The Values of Illustration in the Economic Society of Asturias and Its Reflection in Mathematics Education at the Royal Asturian Institute of ...
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mathematics
Article
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
Carmen López-Esteban * and Fernando Almaraz-Menéndez
Departamento de Didáctica de la Matemática, Facultad de Educación, Universidad de Salamanca, Canalejas 169,
37008 Salamanca, Spain; falmaraz@usal.es
* Correspondence: lopezc@usal.es
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
Citation: López-Esteban, C.; of the Technical Training School for Sailors and Miners created in Gijón are made clear, although the
Almaraz-Menéndez, F. The Values of attempt to start it up in such a peripheral place is no less remarkable.
Illustration in the Economic Society
of Asturias and Its Reflection in Keywords: history of mathematics education; technical mathematics; Royal Institute of Nautical
Mathematics Education at the Royal Studies and Mineralogy; Gijón-Asturias-Spain; eighteenth century
Asturian Institute of Nautical Studies
and Mineralogy during the Last MSC: 01A50; 97Dxx
Quarter of the 18th Century.
Mathematics 2022, 10, 1747. https://
doi.org/10.3390/math10101747
Academic Editor: Michael Voskoglou 1. Introduction
Received: 24 April 2022
There is no consensus among historians on the limits of the Enlightenment in Spain.
Accepted: 18 May 2022
The Enlightenment period often refers to the “esprit français” prevailing in Spain, and
Published: 20 May 2022
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
Publisher’s Note: MDPI stays neutral
Herr [2] chronologically simplify Spanish reformism to the time of Carlos III. They also
with regard to jurisdictional claims in
refer to this period as the Century of the Lights, although, as Richard Herr observed, these
published maps and institutional affil-
lights, in truth, “bore little resemblance to the lumières of their northern neighbour” [2]
iations.
(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
Copyright: © 2022 by the authors.
interventionism, and the promotion of culture and regalism [3] (p. 447).
Licensee MDPI, Basel, Switzerland. Culture was promoted through the creation of French style cultural institutions: the
This article is an open access article National Library (1711), the Academy of Language (1714), the Academy of History (1738),
distributed under the terms and etc. The Sociedades Económicas de Amigos del País [Economic Societies of Friends of the Coun-
conditions of the Creative Commons try] were also created throughout Spain, driven by Campomanes, who was a Prosecutor of
Attribution (CC BY) license (https:// the Council of Castile and who tried to mobilise the local ruling classes of the nobility and
creativecommons.org/licenses/by/ the incipient bourgeoisie by the promulgation of a series of regulations which tended to
4.0/). reward commercial, artisanal, and industrial activity.
Mathematics 2022, 10, 1747. https://doi.org/10.3390/math10101747 https://www.mdpi.com/journal/mathematicsMathematics 2022, 10, x FOR PEER REVIEW 2 of 21
Mathematics 2022, 10, 1747 2 of 20
nobility and the incipient bourgeoisie by the promulgation of a series of regulations which
tended to reward commercial, artisanal, and industrial activity.
The
TheEconomic
EconomicSocieties
SocietiesofofFriends
Friendsofofthe theCountry
Countrywere werea afundamental
fundamentalinstrument
instrumentofof
Carlos
CarlosIII’s
III’sreformist
reformist policy
policyandanda vehicle
a vehiclefor for
enlightenment
enlightenment ideas in terms
ideas of theofobjectives
in terms the objec-
they
tivespursued and theand
they pursued activities they carried
the activities out. out.
they carried
Numerous
Numerousstudies studieshave
havefocused
focused ononanalysing
analysing thethe
birth, development
birth, development andand
influence of
influence
the Economic Societies of Friends of the Country (see [4–8]) and the bibliography
of the Economic Societies of Friends of the Country (see [4–8]) and the bibliography refer- referring
toring
specific Societies
to specific in eachin
Societies region
each or city is
region oralso
cityvery extensive;
is also these arethese
very extensive; generally studies
are generally
ofstudies
an institutional nature, often
of an institutional withoften
nature, similarwithfunctioning and activities.
similar functioning andThe Asturias
activities. TheSociety
Astu-
isrias
oneSociety
of the least known,
is one of theespecially
least known,due to the scarcedue
especially documentation
to the scarcepreserved,
documentationsince the
pre-
Acts prior
served, to 1791
since disappeared
the Acts verydisappeared
prior to 1791 quickly due very to the spoliation
quickly due tocarried out in 1808
the spoliation by
carried
the French in the War of Independence, as some of the studies of the
out in 1808 by the French in the War of Independence, as some of the studies of the Eco- Economic Society of
Friends of the Country of Asturias indicate(see [9–13]).
nomic Society of Friends of the Country of Asturias indicate(see [9–13]).
Campomanes’s
Campomanes’sinitiative
initiativetotocreate
createthetheEconomic
EconomicSocieties,
Societies,asaswell
wellasashis
hisobjectives
objectives
and
and proposals for their operation, spread throughout the country followingthe
proposals for their operation, spread throughout the country following theofficial
official
model
modelofofthe theMatritense,
Matritense,asaswe wewill
willsee
seeininthis
thiswork,
work,which
whichwas wasdifferent
differentfrom
fromthethemodel
model
ofofthe Bascongada, created by Xavier María de Munibe e Idiáquez, Count
the Bascongada, created by Xavier María de Munibe e Idiáquez, Count of Peñaflorida, in of Peñaflorida,
in1763,
1763,which
whichwas wasthe
thefirst
first Society
Society ofof this
this kind
kind created
created in in Spain.
Spain. The
Thecreative
creativefever
feverofofthe
the
Economic Societies of Friends of the Country dates from 1774–1784,
Economic Societies of Friends of the Country dates from 1774–1784, and it aimed and it aimed to outline
to out-
a line
complex and ambitious
a complex and ambitioussocio-economic
socio-economic model that encompassed
model that encompassed all economic
all economicsectors,
sec-
but prioritised industry. Figure 1 below is a portrait of Campomanes, the driving force
tors, but prioritised industry. Figure 1 below is a portrait of Campomanes, the driving
behind the creation of the Sociedades Económicas de Amigos del País.
force behind the creation of the Sociedades Económicas de Amigos del País.
Figure1.1.Portrait,
Figure Portrait,by
byAntonio
AntonioCarnicero,
Carnicero,ofofPedro
PedroRodríguez
Rodríguezde deCampomanes
Campomanesy yPérez-Sorriba,
Pérez-Sorriba,first
first
Count of Campomanes (Santa Eulalia de Sorriba, Tineo, Asturias, 1 July 1723—Madrid, 3 February
Count of Campomanes (Santa Eulalia de Sorriba, Tineo, Asturias, 1 July 1723—Madrid, 3 February
1802), who was a Spanish politician, jurisconsult and economist. He was appointed Minister of Fi-
1802), who was a Spanish politician, jurisconsult and economist. He was appointed Minister of
nance in 1760 in the first reformist government of Carlos III’s reign, which was led by the Prime
Finance
MinisterinCount
1760 inofthe first reformist
Floridablanca, andgovernment of Carlos
he was stripped of hisIII’s reign, due
position which wasfear
to the ledthat
by the
thePrime
French
Minister Count
Revolution of Floridablanca,
aroused and he
in King Charles IV was stripped
in 1789. of his
Source: positionCommons.
Wikipedia due to the fear that the French
Revolution aroused in King Charles IV in 1789. Source: Wikipedia Commons.
The Asturian Society of Friends of the Country promoted the creation of the Royal
InstituteAsturian
The Society
of Nautical and of Friends ofof
Mineralogy theGijón
Country
wherepromoted
technicalthe creation of the
Mathematics for Royal
Miners
Institute of Nautical and Mineralogy of Gijón where technical Mathematics
and Sailors were taught. It was founded by Jovellanos. Gaspar Melchor de Jovellanos for Miners
was
and Sailors werefigure
an enlightened taught.
bornIt in
was founded
Gijón by Jovellanos.
(Asturias), Gaspar
a writer, jurist andMelchor
politiciandewho
Jovellanos
was par-
was an enlightened figure born in Gijón (Asturias), a writer, jurist and politician who was
ticularly committed to the economic and cultural development of his country.
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
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,
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
constituted by the set of ideas, values, assumptions, regulations and practical routines that
are often translated into legitimizing discourses and public languages about the
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 disciplinaryMathematics 2022, 10, 1747 3 of 20
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 histori-
cal 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. This was validated by means of a
triangulation of experts on research methods in education, history of mathematics, and
mathematics education.
Table 1. Form for the analysis of mathematical and mathematics education content.
Criteria Items
Name of publication
Date of publication
General data Number of pages dedicated to mathematics or mathematics
education/number of pages of the document
Author (s) (if indicated)
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.
Categories of analysis
Connections: have other editions been published; has the author
published other works on mathematics . . .
Other mentions of mathematics and mathematics education, further
content . . .
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 theMathematics 2022, 10, 1747 4 of 20
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 [20–22]) 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 technologi-
cal 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].Mathematics 2022, 10, 1747 5 of 20
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]:
1. That of the “patriotic schools”, especially weaving schools and first letters schools.
2. That of special teachings, where the Societies acted as centres for the spread of En-
lightenment 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.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
Mathematics 2022, 10, 1747 local authorities were invited and where achievements were publicly announced, 6prizes of 20
were awarded, etc. The Asturian Society generally followed the Matritense’s organisa-
tional model. Figure 2 shows the cover of the Estatutos de la Sociedad Económica de Asturias.
Figure 2. Statutes of the Economic Society of Asturias, 1781 [27].
Figure 2. Statutes of the Economic Society of Asturias, 1781 [27].
TheStatutes
The Statutesofofthe the Asturian
Asturian Society,
Society, in their
in their preamble,
preamble, quotequote
the the speech
speech Extracto
Extracto de losde
fundamentales principios que han motivado el establecimiento de la Sociedad Económica [Extract[Ex-
los fundamentales principios que han motivado el establecimiento de la Sociedad Económica of
tract
the of the fundamental
fundamental principlesprinciples
that havethat have motivated
motivated the establishment
the establishment of the Economic of the Economic
Society],
Society],
written in written
1780 by in D.1780
Joaquín by D. Joaquín
José Queipo José
deQueipo de Llano,
Llano, Count Countand
of Toreno of Toreno and major
major ensign of
ensign of the General Board of the Principality of Asturias. The
the General Board of the Principality of Asturias. The Extracto tries to justify the creation Extracto tries to justify the
ofcreation
the Economicof the Economic
Society bySociety expressingby expressing
the enormous the enormous
benefit that benefit that the Economic
the Economic Society
Society would bring and by specifying the Society’s
would bring and by specifying the Society’s goals. The aim was “desterrar la goals. The aim was “desterrar
ociosidad,layoci-
la
osidad, y ladestinando
mendiguez, mendiguez, losdestinando
niños á laslos niños
Artes, á las
y las Artes,
niñas y las
á todo niñasdeá hilados
género todo género de hilados
con que adelantencon
que
las adelanten
fábricas las fábricas
sus texidos, sus texidos,
se aumente se aumente la
la Agricultura, Agricultura,
Comercio y artesComercio y artespopular
y la industria y la industria
tenga
popular
sus tenga
efectos” [tosus efectos”
banish [to banish
idleness andidleness
beggars,and bybeggars,
destining byboys
destining
to theboys arts,toand
the arts,
girls and
to
girls
all kindsto all
of kinds
weaving, of weaving,
so that the so factories
that the factories
will advancewill advance their textiles,
their textiles, so that agri-
so that agriculture,
culture, commerce
commerce and the arts and willtheincrease,
arts willand increase,
so that and so that
popular popular
industry willindustry
have its will have
effects] [27]its
effects]
(p. 4). In[27]the(p. 4). In the
Statutes, theStatutes, the first
first chapter chapterthat
indicates indicates that itsisobjective
its objective “conferir;is y“conferir;
produciry
producir
las memorias las para
memorias
mejorar parala mejorar
industrialapopular
industria popular
y los oficios,y los secretos
oficios, los
de lassecretos
artes,de
laslas artes, las
máquinas
máquinas
para para
facilitar lasfacilitar
maniobras las maniobras
a y auxiliar a y auxiliar la enseñanza.
la enseñanza. El fomento
El fomento de la de la agricultura,
agricultura, plan-
plantíos,
cría
tíos,decría
ganados, pesca,pesca,
de ganados, comercio navegación,
comercio navegación,minerales, y mármoles
minerales, y mármolesseráserá otraotra
de sus principales
de sus principa-
ocupaciones
les ocupaciones comocomo
tan importantes
tan importantes á este país,país,
á este tratando por menor
tratando por menorlos ramos
los ramos subalternos relativos
subalternos relati-
la labranza,
á vos plantíos, y cría” [to confer; and to produce memories
á la labranza, plantíos, y cría” [to confer; and to produce memories to improve the po- to improve the popular
industry and theand
pular industry commerces,
the commerces, the secrets theofsecrets
the arts,
of the machines to facilitate
arts, the machines to manoeuvres
facilitate ma-
and to helpand
noeuvres the to
teaching.
help theThe promotion
teaching. of agriculture,
The promotion plantations,plantations,
of agriculture, cattle breeding, fishing,
cattle breed-
commerce,
ing, fishing, navigation,
commerce, minerals,
navigation, and marbles
minerals, will
and bemarbles
others ofwillits main
be othersoccupations as being
of its main occu-
sopations
important to this
as being socountry,
important dealing
to this in country,
the minordealing
branches related
in the minor to tillage,
branches plantations,
related to
and animal
tillage, breeding].
plantations, and animal breeding].
The
The AsturiasSociety,
Asturias Society,like likemany
manyothers,
others,devoted
devotedmuch muchofofits itsbudget
budgettotogiving
givingprizes
prizes
and
and rewards, a controversial way of boosting the economy. In fact, it was a symbolicform
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, thank-
ing 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 thatMathematics 2022, 10, 1747 7 of 20
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 consid-
ered 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 ad-
dressed to the Society with the objective of promoting the economic growth of the Principal-
ity 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 andMathematics 2022, 10, 1747 8 of 20
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 becauseMathematics 2022, 10, 1747 9 of 20
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 InstituteMathematics 2022, 10, 1747 10 of 20
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 pro-
nounced 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 ofof the Institute the possibility of completing their studies with a humanist base and per-
spective 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
Mathematics 2022, 10, 1747 his thoughts, to give order and clarity to one’s ideas and to write with purity and preci- 11 of 20
sion. 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
ofthe
theInstrucción
Instrucción u Ordenanza
u Ordenanza para
para la nueva
la nueva escuela
escuela de Matemáticas,
de Matemáticas, Física,
Física, Química,
Química, Mineral-y
Mineralogía
ogía y Náutica [Instruction or Ordinance for the new school of
Náutica [Instruction or Ordinance for the new school of Mathematics, Physics, Chemistry, Mathematics, Physics,
Chemistry,
Mineralogy and Nautical Studies], from 1 December 1793, “De la disciplina literarialit-
Mineralogy and Nautical Studies], from 1 December 1793, “De la disciplina del
eraria del Instituto”
Instituto” [On the [On the discipline
literary literary discipline of the Institute],
of the Institute], a document a document
signed by signed by the
the minister
minister
AntonioAntonio Valdés
Valdés [32] [32] (volume
(volume II, pp. 399–420).
II, pp. 399–420).
There
Therewere
weredifferent
different types
types of of exams:
exams: thetheapproval
approvalexams
examswerewereusedused toto check
check thethe de-
degree
gree of achievement only in the core subjects before changing classes
of achievement only in the core subjects before changing classes and did not consider the and did not consider
the progress
progress made
made in in
thethe auxiliarycourses
auxiliary courses[33][33](art.
(art.496).
496). The
The final
final grading
grading exams
examsdid didnot
not
include
include special examinations in languages and drawing, although pupils were askedasked
special examinations in languages and drawing, although pupils were about
about
them them [33]514).
[33] (art. (art.On 514).
theOn thehand,
other otherthehand, the graduation
graduation exams,were
exams, which whichonlywere only
accessible
accessible
to pupils to pupils
who had who had distinguished
distinguished themselves themselves in the previous
in the previous examinations,
examinations, assessedas- all
sessed
subjects all in
subjects
the samein the
waysame[33] way [33] (art.
(art. 532), 532), by
by means of means
a publicofcompetition
a public competition
and with andfinal
with final awarding
awarding of prizes. of prizes.
3.4.Mathematics
3.4. MathematicsEducation
EducationininSpain
Spain
InInSpain,
Spain,the
thestudy
studyofofmathematics
mathematicsand
andscience
scienceininthe
the18th
18thcentury
centurywas
waspromoted
promotedbyby
thecentres
the centresofofmilitary
militarystudies
studiesand
andfrom
fromthe
theJesuit
Jesuitcentres.
centres.According
AccordingtotoArenzana
Arenzana(1987),
(1987),
99mathematical
99 mathematicalworks
workswere
werepublished
publishedininthe
the18th
18thcentury,
century,7171ofofwhich
whichwere
werepublished
published
between 1760 and 1790. Figure 3 shows the distribution of these publications
between 1760 and 1790. Figure 3 shows the distribution of these publications during the during the
century. Differential calculus was introduced during this time
century. Differential calculus was introduced during this time [36]. [36].
Distributionby
Figure3.3.Distribution
Figure bydecades
decadesofofmathematical
mathematicalworks.
works.The Thestriped
stripedarea
areaofofthe
thegraph
graphcorresponds
corresponds
totoCarlos
CarlosIII’s
III’sreign,
reign,1759–1788.
1759–1788.Total
Totalnumber
numberofofclassified
classifiedworks:
works:170.
170.Number
Numberofofworks
workswithout
without
date
dateororofofunknown
unknowndate:date:29.
29.Unpublished
Unpublishedworks:
works:3 3([36],
([36],p.p.130).
130).
Scientificstudies
Scientific studiesbegan
begantotoexpand
expandthrough
throughthethecentres
centresthat
thatwere
werecreated
createdaround
aroundthethe
Court(School
Court (SchoolofofNobles,
Nobles,SanSanFernando
FernandoAcademy,
Academy,and andthetheMilitary
MilitaryAcademy
AcademyofofSegovia),
Segovia),
ininthethemore
morecommercially
commerciallyactive
activeperipheral
peripheralregions
regionsofofSpain
Spain(School
(SchoolofofGuardamarinas
Guardamarinasofof
Cádiz),etc.
Cádiz), etc.The
TheJesuits
Jesuitsalso
alsopromoted
promotedtheir
theirstudy
studyuntil
untilthe
theOrder
Orderwas
wasexpelled
expelledfrom
fromSpain
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 quarterMathematics 2022, 10, 1747 12 of 20
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 SantiagoYou can also read
