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Jesuit Mathematical Practice in Portugal, 1540–1759

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Part of the book series: Archimedes ((ARIM,volume 6))

Abstract

Divine providence — as a contemporary Jesuit would undoubtedly have called it — or the more prosaic historical coincidence caused the Society of Jesus to be founded at the height of Portuguese and Iberian overseas expansion. And while Ignatius Loyola’s original wish to serve God and spread Christianity to Jerusalem had been both the dream and (mythical) locus of consummation, as things turned out “the Indies” became their quotidian embodiment.

This work was partiallv supported by a research grant from the Fundação Oriente, Lisbon.

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Notes

  1. Easily accessible to English-speaking readers are the somewhat dated, but still balanced, works by Charles R. Boxer: The Portuguese Seaborne Empire, 1415–1825 (London, 1969); The Golden Age of Brazil, 1695–1750 (Berkeley and Los Angeles, 1969); The Christian Century in Japan, 1549–1650 (Berkeley and Los Angeles, 1967). See also Bailey W. Diffie and George D. Winnius, Foundations of the Portuguese Empire, 1415–1580 (Minneapolis, 1977); A. J. R. Russell-Wood, A World on the Move: The Portuguese in Africa, Asia, and America, 1415–1808 (Manchester, 1992); Sanjay Subrahmanyam, The Portuguese Empire in Asia, 1500–1700 (London, 1993).

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  2. António da Silva Rego, O Padroado Português do Oriente. Esboç Histórico (Lisbon, 1940).

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  3. The fundamental study of the Portuguese Assistancy, although dated and sometimes apologetic, is Francisco Rodrigues’ massive História da Companhia de Jesus na Assistência de Portugal, 7 vols. (Porto, 1931–1950). Equally important is Serafim Leite’s monumental História da Companhia de Jesus no Brasil, 10 vols. (Rio de Janeiro, 1938–1950). For all their deficiencies these two works have not been superseded. The recent work by Dauril Alden, The Making of an Enterprise: The Society of Jesus in Portugal, Its Empire, and Beyond, 1540–1750 (Stanford, 1996), includes much new information but is weak on the cultural dimension. For the educational and cultural aspects, Francisco Rodrigues S.J., A Formaçdo Intellectual do Jesuíta. Leis e Factos (Porto, 1917) is still useful, while João Pereira Gomes’ Os Professores de Filosofia da Universidade de Évora (Évora, 1960) is a mine of information and an excellent guide to primary sources.

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  4. See, for example, Teófilo Braga, História da Universidade de Coimbra, 4 vols. (Lisbon, 1892–1902). The most influential synthesis of the history of mathematics in Portugal, by Francisco Gomes Teixeira, História das Matemáticas em Portugal (Lisbon, 1934), is also violently anti-Jesuit. Subsequent historiography has moderated many of these evaluations, but there is still much investigation to be carried out before a more balanced iudgement can be made.

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  5. Domingos Maurício, “Os Jesuítas e o ensino das Matemáticas em Portugal,” Brotéria, 20 (1935), 189–205.

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  6. The scientific activity of Jesuit missionaries in China has attracted a great deal of attention lately and cannot be discussed here. See, for example, E. Zürcher, N. Standaert and A. Dudink, A Bibliography of the Jesuit Mission (ca. 1580-ca. 1680) (Leiden, 1991);

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  7. Federico Masini (ed.), Western Humanistic Culture Presented to China by Jesuit Missionaries (XVIIth — XVIIIth centuries) (Rome, 1996);

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  8. Peter Engelfriet, Euclid in China. The Genesis of the First Translation of Euclid s Elements in 1607 and its Reception up to 1723 (Leiden, 1998);

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  9. Roman Malek (ed.), Western Learning and Christianity in China. The Contribution and Impact of Johann Adam Schall von Bell, SJ (1592–1666), 2 vols. (Nettetal, 1999). However, speaking from the more restricted point of view of the Portuguese Jesuits in China, it is necessary to emphasize that much is still to be studied and understood.

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  10. Most scholars accept 1288 as the year that the University in Lisbon, the first in Portugal, was founded. See Artur Moreira de Sá, “La fondation de ĺUniversité à Lisbonne en 1288 et son role dans le developpement de la culture portugaise jusqúau milieu du XVe siècle,” Revista da Faculdade de Letras (Lisbon), 12 (1970), 29–36;

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  11. Rómulo de Carvalho, História do Ensino em Portugal, 2nd ed. (Lisbon, 1996), 43–71.

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  12. Luís de Albuquerque, “A Náutica e a Cartografia em Portugal nos séculos XV e XVI,” in A Universidade e os Descobrimentos (Lisbon, 1993), 91–101.

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  13. The Cosmógrafo-Mor and nautical teaching more generally are analyzed in A. Teixeira da Mota, “Os Regimentos do Cosmógrafo-Mor de 1559 e 1592 e as origens do ensino náutico em Portugal,” Memórias da Academia das Ciências de Lisbon (Classe de Ciências), 13 (1969), 227–291.

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  14. The numbers are drawn from Francisco Rodrigues, História da Companhia de Jesus na Assistência de Portugal. Such information should be handled with care as some colleges were shortlived while the survival of others was rather tenuous.

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  15. António Leite, “Pombal e o ensino secundário,” in Como Interpretar Pombal? (Lisbon, 1983), 165–181.

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  16. While such numbers may not seem too impressive compared with other European countries, they are so within the Portuguese context. Not until the late nineteenth century do we find a comparable number of students in secondary education

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  17. For the pre-1640 period, see Ugo Baldini, “As Assistências ibéricas da Companhia de Jesus e a actividade científica nas Missões Asiáticas (1578–1640). Alguns aspectos culturais e institucionais,” Revista Portuguesa de Filosofia, 54 (1998), 195–245; “The Portuguese Assistancy of the Society of Jesus and Scientific activities in its Asian missions until 1640,” in História das Ciências Matemáticas: Portugal e o Oriente (Lisbon, 2000), 49–104.

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  18. See Luís de Albuquerque, “A ’Aula da Esfera’ do Colégio de Santo Antão no século XVII,” Anais da Academia Portuguesa de História, 21 (1972), 337–391, and the Baldini works listed above.

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  19. Lists of teachers and descriptions of surviving lecture notes are given by Luís de Albuquerque, “A Aula da Esfera.” Baldini corrected and augmented that information.

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  20. “Oltre de questa lectione de Gesuiti se ne legge un’altra del cosmografo maggiore de S. M.ta provisionate per questo, et se leggono queste lectione nel idioma portoghese, duendo seruire à molti che nõ possiedono la lingua latina.” Della grandezza et magnificenza della citta di Lisbona, Ms. Fondo Confaloniere, Vatican Archives, 45, fol. 34, cited in Teixeira da Mota, “Os Regimentos do Cosmógrafo-Mor,” 257.

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  21. See, especially, Baldini, “The Portuguese Assistancy of the Society of Jesus.”

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  22. Joaquim de Carvalho, “Galileu e a cultura Portuguesa sua contemporânea,” Biblos, 19 (1943), 399–482.

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  23. Domingos Maurício Gomes dos Santos, “Vicissitudes da obra do Pe. Cristóvão Borri,” Anais da Academia Portuguesa de História, 3 (1951), 117–150.

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  24. As noted long ago by J. Pereira Gomes, and recently discussed in greater detail in Baldini’s “The Portuguese Assistancy of the Society of Jesus.”

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  25. “A mesma obseruação fiz os meses passados estando iá aqui em Lixboa e a mostrei não somente a meus ouuintes mas tambem a outras pessoas curiosas muitas que a virão com pontas do mesmo modo que a lua no princípio menores, depois maiores cada vez mais. Falo com testemunhas de vista.” Arquivo Nacional da Torre do Tombo, Manuscritos de Livraria, 1770, fol. 33v.

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  26. See William Wallace, “The Early Jesuits and the Heritage of Domingo de Soto,” History and Technology, 4 (1987), 301–320, reprinted in, Galileo, the Jesuits, and the Medieval Aristotle (Aldershot, 1991); Idem, “Late Sixteenth-Century Portuguese Manuscripts Relating to Galileo’s Early Notebooks,” Revista Portuguesa de Filosofia, 51 (1995), 677–698.

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  27. The venture proved short-lived since mathematical classes ceased by the late 1660s.

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  28. Omer van de Vyver, “L’École de Mathématiques des Jésuites de la Province Flandro-Belge au XVIIe siècle,” Archivum Romanum Societatis Iesu, 49 (1980), 265–278; G. H. W. Vanpaemel, “Jesuit science in the Spanish Netherlands” (forthcoming). I thank Professor Vanpaemel for allowing me to consult this work in manuscript.

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  29. ARSI, Lus. 34, I, fol. 168.

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  30. Ordinatio Rev. P. N. Thyrsi Gonsales Praepositi Generalis ad suscitandum, fovendumque in Prov. Lusitana studium mathematicae directa ad P. Emmanuelem da Sylva Provincialem (12 April 1692), Biblioteca Nacional, Lisbon, Cód. 2135, fols. 1r-14r.

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  31. “Cum nulla sit Societatis Provincia cui aeque sint necessariae Disciplinae Mathematicae, ac Provinciae Lusitaniae spectatis non solum celebribus Lusitaniae Academiis, cathredisque Mathematicis Societati commissis, sed etiam Missionibus Orientis tam illustribus, et amplis, quibus illas constat esse perquam necessarias, visum est ad suscitandum, fovendumque in eadem Provincia studium Mathematicae haec ordinare, atque omnino observanda mandare,” Biblioteca Nacional, Lisbon, Cód. 2135, fol. 1 r.

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  32. Ordinatio R. P. N. Thyrsi Gonzales Praepositi Generalis de forma et legibus examinis Mathematici in Provincia Lusitanorum (17 January 1693), Biblioteca Nacional, Lisbon, Cód. 2135, fols. 15v-19r.

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  33. Confirmatio et extensio R. P. N. Thyrsi Gonzales cc.a ordinationem de forma et legibus examinis Mathematicae (1 August 1693). Biblioteca Nacional, Lisbon, Cód. 2135, fols. 21v-23r.

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  34. Declarationes Praepositi Generalis circa studia Mathematicae (4 February 1702), Biblioteca Nacional, Lisbon, Cód. 2135, fols. 14v-15r.

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  35. Michelangelo Tamburini, who succeed Gonzalez as General in 1706, continued his predecessor’s efforts. In addition to the Ordinances, various other letters devoted to mathematical instruction were dispatched from Portugal during the first decade of the eighteenth century.

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  36. Baldini, “The Portuguese Assistancy of the Society of Jesus.”

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  37. Marcus Hellyer, The Last of the Aristotelians: The Transformation of Jesuit Physics in Germany, 1630–1773, unpublished Ph.D. Dissertation, University of California, San Diego (1998), 299.

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  38. F. Rodrigues, História da Companhia de Jesus na Assistência de Portugal, III. i. 213–219.

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  39. M. Lopes de Almeida, “Uma nota sobre o Pe. João König (dos Reis) professor de Matemática na Universidade,” Revista da Faculdade de Ciências da Universidade de Coimbra, 14 (1945), 123–135.

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  40. Obediencias do padre provincial perpetuas, Biblioteca Nacional, Lisbon, Cód. 4458, fols. 267r, 273r. Similar instructions are also included in this volume.

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  41. The Congregation of the Oratory was founded in Rome by S. Filipe de Neri in 1565 and approved by Pope Gregory XIII in 1575. Its introduction into Portugal is due to Fr. Bartolomeu do Quental (1627–1698). For the history of this congregation in Portugal, see Eugénio dos Santos, O Oratório no Norte de Portugal (Lisbon, 1982).

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  42. For a lucid analysis of the problems involved, see Francisco Contente Domingues, Ilustraçdo e Catolicismo: Teodoro de Almeida (Lisbon, 1994).

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  43. See, for example, Lúcio Craveiro da Silva, “Inácio Monteiro. Significado da sua vida e da sua obra,” Revista Portuguesa de Filosofia, 29 (1973), 229–266;

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  44. António Banha de Andrade, “Inácio Monteiro e a evolução dos estudos nas aulas dos Jesuítas de setecentos,” Revista Portuguesa de Filosofia, 29 (1973), 289–304;

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  45. Ana Isabel Rosendo, “O Compendio dos Elementos de Mathematica do P. Inácio Monteiro,” Revista Portuguesa de Filosofia. 54 (1998), 319–353

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  46. The scientific activities of the Portuguese Jesuits in China have never been carefully studied, despite the abundance of documentation in Portuguese archives. Francisco Rodrigues, Jesuítas Portugueses astrónomos na China (Macau, 1990), is still the best survey, but it is incomplete. Several contributions in História das Ciências Matemáticas: Portugal e o Oriente add important new information.

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  47. A. Delduque da Costa, “Os padres matemáticos no observatório de Jaipur,” Oriente Português, 4 (1932), 58–64;

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  49. F. Rodrigues, História da Companhia de Jesus na Assistência de Portugal, IV. i. 413–418.

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  50. A comprehensive study of this Jesuit is still a desideratum. A good starting point is Bernardino Ferreira Cardoso, O P. Jodo Carbone na Corte do Magnânimo. Subsídios para uma história diplomática do reinado deD.Jodo V, unpublished Ph.D. dissertation, University of Lisbon (1956).

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  52. Jaime Cortesão, “A missão dos padres matemáticos no Brasil,” Studia, 1 (1958), 123–150;

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  54. Rómulo de Carvalho, A astronomia em Portugal no século XVIII (Lisbon, 1983).

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  55. Mostly due to G. B. Carbone. See Rómulo de Carvalho, “Portugal nos Philosophical Transactions, nos séculos XVII e XVIII,” Revista Filosófica, 15–16 (1955–56).

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Leitão, H. (2003). Jesuit Mathematical Practice in Portugal, 1540–1759. In: Feingold, M. (eds) The New Science and Jesuit Science: Seventeenth Century Perspectives. Archimedes, vol 6. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0361-1_5

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  • DOI: https://doi.org/10.1007/978-94-017-0361-1_5

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