEA archive of the selection of prizes planned to be given in different years, as well as those finally awarded, allows us to observe the priorities established by the Society of Friends of the Country and their evolution over time.

It is worth highlighting that the emerging Society kept in contact with Campomanes during its early years; on 10 July 1780, he wrote to the Counts of Toreno and Peñalba, thanking them for his appointment as a member and sending instructions so that plantations, commerce, navigation and fishing would be considered in the statutes, despite the fact that these sectors were not taken into account by the Matritense Society, which was the model to be followed. Likewise, the Society appealed to his power and influence and asked for his support; they asked for his protection to raise funds (AC, 48-8) and he even took care of the payment of the 1000 copies of the Statutes that were printed (AC, 48-80). Campomanes was subsequently appointed perpetual director in 1789 (ARIDEA, Secretariat, leg. 4, no. 23, extraordinary meeting of 30 November 1798), a position that he held until his death.

It is also necessary to highlight Jovellanos’s involvement with the Society in its early years [28]; he was appointed honorary member on 1 July 1780, and director of the Society at the Meeting of 10 May 1782, a position which had been held until then by the Councillor of the Military Orders, although in practice the post’s responsibilities were carried out by his vice-director, D. Bernadino Sierra [28] (pp. 133 and 184).

In the speech Discurso económico sobre los medios de promover la felicidad del principado [Economical speech about the means to promote the hapinness of the Principality] (1781), addressed to the Royal Society of Friends of the Country of Asturias on 22 April 1781, Jovellanos referred to Asturias as “una provincia retirada al norte de España, distante de sus principales capitales y separada del comercio con ellas por su distancia, por la aspereza de sus puertos y por la fragosidad de su terreno…” [a secluded province in the north of Spain, distant from its main capitals and cut off from commerce with them by its distance, the ruggedness of its ports and the roughness of its terrain…] [29] and it contained a comprehensive programme of economic reforms that aimed to transform Asturias from “la Siberia del norte” [the northern Siberia], a poor and isolated region, into “la Sajonia española” [the Spanish Saxony], that is, an urban, industrial and commercial economy [30] (p. 151).

3.3. The Royal Asturian Institute of Nautical Studies and Mineralogy

The Royal Asturian Institute of Nautical Studies and Mineralogy celebrated the two hundred and fiftieth anniversary of its inauguration on 7 January 2019. It can be considered the first intermediate-level professional school to exist in Spain. Gaspar Melchor de Jovellanos focused his efforts, especially during his years of exile in Gijón (1790–1797 and 1798–1801), to the task of implementing his pedagogical theories and materialising them into the Royal Institute.

Within Jovellanos’s extensive production, we must highlight the two writings addressed to the Society with the objective of promoting the economic growth of the Principality of Asturias. In the Discurso dirigido a la Real Sociedad de Amigos del País de Asturias sobre los medios de promover la felicidad de aquel Principado [speech addressed to the Royal Society of Friends of the Country of Asturias on the means of promoting the happiness of that Principality], delivered on 22 April 1781 in Madrid, he made a very lucid analysis of the serious problems of the regional economy and he proposed a very complete development program; he proposed the promotion of agriculture, industry, fishing, roads, commerce and navigation, also giving an essential place to education, including both the education of the nobility and of the people. We must also mention the Discurso pronunciado en la Sociedad de Amigos del País de Asturias sobre la necesidad de cultivar en el Principado el estudio de las ciencias naturales [speech delivered at the Society of Friends of the Country of Asturias on the need to cultivate the study of natural sciences in the Principality], delivered on 6 May 1782, shortly after his arrival in Asturias [31] (pp. 267–304 and 305–311). To this end, Jovellanos set out a twelve-point plan and recommended the Economic Society of Friends of the Country of Asturias to set a membership fee that should raise 69,200 reales to send two students to the Seminary of Vergara for four years and one more year after that to France, England and other European countries to study mathematics, experimental physics, chemistry, mineralogy, and metallurgy. Thus, he intended to create a Seminary of Nobles to train young people, as well as to buy books, instruments and set up laboratories and cabinets for the teaching of science, which would serve to promote commerce, arts and agriculture. The idea was very well received, but nothing effective was done.

In 1789, due to a report on the shipment of coal out of the port of Gijón, the Council of State requested that Jovellanos, who was a member of the Board of Commerce and Currency, report on the exploitation of the coal mines in Asturias. In this report, dated 9 April of the same year [31] (p. 113 and ss.), he requested, among other things, that a school of mineralogy be established in Asturias so that the work in the mines could cease to be a hazardous operation, made by men without scientific or technical knowledge, and so that they could progress and achieve the level that corresponded to them. In two new reports dated 15 May 1791, Proposición de una escuela náutica y física para educar buenos pilotos y mineros [Proposal for a nautical studies and physics school to educate good sailors and miners] and Proposición de los medios para dotar el camino y la escuela propuestos y para la ejecución y planificación de uno y otro [Proposal for the means to equip the proposed path and school and for the execution and planning of both] [31] (p. 915 and ss.) addressed to the Minister of the Navy, Antonio Valdés y Bazán, Jovellanos proposed more clearly the creation of a School of Mineralogy and Nautical Studies in Gijón. According to him, it seemed advisable to unite the teaching of Nautical Studies and Mining; he analysed and proposed all aspects related to the director, the teachers and the staff that the school should have, as well as the teachings, the study plan and the awards given to the student. Jovellanos, in these documents of May 1791, showed that he was aware of the existing difficulties for finding the necessary teachers to staff the projected establishment; he knew that they had to be recruited from outside Asturias and, probably, from outside of Spain, for which it was necessary to make an attractive offer. He suggests, in his writings, that the professors of the new institution should be selected by a jury from Madrid, including professors from the Royal Studies of Physics and from the Royal School of Mineralogy, and he specifically mentions Gutiérrez Bueno and Chavaneau [31] (p. 916).

The proposal for the school was accepted by the Council of State on 9 July 1792: “es digna de aprobación y muy propia de su conocimiento y celo” [it is worthy of approval and very much in keeping with his knowledge and zeal], that is, worthy of Jovellanos’s knowledge. In the proceedings signed by Eugenio de Llaguno y Amírola, secretary of the Council of State and the Supreme Council of State, it is stated that one way to promote and encourage the mines of Asturias and the trade and extraction of their coals by sea is the following: “que promete ventajas más extensas, es el establecimiento en aquel Principado de una Escuela de Matemáticas, Física, Química, Mineralogía y Náutica, a fin de que se difundan entre sus naturales los conocimientos científicos de que ahora carecen para ejercer la minería, sin los cuales nunca podrán hacer grandes progresos” [the establishment of a School of Mathematics, Physics, Chemistry, Mineralogy and Nautical Studies in the Principality promises more extensive advantages to spread the scientific knowledge that the natives now lack, without which they will never be able to make great progresses] [32] (pp. 378–379). “Asturias tiene más de treinta puertos sobre una costa de más de quarenta leguas de frente; pero no pudiendo residir la escuela, sino en uno solo, preferí el de Gijón, no por las razones que suponen los que no me conocen, sino por las siguientes: 1ª poque mis proposiciones iban principalmente dirigidas a fomentar la extracción de los carbones, y ésta solo se hacia por Gijón; 2ª por que las escuelas Náuticas se han mandado establecer con preferencia en los puertos habilitados para el comercio de Indias y Gijón lo es; 3ª por que situado Gijón en medio de costas Asturias, me parecía estar en mejor proporción para difundir por ella la enseñanza; 4ª por que me constaba que Gijón tenía pretendido formalmente este establecimiento desde 1789; 5ª por que me consta asimismo, que mi hermano mayor tenía desde entonces ofrecido a S.M. una casa propia para situarle, y además la enseñanza gratuita de las Matemáticas; y 6ª por que comparadas las circunstancias de los puertos y sus poblaciones, no me parecía Gijón menos merecedor que otro de esta ventaja” [Asturias has more than thirty ports on a coast of more than forty leagues; but the school is able to reside in only one, so I preferred that of Gijon, not for the reasons that those who do not know me suppose, but for the following reasons: first because my proposals were mainly aimed at promoting the extraction of coal, and this was only being done through Gijón; second because Nautical schools have been ordered to be established with preference in the ports authorised for the commerce of the Indies and Gijón is one of them; third because Gijón is located in the middle of the Asturias coast so it seemed a better position to spread the education through it; fourth because I was aware that Gijón had formally intended this establishment since 1789; fifth because I am also aware that my eldest brother had offered your majesty a house there, and also free teaching of Mathematics; and sixth because Gijón did not seem to me less deserving of this advantage that any other, after comparing the circumstances of their ports and populations] [33] (pp. 137–145).

However, there were reactions against this from the University, the Provincial Council and the City Council of Oviedo, whose arguments try to discredit Jovellanos and the School, giving priority to the interests of the University of Oviedo. The City Council of Oviedo, through Antonio Carreño y Cañedo, major ensign of the City Council, asked Jovellanos about his reasons for preferring Gijón over Oviedo as the site of the new establishment. Jovellanos’s answer of 27 December 1792, is clear in all its points:

“Si todavía se hace la pregunta por qué no procuré reunir esta enseñanza a las demás que se dan en nuestra Universidad, y fijarla en ella, diré que además de las razones indicadas tuve para ello las siguientes: lª, que la Universidad no necesita cátedra de Matemáticas, pues la tiene ya; 2ª, que no necesita cátedra de Náutica, porque este estudio no puede pertenecer a su plan; 3ª, que, aunque necesita la enseñanza de Física experimental, la podrá tener cuando quiera, si en lugar de la Física especulativa, que es tan inútil, enseñare la experimental, que es tan provechosa; esto es, si en vez de explicar la Física del Goudin explicare la de Muschen-Broek; 4ª, que es mejor multiplicar que disminuir los institutos literarios; 5ª, que es mejor dividirlos que amontonarlos; 6ª, que es difícil combinar la enseñanza de las ciencias intelectuales con la de las ciencias demostrativas; 7ª, que es mucho más difícil todavía conciliar el espíritu de los que profesan las primeras con el de los que cultivan las últimas; 8ª, que siendo—enteramente distintas las vocaciones de los que se dan a unas y otras, no pueden robarse los discípulos, ni dañarse en manera alguna; 9ª, que la Universidad trataba de mejorar y completar su plan y no me tocaba a mí trastornar sus ideas ni incluirme en ellas; 10ª, que, aunque trataba también de completar su dotación, todo mi cuidado debía reducirse a no embarazar sus propuestas con las mías; y así lo hice, huyendo muy de propósito de los objetos de dotación a que tenía dirigidos sus deseos y en que fundaba sus esperanzas. Y por último, que si la Universidad no logra sus deseos, no podrá estar mal al país tener un establecimiento en que su juventud estudie las ciencias útiles, y que si lo logra, lejos de envidiar el establecimiento concedido a Gijón, deberá celebrarle, porque nunca su Instituto será más útil que cuando difundidos por todas partes los útiles conocimientos, una noble emulación perfeccione lo que ruin envidia atrasa y destruye” [If the reason why I did not try to combine this teaching with the others given at our University is still being asked, as well as the reason as to why not set it there, I will say that in addition to the reasons indicated above, I had the following: first, that the University does not need a chair of Mathematics, as it already has one; second, that it does not need a chair of Nautical Studies, because this study cannot belong to its plan; third, that, although it needs the teaching of Experimental Physics, it can have it whenever it wishes, if instead of Speculative Physics, which is so useless, it taught Experimental Physics, which is so profitable; that is, if instead of explaining the Physics of Goudin, it explained the Physics of Muschen-Broek; fourth, that it is better to multiply than to reduce the literary institutes; fifth, that it is better to divide them than to pile them up; sixth, that it is difficult to combine the teaching of the intellectual sciences with that of the demonstrative sciences; seventh, that it is even more difficult to reconcile the spirit of those who profess the former with that of those who cultivate the latter; eighth, that given that the vocations for those two types of sciences are entirely different, they cannot steal disciples from each other, nor can they harm each other in any way; ninth, that the University was trying to improve and complete its plan, and that it was not for me to disrupt its ideas or include myself in them; 10th, that, given that it was also trying to complete its resources, all my care should be put to not to hinder its proposals with mine; and so I did, very deliberately avoiding the objects of resource to which its wishes were directed and on which it based its hopes. And lastly, that if the University does not achieve its wishes, it cannot be bad for the country to have an establishment in which its youth can study useful sciences, and that if it succeeds, far from envying the establishment granted to Gijón, it should celebrate it, because its Institute will never be more useful than when useful knowledge is spread everywhere, a noble emulation perfects what despicable envy delays and destroys] [31] (volume II, p. 547). In this letter, Jovellanos defends the practical character of the Institute, which radically differentiates it from the University’s objectives, and uses the argument that, in order to introduce experimental sciences in the University, it is necessary to modify its spirit, or in other words, it needs to stop being scholastic and to adopt more modern methods.

Finally, by the Royal Decree of 24 August 1792 (which established the rules to be observed in the way of benefiting coal mines; allows free commerce of this type of coal, and grants various graces to promote its trade and extraction outside the Kingdom), by its article VIII, the Royal Asturian Institute of Nautical Studies and Mineralogy was created [32] (p. 385).

The Institute had always been burdened by economic problems and this reason, among many others, made Jovellanos inclined to establish it in his native town. Jovellanos communicated this decision to Ceán in a letter, “ha dado celos a la capital, y particularmente los doctores de su Universidad han creído que esto como todo lo bueno, toca exclusivamente a la capital, o por mejor decir, que no toca aquí; porque hablando en puridad, estoy seguro de que, si esta escuela se fijase en Langreo, no tendría la menor contradicción” [it has made the capital jealous, and particularly the doctors of its University have believed that this, like all good things, belongs exclusively to the capital, or rather, that it does not belong here; because strictly speaking, I am sure that if this school were to be established in Langreo, it would not have the slightest opposition] [31].

On 7 January 1794, the Royal Institute was solemnly inaugurated. It was first located in the Casa del Forno, owned by Jovellanos’s brother and first director of the Institute, Francisco de Paula de Jovellanos; and in 1797, the construction of a new building began, which would not be completed until 1807. The day of the inauguration, Jovellanos pronounced his Oración inaugural a la apertura del Real Instituto Asturiano de Náutica y Mineralogía [Inaugural speech at the opening of the Royal Asturian Institute of Nautical Studies and Mineralogy] [34], a brief speech that summarised Jovellanos’s line of thought, exhorting the study of Natural Sciences, a pedagogical and programmatic manifesto of the Institute. This document shows that his aims were very different from those of the University, and that the latter did not understand exactly what he intended. As opposed to university degrees, the Institute not only wanted to train specialists in certain economic activities, but specialists with a theoretical basis. Therefore, the existence of an educational establishment which could be considered a novelty in its time began [35]. Its originality consisted in providing both technical training as well as scientific and humanistic development to its students. The basic idea was to train mine foremen and skilful sailors, but also to awaken the desire for experimental scientific research among the well-to-do people of the Principality of Asturias who were not involved in university studies or the army.

Jovellanos, in all his writings prior to the inauguration of the Royal Asturian Institute, proposed the creation of three chairs for three Teachers: The Teacher of Mathematics to teach arithmetic, geometry, and plane and spherical trigonometry; The Teacher of Nautical Studies to teach cosmography, navigation, manoeuvring and some drawing; and the Teacher of Physics to teach general physics, chemistry and mineralogy. However, from the beginning Jovellanos thought that the librarian, as he also says [31] (p. 1159), should teach French and English languages in addition to what he would call “Humanidades castellanas” [Castilian Humanities], conceived as a basic teaching to facilitate the transition of students from the school for poor people to the Institute and as well as to offer the students of the Institute the possibility of completing their studies with a humanist base and perspective which they lacked, given the curriculum taught in the school. This opinion can be found in a letter to González Posada [28] (p. 402), when he comments that the perfection of knowledge depends precisely on the perfection with which one knows how to express his thoughts, to give order and clarity to one’s ideas and to write with purity and precision. It is here, in the conjunction of these three aspects, that the originality of Jovellanos’s educational programme lies. The study plan, attributed to Jovellanos, is set out in title III of the Instrucción u Ordenanza para la nueva escuela de Matemáticas, Física, Química, Mineralogía y Náutica [Instruction or Ordinance for the new school of Mathematics, Physics, Chemistry, Mineralogy and Nautical Studies], from 1 December 1793, “De la disciplina literaria del Instituto” [On the literary discipline of the Institute], a document signed by the minister Antonio Valdés [32] (volume II, pp. 399–420).

There were different types of exams: the approval exams were used to check the degree of achievement only in the core subjects before changing classes and did not consider the progress made in the auxiliary courses [33] (art. 496). The final grading exams did not include special examinations in languages and drawing, although pupils were asked about them [33] (art. 514). On the other hand, the graduation exams, which were only accessible to pupils who had distinguished themselves in the previous examinations, assessed all subjects in the same way [33] (art. 532), by means of a public competition and with final awarding of prizes.

3.4. Mathematics Education in Spain

In Spain, the study of mathematics and science in the 18th century was promoted by the centres of military studies and from the Jesuit centres. According to Arenzana (1987), 99 mathematical works were published in the 18th century, 71 of which were published between 1760 and 1790. Figure 3 shows the distribution of these publications during the century. Differential calculus was introduced during this time [36].

Scientific studies began to expand through the centres that were created around the Court (School of Nobles, San Fernando Academy, and the Military Academy of Segovia), in the more commercially active peripheral regions of Spain (School of Guardamarinas of Cádiz), etc. The Jesuits also promoted their study until the Order was expelled from Spain in 1767; a figure of note was Tomás Cerdá, the Jesuit mathematics teacher at the School of Nobles of Cordelles from 1756 to 1765. In 1758, he published his Nociones de Matemáticas o elementos generales de aritmética y algebra [Notions of Mathematics or general elements of arithmetic and algebra], in which he showed his knowledge of the latest developments in Europe. He introduced natural logarithms, including their tables because “no se suelen encontrar en lo común de las Tablas Logarítmicas, pondré aquí para los aficionados al cálculo integral… (siguiendo planteamientos recientes de Euler)” [they are not usually found in the common Logarithmic Tables, I will put them here for the amateurs of integral calculus … (following Euler’s recent approaches)] [37] (p. 479).

From the middle of the century until the expulsion of the Jesuits in 1767, the work of military and religious organizations to try to incorporate scientific knowledge of calculus into the traditional curriculum was fundamental but limited. However, in the last quarter of the century, the beneficial Enlightenment policy of Carlos III encouraged the different institutions where mathematics was studied to ask their professors to write and publish textbooks, which would be used as references for students and teachers during the lessons, and to improve and lay the foundations for updated, quality curriculum [38].

There is no doubt that the director of the Academy of Guardamarinas of Cádiz, Jorge Juan y Santacilia, was one of the first to introduce infinitesimal calculus in Spain. Proof of this is the good use he made of it in the works he published in 1748, Observaciones astronómicas y físicas hechas en los reinos del Perú [Astronomical and physical observations made in the kingdoms of Peru] and Exámen maritimo teórico práctico o Tratado de mechanica aplicado á la construccion [Practical-theoretical maritime examination or Treaty of mechanics applied to construction] in 1771 [39]. In addition, at the School of Guardamarinas of Cádiz, Jorge Juan had managed to fulfil Count of Aranda’s proposal to the Royal Academy of San Fernando and two chairs of mathematics had been created, officially awarded to Francisco Subirás and Benito Bails in 1768, although they had been part of the Academy since a few years before [40] (p. 703).

In 1759, in the Academy of Fine Arts of San Fernando, a reform of the teaching of Architecture was approved, which considered the need for updated textbooks written in Spanish. Bails was entrusted with elaborating a more elementary work and another more extensive and advanced one, under Jorge Juan’s supervision [36]. This great work, which spread the novelties on mathematics and infinitesimal calculus throughout Spain, was titled the Elementos de Matemáticas [Elements of Mathematics], and was composed of 11 books in 10 volumes, published between 1772 and 1783, each one destined to different areas of mathematics, physics, astronomy, and civil architecture. Volume III, of 688 pages, which was published in 1779, presents differential and integral calculus [36] (p. 699).

In 1756, Captain Pedro Padilla y Arcos, teacher at the Academy of Segovia, also published a work on the theory of infinitesimal calculus, included in the fourth book of Curso Militar de Mathemáticas sobre las partes de estas ciencias pertenecientes al Arte de la Guerra, para el uso de la Real Academia establecida en el Quartel de Guardias de Corps [Mathematics Military Course on the parts of these sciences belonging to the Art of War, for the use of the Royal Academy established in the Guardias de Corps’s Quarter] (1753–1756), undoubtedly the first work that truly constitutes a textbook which includes the principles of infinitesimal calculus and aims to teach this branch of mathematics. Volume IV, published in 1756, includes results on infinitesimal calculus and is entitled Geometría superior ó de las curvas y de los cálculos diferencial é integral o Methodo de las Fluxiones [Higher geometry or geometry of curves and differential and integral calculus or Fluxions Method]. The author cites both Leibniz and Newton, he uses the notation of the former, but follows a Newtonian approach characterised by descriptions with a strong geometrical sense. Regarding the method for calculating maxima and minima, Padilla takes as a reference the Treatise of fluxions by McLaurin (1742), which presents the first algorithm to solve this through successive fluxions and Taylor’s series development, but which still determines whether the values obtained were really maxima or minima from the context in which the problem was posed [41].

3.5. Mathematics Teaching at the Royal Asturian Institute of Nautical Studies and Mineralogy

In the teaching of mathematics at the Asturian Institute of Nautical Studies and Mineralogy, Jovellanos was assisted by another Asturian, Agustín de Pedrayes y Foyo (1744–1815), one of the most eminent Spanish mathematicians of the time, an expert in sublime Mathematics or infinitesimal analysis [42].

Pedrayes was a friend of Jovellanos’s, who tried unsuccessfully to get him to become a mathematics teacher at the Institute, although he did agree to actively collaborate in planning the teaching of mathematics at the Gijón institution [43] (p. 243), following the example of the Academies of Guardamarinas of Cadiz, Cartagena and Ferrol where the Examen Marítimo o Tratado de mecánica [Maritime Examination or Treatise on mechanics], written by Jorge Juan in 1771 and expanded and corrected by Gabriel Císcar in 1793, was used as a teaching textbook [44] (p. 126). Pedrayes was born in Lastres, studied in Santiago de Compostela and taught mathematics at His Majesty’s Royal House of Page Gentlemen and at the Seminary of Nobles of Madrid. He is the author of a Nuevo y universal método de cuadraturas determinadas [New and universal method of determinated quadratures] (1777) and Solución del problema propuesto el año 1797 [Solution of the Proposed Problem in the Year 1797] (1805), in which he presented a method to solve a problem posed by Pedrayes, which consisted of the integration of a complicated differential equation with 16 terms [42].

Navy pilot Diego Cayón taught mathematics during the first two years, and after him Cayetano Fernández Villamil took this position until 1804. Both Pedrayes and Jovellanos saw the need to train students from the school as future science teachers. Following this guideline, the student Timoteo Álvarez Veriña was granted a scholarship to study theoretical and practical mineralogy in Paris, while José Alvargonzález Zarracina, a mathematics assistant, moved to Segovia to further his Chemistry studies at the Royal School of Artillery, under Louis Proust’s mentoring. The former remained in Paris until 1803 and the latter returned to Gijón in 1799, becoming a member of the teaching staff of the Institute as professor of physics and chemistry until 1804 [45] (p. 275).

In the development of the Institute, Jovellanos followed the successful model of the Seminary of Vergara, so he requested Jerónimo Mas to implement in the Institute of Gijón [46] its Plan y Método que propone el Maestro de Matemáticas del Real Seminario Bascongado para su enseñanza [Plan and Method proposed by the Master of Mathematics of the Royal Basque Seminary for its teaching].

This Plan is analysed in

Table 2. Analysis of the mathematical content and mathematical education in the study plan for the training of Sailors and Miners followed at the Royal Asturian Institute of Nautical Studies and Mineralogy by Jovellanos at the end of the 18th century.

Criteria	Items
General data	Title: Extractos de las Juntas Generales de la Real Sociedad Bascongada de los Amigos del País [Extracts from the General Meetings of the Basque Royal Society of Friends of the Country]
	Date of publication: 1785
	Number of pages dedicated to mathematics or mathematics education: 134–144
	Author(s): Real Sociedad Bascongada de los Amigos del País [Royal Basque Society of the Friends of the Country]/Jerónimo Mas
Categories of analysis	Mathematical content: Unification into a single programme by Mas of disciplines as varied as Arithmetic, Geometry, Mechanics, Hydraulics, Optics, Astronomy, Fortification, civil Architecture, etc. Context: educational.
	Up-to-date relevance of the contents: includes the latest discoveries on infinitesimal calculus and draws inspiration from, among others, the Examen Marítimo by Jorge Juan, and the works of Benedict Bails, Bernouilli and D’Alembert.
	Connections: We do not know if it has been used in other centres besides the Seminary of Vergara and the Institute of Gijón.
	Other mentions of mathematics and mathematics education, further content: a method of teaching mathematics focused on “action by a lively and continuous exercise by the teacher” is proposed.

by following the content analysis methodology proposed in Section 2 of this paper.

The Plan y Método que propone el Maestro de Matemáticas del Real Seminario Bascongado para su enseñanza [Plan and Method proposed by the Teacher of Mathematics of the Royal Basque Seminary for its teaching], was presented by Jerónimo Mas Real to the General Meeting of the Basque Society of the Friends of the Country on 28 January 1779, but it was not published until 1785, with some modifications: Extractos de las Juntas Generales de la Real Sociedad Bascongada de los Amigos del País [Extracts from the General Meetings of the Royal Basque Society of the Friends of the Country], 1785, 8:134–144.

We know little about Jeronimo Mas’s origins, except that he was born in Valencia. Professor Leandro Silvan defines him as “persona de clara inteligencia, constante y tenaz en el esfuerzo; su formación científica estuvo muy por encima de lo usual y corriente en aquellos tiempos” [a person of clear intelligence, constant and tenacious effort; his scientific training was far above what was usual and common in those times] [47] (p. 78).

We do not know how the Basque Society of Friends of the Country contacted this mathematician, but his contribution to the development of this subject at the Seminary of Vergara was undoubtedly fundamental. He was there for 18 years, from the opening of the School in September 1776 until the dissolution of the Seminary in 1794, also teaching physics and chemistry, which he learned during his stay as commissioner in Paris, from June 1787 to April 1789, where he learned about Lavoisier’s new chemical theory and Fourcroy’s Elements of Chemistry. He returned to Vergara having acquired new equipment for the chemistry laboratory and the physics office.

In his Plan and Method for Teaching Mathematics, Mas denounces the Spanish backwardness in the teaching of physical and mathematical disciplines and, to remedy this, he drew upon the “mejores autores y métodos que tratan de la matemática” [best authors and methods that deal with Mathematics], so that “se tenga presente lo mejor que ha salido en la Europa, para que sirva de modelo a toda la nación, con aplauso de las extrajeras” [the best that has arised in Europe may serve as a model for the whole nation, with the applause of foreign countries]. In this respect, Mas’s unification of various disciplines into a single programme was important, demonstrating that fundamentals of calculus and geometry had application in interrelated disciplines, such as “la aritmética, geometría, trigonometría plana y esférica, el álgebra con sus aplicaciones a la aritmética, geometría y trigonometría, las secciones cónicas, el cálculo diferencial e integral, con sus respectivas aplicaciones a la geometría sublime y transcendente. La mecánica, estática, hidráulica, óptica, catóptrica, dióptrica, astronomía, geografía, navegación, gnomónica, cronología, fortificación y artillería” [arithmetic, geometry, plane and spherical trigonometry, algebra with its applications to arithmetics, geometry and trigonometry, conic sections, differential and integral calculus, with their respective applications to sublime and transcendental geometry. Mechanics, statics, hydraulics, optics, catoptrics, dioptrics, astronomy, geography, navigation, gnomonics, chronology, fortification, and artillery] [48] (p. 136).

He drew inspiration from sources such as Jorge Juan’s Examen Marítimo [Maritime Examination] and the works of Benito Bails, Bernouilli and D’Alembert among many others: “Pudiéramos con justicia nombrar el de Bezout, Bossut, La Caille, aumentado por el Abate Marie Gherli y otros; pero todos son imcompletos. El que más se llega a nuestros intentos es el de Don Benito Bails, obra escrita con sublimidad, exactitud y método por un hombre lleno de conocimientos útiles, de variada erudición, y juicio solido, que la ha compuesto teniendo a la vista quanto bueno y útil han escrito Juan y Daniel Bernoulli, Mr. D’Alembert, Euler, Bouguer, Clairaut, Mcheloti, La Lande, el Marqués de Condorcet, Bossut, Bezout, Lambert, Halley, La Caille, Cramer, Mauduit, Ricati, Stirling, etc. … pero como no trae los tratados de navegación, fortificación y artilleria adoptaremos para aquella los de Don Jorge Juan, Bouguer, o Bezout, y para esta los de Robins y Juan Muller, … o del Mr. D’Alembert, para los que teniendo mas tiempo hicieren sus estudios con mayor amplificación, versándose en los cálculos diferenciales e integrales y la geometría sublime. La extensión de la obra de Bails es tal, que se puede explicar en quatro años, que es el tiempo necesario para los expresados fines; y conforme a él se puede proporcionar los volúmenes, dando a cada año lo que corresponda” [We could justly name the works of Bezout, Bossut, La Caille, even Abate Marie Gherli and others; but they are all incomplete. The one that most closely matches our attempts is that of Don Benito Bails, a work written with sublimity, accuracy and method by a man full of useful knowledge, of varied learning, and solid judgment, who composed it by keeping in mind all the good and useful things written by Juan and Daniel Bernoulli, Mr. D’Alembert, Euler, Bouguer, Clairaut, Mcheloti, La Lande, Marqués de Condorcet, Bossut, Bezout, Lambert, Halley, La Caille, Cramer, Mauduit, Ricati, Stirling, etc… but given that it does not include the treatises on navigation, fortification and artillery, we will adopt those of Don Jorge Juan, Bouguer, or Bezout, and those of Robins and Juan Muller, … or those of Mr. D’Alembert, for those who have more time to do their studies with greater amplification, dealing with differential and integral calculations and sublime geometry. The extent of Bails’s work is such that it can be explained in four years, which is the time necessary for the stated purposes; and according to it, the volumes can be provided, giving what corresponds to each year] [48] (pp. 137 and 138).

Although the document that appears in the Extracts does not clearly distribute the subjects into each of the courses, by reading the paragraph of the manuscript entitled Suplemento del Plan [Supplement to the Plan] it is possible to get an idea of this distribution. This manuscript was published by F. Arocena in 1965 in Volume 6 of the collection of unpublished documents for the History of Guipúzcoa [49].

“En el primero se enseñarán la Arismética i el Algebra bien a fondo (como lo pide un Establecimiento que deve servir de modelo a los demás). En el segundo se explicará lo restante del primer tomo, esto es, la Geometría especulativa y práctica, la Trigonometría especulativa y práctica, la aplicación del Algebra a la Arismética, Geometría i Trigonometría, las Secciones cónicas, los Cálculos diferencial e integral con sus aplicaciones a la Geometría sublime, la Trigonometría esférica i la Fortificación, para los que tiran por la milicia. En el tercero se dará el segundo, esto es, la Estática y Dinámica, la Hydrostática, la Aerometría, la Hidráulica, la Optica, la Catóptrica, la Dioptría i la Astronomía, juntamente con la Estática i Dinámica que encierra el profundo Examen Marítimo de Dn. Jorge Juan i algunas noticias útiles de sus Observaciones Astronómicas i Físicas. En el quarto se dará fin al curso con el tercer tomo que contiene la Geografía, Gnomónica, Architectura, Perspectiva i el Calendario; se explicará también la Hydrodinámica del mismo Dn. Jorge Juan con su aplicación a la construcción, conocimiento i manejo de los navios y demás embarcaciones” [In the first, Arithmetics and Algebra will be taught in depth (as requested by an Establishment that must serve as a model for others). In the second, the rest of the first volume will be explained, that is, speculative and practical Geometry, speculative and practical Trigonometry, the application of Algebra to Arithmetics, Geometry and Trigonometry, Conic Sections, Differential and Integral Calculus with its applications to Sublime Geometry, Spherical Trigonometry and Fortification, for those who shoot for the military. In the third, the second will be taught, that is, Statics and Dynamics, Hydrostatics, Aerometry, Hydraulics, Optics, Catoptrics, Diopters and Astronomy, as well as Statics and Dynamics which contain Dn. Jorge Juan’s deep Maritime Examination and some useful motions from his Astronomical and Physical Observations. In the fourth, the course will end with the third volume which contains Geography, Gnomonics, Architecture, Perspective and the Calendar; Dn. Jorge Juan’s Hydro-dynamics will also be explained with its application to construction, knowledge and management of ships and other vessels] [49] (pp. 87–97).

The method of teaching mathematics proposed by Mas consists of “acción por un vivo y continuado exercicio del maestro” [action by a lively and continuous exercise by the teacher], outlining the steps to present the subjects and to propose and solve exercises and activities of revision of everything that has been taught “yendo todos los discípulos prevenidos para preguntar y responder á cerca de ello” [all the disciples being prepared to ask and answer questions about it] and proposing weekly and monthly exercises so that “el maestro, habiendo exáminado las resoluciones, las censurará con solo leer y aprobar las que estuvieren bien hechas” [the teacher, having examined the resolutions, will censure them just by reading and approving those that are well done], also indicating that although “los principios salgan con imperfección y desorden, no por esto se les ha de desanimar, sino esperanzarlos de que con la aplicación y exercicio se irán habilitando. En todos estos exercicios se procurará juntar la teórica con la practica, exercitando á los discípulos en toda suerte de operaciones, y en el uso de los instrumentos” [the principles will be imperfect and disorderly, they should not be discouraged for this reason, but rather hope that with the application and exercise they will become skilled. In all these exercises, an attempt will be made to combine theory with practice, exercising the students in all kinds of operations and in the use of instruments]. At another point in his proposal, he indicates that “como la última y principal utilidad de las matemáticas resulta de la práctica, y para dirigirla con acierto conviene emplear el mayor número de verdades, no basta haber señalado las materias y el modo de dirigir la enseñanza, si juntamente no se provee de los instrumentes necesarios para: las operaciones” [as the last and main usefulness of Mathematics comes from practice, and in order to direct it correctly, it is convenient to use the greatest number of truths, it is not enough to have indicated the subjects and the way of directing the teaching, if at the same time the necessary instruments are not provided for: the operations] [48] (p. 139).

The dissolution of the Seminary, in 1794, put an end to the most brilliant scientific experience to ever take place in the Basque Country. Mas moved to the Institute in Gijón, which Jovellanos had just founded, and from there he moved again to the San Telmo School in Malaga, where he died in 1804 from a yellow fever epidemic.

3.6. Difficulties and Decline of the Royal Asturian Institute of Nautical Studies and Mineralogy

Teaching at the Gijón Institute was not easy. The Inquisition immediately became suspicious, first about permission for the library to have forbidden books on physics and mineralogy requested by Jovellanos on 12 November 1794, and denied by Cardinal Lorenzana; and later requested and denied again on 6 August 1795 and 18 July 1796. A new incident with another commissioner of the Inquisition, Antonio Vigil Sariego, alias Machacón, occurred on 18 July 1796. He ordered the librarian to send him a list of the reserved books in the library. Jovellanos protested and ordered that he should deal with him directly and by official order. Commissioner Machacón did so on the 21st, but the day before Jovellanos had written to the Inquisition prosecutor of Valladolid, Mata Linares, complaining about the form, explaining the origin of the funds, and assuring that he did not believe he had any forbidden books in the library. Valladolid asked him for a list of the books, and Jovellanos sent it on August 21. Some are described as suspicious, but only one is a forbidden book: De Officio hominis et civis secundum legem naturalem, by Samuel Puffendorf, which the Inquisition ordered to be collected shortly afterwards [28] (p. 405).

Even so, the Institute went ahead and the first competition of the Royal Institute was held at the end of April 1797, where Jovellanos read his Oración sobre la necesidad de unir el estudio de la literatura al de las ciencias [speech about the need to unify the studies of Literature and Sciences] [49], whose argument is that “las ciencias esclarecen el espíritu, la literatura le adora: si aquellas le enriquece, esta pule y avalora sus tesoros. Las ciencias rectifican el juicio y le dan exactitud y firmeza y la literatura le da discernimiento y gusto, y le hermosa y perfecciona” [science enlightens the spirit, literature adores it: if the former enriches it, the latter polishes and enhances its treasures. Science rectifies the judgement and gives it accuracy and firmness, and literature gives it discernment and taste, and makes it beautiful and perfect] [50] (p. 320).

The first building of the Asturian Institute was a house owned by Francisco de Paula Jovellanos, its first director. Very soon its promoter thought of erecting a larger and more sufficient one [28] (p. 408). At the beginning of 1797, he already had a plot of land ceded by the municipality and commissioned the plans for the new building to the architect Ramón Durán. Jovellanos laid the first stone on 12 November 1797. When Durán died in 1798, the famous architect Juan de Villanueva became responsible for the new project and began to work on it in June 1798 [28] (p. 411). In the two long years that Jovellanos spent in Gijón, after his period as Minister of Grace and Justice and before his imprisonment in Bellver Castle in Mallorca (from 5 May 1802, to 6 April 1808), he managed to build almost the entire first floor. When the Royal Asturian Institute was suppressed on 26 October 1803 and replaced by an elementary Nautical Studies School, the construction was practically at a standstill. The roof was placed in 1805 and, in 1807, teaching transferred to the new building [28] (p. 495).

Francisco de Paula Jovellanos, the first director of the Asturian Institute, died on 4 August 1799. In June 1799, he appointed José Valdés Bazán as director, who requested his retirement due to the difficulties caused by the imprisonment of the Institute’s founder and the lack of sources of financing, and so he was succeeded by the second director, José Cienfuegos Quiñones, on 1 February 1804, after the institution had been converted into a Nautical Studies School [28] (p. 497) and had a smaller number of students: only sixteen at the beginning of that academic year, on 15 July 1805, and four teachers, among them Antonio Condres, responsible of teaching French and English [51] (pp. 40–42). Afterwards, it remained closed during the War of Independence, and it was able to restart its activity in 1813, after Jovellanos’s death and various restructurings and changes of name [52] (pp. 56–57). We are referring to the entry of French troops into Spain in the spring of 1808, with the consequent replacement of the Royal House of the Borbones by that of Napoleon Bonaparte’s family, which triggered the devastating War of Independence, which did not cease until 1814.

4. Discussion

This paper presents a descriptive and ex post facto research, focused on the analysis of ancient texts from the perspective of the history of mathematics and mathematics education. The analysis technique used was content analysis, a technique widely used in research on the history of mathematics and mathematics education. This heuristic, hermeneutic and critical analysis provides detailed information on the mathematical education that was intended to be provided to nautical pilots and miners at the end of the 18th century at the Royal Asturian Institute of Nautical and Mineralogy of Gijón. In this research a substantial number of primary sources and original texts have been used in order to be able to affirm that the description of the Royal Asturian Institute of Nautical and Mineralogy is in accordance with the reality of the time, as is the description of the sociogenesis of the discipline of technical mathematics studied there.

In comparison with other centers of the time, from the mathematical point of view, the contents indicated in the Plan and Method proposed by the Teacher of Mathematics of the Royal Bascongado Seminary for its teaching, used in the instruction of mathematics in the Institute of Gijón, are more extensive than those indicated, for example, in the Ordinances for the Royal College of San Telmo in Seville in 1786, an institution whose objective was to train pilots for the fleets and ships of the Carrera de Indias. Article CCII of these ordinances states that they will teach:

“principios del Algebra, la resolución de ecuaciones y la aplicación del Algebra a varias qüestiones artimeticas y geométricas, y a las curvas” (principles of algebra, the solution of equations and the application of algebra to various mathematical and geometrical questions, and to the curves) [53] (p. 95).

At the Institute of Gijón all this is studied together with differential and integral calculus, with their respective applications to sublime and transcendent geometry, mechanics, statics, hydraulics, optics, catoptric, dioptric, astronomy, geography, navigation, gnomonics, chronology, fortification and artillery, for Mas was inspired to write his Plan, among other sources, in the works of Benito Bails and in the Maritime Examination of Jorge Juan used as a textbook in the Academy of Marine Guards of Cadiz, a training center for future officers of the Spanish Navy, where Jorge Juan was Director since 1752.

It can be argued that the “program of Mathematics” suggested in the Plan could be too ambitious for the type of students to whom it was addressed, unless it was given an eminently practical treatment, as indicated by the method of teaching mathematics proposed by Mas, which consists of the «acción por un vivo y continuado exercicio del maestro» (“action by a lively and continuous exercise of the teacher”).

Regarding the institutional context of the Royal Asturian Institute of Nautics and Mineralogy, we can point out that its creation was due to the support of the Economic Society of Asturias, but that its geographical location and the scarce economic support meant that it had less funds than others, such as the Matritense or the Bascongada.

The educational trials of the Economic Societies were inserted in general teaching guidelines theoretically supported by the Government, although they basically responded to the reformist private initiative, as in the case of Jovellanos and the Asturian Institute. Even so, the Sociedades Económicas de Amigos del País maintained three common objectives of action: literacy, professional training and the promotion of the so-called useful sciences.

In comparison with the studies at the Royal Patriotic Seminary of Vergara, at the Royal Asturian Institute of Nautical and Mineralogy, the subjects are not only focused on the three scientific subjects, mathematics, mineralogy and nautical studies, and physics and chemistry, but also on the study of the “Castilian Humanities” and the French and English languages taught by the librarian, as a way of offering the students of the Institute the possibility of completing their studies with a humanistic base and perspective. It is here, in the conjunction of these three aspects, science, humanities and languages, where the main originality of Jovellanos’ educational program at the Royal Asturian Institute of Nautical and Mineralogy lies.

5. Conclusions

Both the school disciplines and mathematics for technical training, such as the training of miners and sailors, at the Jovellanos Institute are part of a special type of knowledge that can only be studied within its institutional context. This is what is called a disciplinary code, constituted by the set of ideas, values, assumptions, regulations, and practical routines that are often transformed into legitimising public discourses on the educational value of the discipline, and which guide the professional practice of teachers. The disciplinary code is not a static reality, but a social creation that has a process of construction rather than creation. Our specific concern has been to carry out a social, scientific, and academic contextualisation.

The Economic Societies reflected the ideas and values of the Enlightenment. Projectism was used in Asturias in the search for economic development, with the enlightened elite expressing their interests and concerns through various memorials.

The Economic Society of Asturias had less funds than others, such as the Matritense or the Bascongada; it had few members and received little financial support from the Government.

The Royal Patriotic Seminary of Vergara was one of the most important educational centres of the Enlightenment in Spain. It served as a model for Jovellanos to found the Royal Asturian Institute of Nautical Studies and Mineralogy so that students could have access to a technical and humanistic education based on the curriculum planned by Jovellanos. The idea matured and was eventually consolidated in the Institute, which had a significant number of students from its opening, as sixty were enrolled in the first year. Its originality lies in the fact that it was simultaneously concerned with the intellectual training, scientific promotion, and humanistic development of its pupils.

The mathematics taught at the Asturian Institute was in line with the latest trends in the discipline in Spain, including the new infinitesimal calculus. The teaching method followed was Método con que se han de enseñar las matematicas en el Seminario Bascongado [Method with which Mathematics must be taught at the Basque Seminary], by Jerónimo Mas. This method explains the content of the works by the authors on which it was based, introducing the book by Benito Bails as a textbook or teaching support book: “es el que más llega a nuestros intentos” [it is the one that is most relevant to our attempts]; classes were organised to include a practical part through the use of materials and exercises that included field trips. This pedagogical proposal shows an interest in the teaching of utilitarian mathematics, showing a concern for didactic-methodological renewal. The teaching of mathematics was perfectly calculated and planned, considering new developments on the subject in Europe.

The Institute’s life did not evolve as its creator would have wished, who, after being banished, saw its teaching reduced to nautical subjects from 1803 onwards, which once again showed how much the movement of the Friends of the Country owed to the specific will of a small number of men.

This work has made clear the limitations of the Jovellanist model of the technical training school for sailors and miners created in Gijón, although the attempt to set it up in such a peripheral location is no less remarkable. The social, economic, and political conditions at the time were not yet favourable to professional training in a strict sense, for which we would have to wait until the period between the wars of the 20th century, with the Industrial Apprenticeship Law of 1911 and the Statute of Professional Training of 1928, but the pedagogical experience carried out in Gijón in the late 18th and early 19th is nonetheless of great interest and prominence.