{
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"references": [
{
"type": "Article",
"id": "bib-bib1",
"authors": [],
"title": "\nL. Albuquerque, Introdução, to the fac-simile edition of the Almanach Perpetuum.\nImprensa Nacional-Casa da Moeda, Lisboa (1986)\n"
},
{
"type": "Article",
"id": "bib-bib2",
"authors": [],
"title": "\nB. Almeida and H. Leitão, Pedro Nunes (1502–1578) mathematics, cosmography and nautical science in the 16th century,\npedronunes.fc.ul.pt/index.html (2009)\n",
"url": "http://pedronunes.fc.ul.pt/index.html"
},
{
"type": "Article",
"id": "bib-bib3",
"authors": [],
"title": "\nA. Alselmo, Origens da imprensa em Portugal.\nImprensa Nacional-Casa da Moeda, Lisboa (1991)\n"
},
{
"type": "Article",
"id": "bib-bib4",
"authors": [],
"title": "\nJ. Chabàs and B. R. Goldstein, Astronomy in the Iberian Peninsula: Abraham Zacut and the transition from manuscript to print.\nTransactions of the American Philosophical Society 90.2, American Philosophical Society, Philadelphia, PA (2000)\n"
},
{
"type": "Article",
"id": "bib-bib5",
"authors": [],
"title": "\nA. J. Franco de Oliveira, Anastácio da Cunha and the concept of convergent series.\nArch. Hist. Exact Sci. 39, 1–12 (1988)\n"
},
{
"type": "Article",
"id": "bib-bib6",
"authors": [],
"title": "\nJ. A. Gaspar and H. Leitão, How Mercator did it in 1569: from tables of rhumbs to a cartographic projection.\nEur. Math. Soc. Newsl. 99, 44–49 (2016)\n"
},
{
"type": "Article",
"id": "bib-bib7",
"authors": [],
"title": "\nD. E. Knuth, Mathematical typography.\nBull. Amer. Math. Soc. (N.S.) 1, 337–372 (1979)\n"
},
{
"type": "Article",
"id": "bib-bib8",
"authors": [],
"title": "\nJ. F. Rodrigues, Portuguese mathematical journals: some aspects of (almost) periodical research publications.\nIn The Practice of Mathematics in Portugal, edited by L. Saraiva and H. Leitão, Acta Univeritatis Conimbrigensis, Coimbra, 601–627 (2004)\n"
},
{
"type": "Article",
"id": "bib-bib9",
"authors": [],
"title": "\nJ. F. Rodrigues, António Monteiro and his modernist essay.\nCIM Bulletin 42, 3–10 (2020)\n"
},
{
"type": "Article",
"id": "bib-bib10",
"authors": [],
"title": "\nJ. F. Rodrigues, The Nunes’ spiral and the prehistory of the infinitesimal calculus (in Portuguese).\nIn 33rd Portuguese National Seminar on the History of Mathematics (October 2020), Boletim SPM (in press)\n"
},
{
"type": "Article",
"id": "bib-bib11",
"authors": [],
"title": "\nL. M. R. Saraiva, Mathematics in the Memoirs of the Lisbon Academy of Sciences in the 19th century.\nHistoria Math. 35, 302–326 (2008)\n"
},
{
"type": "Article",
"id": "bib-bib12",
"authors": [],
"title": "\nJ. Sebastião e Silva, Su certe classi di spazi localmente convessi importanti per le applicazioni.\nRend. Mat. e Appl. (5) 14, 388–410 (1955)\n"
},
{
"type": "Article",
"id": "bib-bib13",
"authors": [],
"title": "\nTipografia Matemática Portuguesa: 1496–1987 – Catalogue (Portuguese),\nipleiria.pt/sdoc/tipografia-matematica-portuguesa-1496-1987/",
"url": "https://www.ipleiria.pt/sdoc/tipografia-matematica-portuguesa-1496-1987/"
},
{
"type": "Article",
"id": "bib-bib14",
"authors": [],
"title": "\nA. P. Youschkevitch, J. A. da Cunha et les fondements de l’analyse infinitésimale.\nRev. Histoire Sci. Appl. 26, 3–22 (1973)\n"
},
{
"type": "Article",
"id": "bib-bib15",
"authors": [],
"title": "\nA. P. Youschkevitch, C. F. Gauss et J. A. da Cunha,\nRev. Histoire Sci. Appl. 31, 327–332 (1978)\n"
}
],
"title": "Portuguese mathematical typography: A brief overview from 1496 until 1987",
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"’s tables were calculated in Salamanca in the Alphonsine tradition with reference to the period 1473–1476 [",
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"].\nIt was translated and edited by the Portuguese José Vizinho and printed by the Jewish typographer Abraham d’Ortas.\nIt appeared just a few years after a first edition of the ",
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" of 1489, which is the first Christian text in Portuguese and was printed in Chaves, in the north of the country [",
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"].\nIt should be noted that the Gutenberg Bible, the first book ever printed in Europe, dates from 1455, and the first printing of Euclid’s ",
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" in 1482 was done by the printer Erhard Ratdolt in Venice, in a Latin edition containing the first geometric diagrams ever printed."
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" was the main incentive for the recent book exhibition ",
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" to be electronically composed in TeX.\nWith 32 significant original works in Portuguese mathematical typography, many of them rare books containing unknown or still barely known yet highly interesting pages, the exhibition presents nine sections that traverse the whole history of the mathematical sciences in Portugal, from the age of ocean navigation and the first European globalisation through military engineering, essential in the wars of Restoration (1640–1668) after the end of the Iberian Union, to the successive reforms of Colleges, Military Academies and Universities (1772 and 1911) and finally the scientific research of the 20th century."
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" is a landmark of the beginning of the culture of mathematical sciences in Portugal through the influence and use of the art and knowledge of navigation, namely in the first ocean voyages of Vasco da Gama to India and Pedro Álvares Cabral to Brazil [",
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"].\nIt had several editions in the 16th century and it was used in the preparation of the ",
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", a set of popular time calendars and almanacs also used in astrology; a certain Gaspar Nicolas participated in the elaboration of the one from the year 1518."
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", a book of a technical and utilitarian nature about the rules of arithmetic, also “for overseas trade”; it went through ten new editions over the course of the next two centuries.\nIn his preface, Nicolas acknowledges practical arithmetic as “very necessary in these Portuguese kingdoms and territories for the sake of the flourishing of the merchant trades of India and Persia and Arabia and Ethiopia and other major parts that have come to us”.\nBetween 1472 and 1519, about forty books on arithmetic were published in Europe, including Luca Pacioli’s ",
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"Subsequently this Portuguese mathematician suggested the rectification of the rhumb line for the maritime chart and developed original methods, in particular for the approximation of the rhumb line, which laid the foundations for the elaboration of nautical tables and the cartographic projection made in 1569 by Mercator in his famous ",
{
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" [",
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"].\nThe broken line invented by Pedro Nunes to approximate the loxodrome was composed of small sections of great circles.\nIt was first published in Latin in his ",
{
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", in 1566 in Basel; it is now called the ",
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" and was chosen for the logo of the Leiria exhibition.\nIt is the natural idea of approximating the loxodrome that corresponds to Euler’s modern method for integrating differential equations, and it was used numerically by Edward Wright in the secants’ method to construct nautical tables in 1596 [",
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"Mathematics book printing continued in Portugal for the navy and the army schools throughout the 18th and 19th centuries among others, with the Portuguese translations of the important book by Lagrange, ",
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", the printing of which was completed in Lisbon only in 1790, by José Anastácio da Cunha (1744–1787), the military mathematician and “lente penitenciado”, a professor at the University of Coimbra from 1773 to 1778 who was then imprisoned by the Inquisition from 1978 to 1781.\nThe ",
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", which was translated into French (Bordeaux, 1811) consisted of 21 chapters with 18 prints, and was intended to be the basis of all of mathematics, including geometry and arithmetic, algebra and series, differential and integral calculus.\nIt also contains new and original theoretical contributions, such as the first rigorous definition of the convergence of a series, and the new concept of infinity and infinitesimal as variable quantities [",
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]
},
" (1866), which included a few mathematics articles, including an original article in Portuguese by Daniel da Silva on the amortisation of pensions in the main Portuguese survivors’ funds (1867), and another one devoted to a comparative study of the population in Portugal (1869)."
]
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"content": [
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"content": [
"In 1853, the Coimbra University Press started publishing the scientific and literary periodical ",
{
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"content": [
"O Instituto"
]
},
", which included few mathematics articles mainly for didactic purposes.\nAlthough it was not a mathematical journal and did not contain any relevant mathematics research contributions, it did publish the interesting short but deep text ",
{
"type": "Emphasis",
"content": [
"Ensaio sobre os Princípios da Mechanica"
]
},
", written in the 1780s by J. A. da Cunha, in which he proposed a clear separation between the Physical and the Rational Mechanics, based on the axiomatic method."
]
},
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"id": "Sx6.p2",
"content": [
"The first Portuguese periodical exclusively dedicated to mathematics, the ",
{
"type": "Emphasis",
"content": [
"Jornal de Sciencias Mathematicas e Astronomicas"
]
},
" by Francisco Gomes Teixeira (1851–1933), started publication in 1877 in Coimbra; it was printed at the University Press but it was independent of the University.\nIt published fifteen volumes, and in addition to internationally promoting the mathematical activity of Portuguese mathematicians, it included international contributions, in particular by the French mathematician C. Hermite.\nLater its publication was transferred to Porto, and in 1905 it was integrated into the ",
{
"type": "Emphasis",
"content": [
"Annaes Scientificos da Academia Polytechnica do Porto."
]
},
" Only more than thirty years later did Portugal get a second mathematical journal, the ",
{
"type": "Emphasis",
"content": [
"Portugaliae Mathematica"
]
},
".\nHowever, following the Faculties of Science of the Universities of Porto, of Coimbra and of Lisbon, each of which created their own scientific journal containing some mathematical papers (in 1927, 1931 and 1937 respectively), in 1950 the ",
{
"type": "Emphasis",
"content": [
"Revista da Faculdade de Ciências de Lisboa"
]
},
" started their 2nd series – A, exclusively dedicated to mathematics [",
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"target": "bib-bib8",
"content": [
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]
},
"].\nIt was directed by J. V. Gonçalves until 1966."
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"id": "Sx7",
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"content": [
"Higher mathematics textbooks in the transition from the 19th to the 20th century"
]
},
{
"type": "Paragraph",
"id": "Sx7.p1",
"content": [
"The publication of original university textbooks by Portuguese authors would only continue a century later with the ",
{
"type": "Emphasis",
"content": [
"Curso de Analyse Infinitesimal"
]
},
" by Francisco Gomes Teixeira, which was first published in 1887 in Porto.\nWritten for the students of the ",
{
"type": "Emphasis",
"content": [
"Academia Polythecnica do Porto"
]
},
", it was later re-edited and expanded to become the reference Portuguese treatise of Mathematical Analysis at the beginning of the 20th century.\nIt was later republished as Volumes III (1906) and VI (1912) of Teixeira’s ",
{
"type": "Emphasis",
"content": [
"Obras"
]
},
", published by the Coimbra University Press."
]
},
{
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"id": "Sx7.p2",
"content": [
"That university practice of writing textbooks had resumed only in the next century, examples being the classical ",
{
"type": "Emphasis",
"content": [
"Curso de Álgebra Superior"
]
},
" by J. Vicente Gonçalves, whose first edition was printed in Coimbra, in 1933, and the modern ",
{
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"content": [
"Lições de Análise Infinitesimal"
]
},
" by F. R. Dias Agudo, printed by the ",
{
"type": "Emphasis",
"content": [
"Tipografia Matemática"
]
},
" in Lisbon in 1973 among several other textbooks."
]
},
{
"type": "Heading",
"id": "Sx8",
"depth": 1,
"content": [
"Historical surveys, expository and popularisation books"
]
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"content": [
"Francisco Gomes Teixeira was the most active and prolific Iberian mathematician of the 19th century.\nHe corresponded with numerous European mathematicians of his time, and was the first rector of the University of Porto, from 1911 to 1918.\nHe was also the author of the remarkable and unsurpassed ",
{
"type": "Emphasis",
"content": [
"Traite des Courbes Spéciales Remarquables Planes et Gauches"
]
},
", which went through several editions and occupies three of the seven volumes of his ",
{
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"content": [
"Obras"
]
},
" with a total of more than 1300 pages."
]
},
{
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"id": "Sx8.p2",
"content": [
"During the short decade 1937–1946, mathematical activity flourished in Portugal.\nFor example, the remarkable little book ",
{
"type": "Emphasis",
"content": [
"Conceitos Fundamentais da Matemática"
]
},
", by Bento de Jesus Caraça (1901–1948), a Mathematics Professor at the Economics Institute in Lisbon who was expelled from the University in 1946 for political reasons, had a first edition in 1941.\nThis was the first Portuguese book aimed at the popularisation of mathematics written in view of the “cultura integral do indivíduo” with a historical and materialistic philosophy."
]
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{
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"id": "Sx9",
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"content": [
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]
},
{
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"id": "Sx9.p1",
"content": [
"The foundation of the scientific journal ",
{
"type": "Emphasis",
"content": [
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]
},
" in 1937 in Lisbon, by António Aniceto Monteiro (1902–1980), who had returned the year before from Paris where he had completed his doctoral degree under Maurice Fréchet, started a modernist movement also in Science with a certain “mathematical effervescence” that lasted for a short decade in Portugal [",
{
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"target": "bib-bib9",
"content": [
"9"
]
},
"].\nIt was followed by the ",
{
"type": "Emphasis",
"content": [
"Gazeta de Matemática"
]
},
", in 1940, which was later printed by the ",
{
"type": "Emphasis",
"content": [
"Tipografia Matemática"
]
},
", and by the creation of the first research mathematical centre in the country, the ",
{
"type": "Emphasis",
"content": [
"Centro de Estudos Matemáticos de Lisboa"
]
},
", the same year.\nThat unique typography was established in 1945 and had a remarkable, although limited, activity in the Portuguese mathematical press for more than three decades until 1977."
]
},
{
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"id": "Sx9.p2",
"content": [
"Finally, we mention some examples of research publications, such as the two doctoral theses printed at the ",
{
"type": "Emphasis",
"content": [
"Tipografia Matemática"
]
},
": the ",
{
"type": "Emphasis",
"content": [
"Publicação #18"
]
},
" of the ",
{
"type": "Emphasis",
"content": [
"Centro de Estudos Matemáticos do Porto"
]
},
", by A. Pereira Gomes (1919–2006), which was the first modern PhD thesis written in a Portuguese university, and ",
{
"type": "Emphasis",
"content": [
"As Funções Analíticas e a Análise Funcional"
]
},
", by José Sebastião e Silva (1914–1972), both published in ",
{
"type": "Emphasis",
"content": [
"Portugaliae Mathematica"
]
},
", respectively in 1946 and in 1950",
{
"type": "Emphasis",
"content": [
"."
]
},
" In his work, J. Sebastião e Silva began work on some deep contributions to Functional Analysis, which would later lead him to introduce in 1955 an important class of locally convex spaces as inductive limits of an increasing sequence of normed spaces with compact inclusions [",
{
"type": "Cite",
"target": "bib-bib12",
"content": [
"12"
]
},
"], later called the Silva LN*-spaces."
]
},
{
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"content": [
"After five centuries of existence, the mathematical typography using movable type, with its specific and distinctive aspects such as tables, figures, diagrams and mathematical formulae, gave way to electronic publishing driven by the TeX program created by Donald Knuth in 1978 [",
{
"type": "Cite",
"target": "bib-bib7",
"content": [
"7"
]
},
"].\nThis electronic composition system was adopted by the American Mathematical Society five years later, and was used in 1987 by the ",
{
"type": "Emphasis",
"content": [
"Sociedade Portuguesa de Matemática"
]
},
" (SPM) for the publication of the fiftieth anniversary volume 44 of ",
{
"type": "Emphasis",
"content": [
"Portugaliae Mathematica"
]
},
", which was chosen for the last book of the Leiria exhibition in order to complete this five-century-long retrospective of Portuguese mathematical typography, from 1496 until 1987."
]
},
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"content": [
"\nJosé Francisco Rodrigues is professor at the Mathematics Department/Faculty of Sciences of the Universidade de Lisboa, where he graduated in 1978 and obtained his PhD in 1982.\nHe had studied also at the Université de Paris VI and spent a short post-doc visit at the Universität Bonn.\nAs vice-president and delegate of the Portuguese Mathematical Society, he participated at the 1990 founding meeting of the EMS in Madralin.\nHe was director of the Portuguese Centro Internacional de Matemática, and he is a member of the Academia das Ciências de Lisboa.\nHis field of research is in nonlinear analysis and PDEs, mainly free boundary problems.\nHe has also interests in the relations of mathematics with other subjects, including history, music, architecture and culture.\n",
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}
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}