{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T17:37:46Z","timestamp":1770745066774,"version":"3.49.0"},"publisher-location":"Dordrecht","reference-count":55,"publisher":"Springer Netherlands","isbn-type":[{"value":"9789048161157","type":"print"},{"value":"9789401703611","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2003]]},"DOI":"10.1007\/978-94-017-0361-1_5","type":"book-chapter","created":{"date-parts":[[2013,2,23]],"date-time":"2013-02-23T12:03:17Z","timestamp":1361620997000},"page":"229-247","source":"Crossref","is-referenced-by-count":12,"title":["Jesuit Mathematical Practice in Portugal, 1540\u20131759"],"prefix":"10.1007","author":[{"given":"Henrique","family":"Leit\u00e3o","sequence":"first","affiliation":[]}],"member":"297","reference":[{"key":"5_CR1","first-page":"1415","volume-title":"The Portuguese Seaborne Empire","author":"CR Boxer","year":"1969","unstructured":"Easily accessible to English-speaking readers are the somewhat dated, but still balanced, works by Charles R. Boxer: The Portuguese Seaborne Empire, 1415\u20131825 (London, 1969); The Golden Age of Brazil, 1695\u20131750 (Berkeley and Los Angeles, 1969); The Christian Century in Japan, 1549\u20131650 (Berkeley and Los Angeles, 1967). See also Bailey W. Diffie and George D. Winnius, Foundations of the Portuguese Empire, 1415\u20131580 (Minneapolis, 1977); A. J. R. Russell-Wood, A World on the Move: The Portuguese in Africa, Asia, and America, 1415\u20131808 (Manchester, 1992); Sanjay Subrahmanyam, The Portuguese Empire in Asia, 1500\u20131700 (London, 1993)."},{"key":"5_CR2","volume-title":"O Padroado Portugu\u00eas do Oriente. Esbo\u00e7 Hist\u00f3rico","author":"A Silva Rego da","year":"1940","unstructured":"Ant\u00f3nio da Silva Rego, O Padroado Portugu\u00eas do Oriente. Esbo\u00e7 Hist\u00f3rico (Lisbon, 1940)."},{"key":"5_CR3","unstructured":"The fundamental study of the Portuguese Assistancy, although dated and sometimes apologetic, is Francisco Rodrigues\u2019 massive Hist\u00f3ria da Companhia de Jesus na Assist\u00eancia de Portugal, 7 vols. (Porto, 1931\u20131950). Equally important is Serafim Leite\u2019s monumental Hist\u00f3ria da Companhia de Jesus no Brasil, 10 vols. (Rio de Janeiro, 1938\u20131950). For all their deficiencies these two works have not been superseded.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\u20131750 (Stanford, 1996), includes much new information but is weak on the cultural dimension. For the educational and cultural aspects, Francisco Rodrigues S.J., A Forma\u00e7do Intellectual do Jesu\u00edta. Leis e Factos (Porto, 1917) is still useful, while Jo\u00e3o Pereira Gomes\u2019 Os Professores de Filosofia da Universidade de \u00c9vora (\u00c9vora, 1960) is a mine of information and an excellent guide to primary sources."},{"key":"5_CR4","volume-title":"Hist\u00f3ria da Universidade de Coimbra","author":"T Braga","year":"1902","unstructured":"See, for example, Te\u00f3filo Braga, Hist\u00f3ria da Universidade de Coimbra, 4 vols. (Lisbon, 1892\u20131902). The most influential synthesis of the history of mathematics in Portugal, by Francisco Gomes Teixeira, Hist\u00f3ria das Matem\u00e1ticas 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."},{"key":"5_CR5","first-page":"189","volume":"20","author":"D Maur\u00edcio","year":"1935","unstructured":"Domingos Maur\u00edcio, \u201cOs Jesu\u00edtas e o ensino das Matem\u00e1ticas em Portugal,\u201d Brot\u00e9ria, 20 (1935), 189\u2013205.","journal-title":"Brot\u00e9ria"},{"key":"5_CR6","volume-title":"A Bibliography of the Jesuit Mission (ca. 1580-ca. 1680)","author":"E Z\u00fcrcher","year":"1991","unstructured":"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. Z\u00fcrcher, N. Standaert and A. Dudink, A Bibliography of the Jesuit Mission (ca. 1580-ca. 1680) (Leiden, 1991);"},{"key":"5_CR7","volume-title":"Western Humanistic Culture Presented to China by Jesuit Missionaries (XVIIth \u2014 XVIIIth centuries)","year":"1996","unstructured":"Federico Masini (ed.), Western Humanistic Culture Presented to China by Jesuit Missionaries (XVIIth \u2014 XVIIIth centuries) (Rome, 1996);"},{"key":"5_CR8","volume-title":"Euclid in China. The Genesis of the First Translation of Euclid s Elements in 1607 and its Reception up to 1723","author":"P Engelfriet","year":"1998","unstructured":"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);"},{"key":"5_CR9","volume-title":"Western Learning and Christianity in China. The Contribution and Impact of Johann Adam Schall von Bell, SJ (1592\u20131666)","year":"1999","unstructured":"Roman Malek (ed.), Western Learning and Christianity in China. The Contribution and Impact of Johann Adam Schall von Bell, SJ (1592\u20131666), 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."},{"key":"5_CR10","first-page":"29","volume":"12","author":"S Moreira de","year":"1970","unstructured":"Most scholars accept 1288 as the year that the University in Lisbon, the first in Portugal, was founded. See Artur Moreira de S\u00e1, \u201cLa fondation de \u013aUniversit\u00e9 \u00e0 Lisbonne en 1288 et son role dans le developpement de la culture portugaise jusq\u00faau milieu du XVe si\u00e8cle,\u201d Revista da Faculdade de Letras (Lisbon), 12 (1970), 29\u201336;","journal-title":"Revista da Faculdade de Letras"},{"key":"5_CR11","first-page":"43","volume-title":"Hist\u00f3ria do Ensino em Portugal","author":"R Carvalho de","year":"1996","unstructured":"R\u00f3mulo de Carvalho, Hist\u00f3ria do Ensino em Portugal, 2nd ed. (Lisbon, 1996), 43\u201371.","edition":"2"},{"key":"5_CR12","first-page":"91","volume-title":"A Universidade e os Descobrimentos","author":"L Albuquerque de","year":"1993","unstructured":"Lu\u00eds de Albuquerque, \u201cA N\u00e1utica e a Cartografia em Portugal nos s\u00e9culos XV e XVI,\u201d in A Universidade e os Descobrimentos (Lisbon, 1993), 91\u2013101."},{"key":"5_CR13","first-page":"227","volume":"13","author":"AT Mota da","year":"1969","unstructured":"The Cosm\u00f3grafo-Mor and nautical teaching more generally are analyzed in A. Teixeira da Mota, \u201cOs Regimentos do Cosm\u00f3grafo-Mor de 1559 e 1592 e as origens do ensino n\u00e1utico em Portugal,\u201d Mem\u00f3rias da Academia das Ci\u00eancias de Lisbon (Classe de Ci\u00eancias), 13 (1969), 227\u2013291.","journal-title":"Mem\u00f3rias da Academia das Ci\u00eancias de Lisbon (Classe de Ci\u00eancias)"},{"key":"5_CR14","unstructured":"The numbers are drawn from Francisco Rodrigues, Hist\u00f3ria da Companhia de Jesus na Assist\u00eancia de Portugal. Such information should be handled with care as some colleges were shortlived while the survival of others was rather tenuous."},{"key":"5_CR15","first-page":"165","volume-title":"Como Interpretar Pombal?","author":"A Leite","year":"1983","unstructured":"Ant\u00f3nio Leite, \u201cPombal e o ensino secund\u00e1rio,\u201d in Como Interpretar Pombal? (Lisbon, 1983), 165\u2013181."},{"key":"5_CR16","unstructured":"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"},{"key":"5_CR17","doi-asserted-by":"crossref","first-page":"195","DOI":"10.17990\/RPF\/1998_54_2_0195","volume":"54","author":"U Baldini","year":"1998","unstructured":"For the pre-1640 period, see Ugo Baldini, \u201cAs Assist\u00eancias ib\u00e9ricas da Companhia de Jesus e a actividade cient\u00edfica nas Miss\u00f5es Asi\u00e1ticas (1578\u20131640). Alguns aspectos culturais e institucionais,\u201d Revista Portuguesa de Filosofia, 54 (1998), 195\u2013245; \u201cThe Portuguese Assistancy of the Society of Jesus and Scientific activities in its Asian missions until 1640,\u201d in Hist\u00f3ria das Ci\u00eancias Matem\u00e1ticas: Portugal e o Oriente (Lisbon, 2000), 49\u2013104.","journal-title":"Revista Portuguesa de Filosofia"},{"key":"5_CR18","first-page":"337","volume":"21","author":"L Albuquerque de","year":"1972","unstructured":"See Lu\u00eds de Albuquerque, \u201cA \u2019Aula da Esfera\u2019 do Col\u00e9gio de Santo Ant\u00e3o no s\u00e9culo XVII,\u201d Anais da Academia Portuguesa de Hist\u00f3ria, 21 (1972), 337\u2013391, and the Baldini works listed above.","journal-title":"Anais da Academia Portuguesa de Hist\u00f3ria"},{"key":"5_CR19","unstructured":"Lists of teachers and descriptions of surviving lecture notes are given by Lu\u00eds de Albuquerque, \u201cA Aula da Esfera.\u201d Baldini corrected and augmented that information."},{"key":"5_CR20","unstructured":"\u201cOltre de questa lectione de Gesuiti se ne legge un\u2019altra del cosmografo maggiore de S. M.ta provisionate per questo, et se leggono queste lectione nel idioma portoghese, duendo seruire \u00e0 molti che n\u00f5 possiedono la lingua latina.\u201d Della grandezza et magnificenza della citta di Lisbona, Ms. Fondo Confaloniere, Vatican Archives, 45, fol. 34, cited in Teixeira da Mota, \u201cOs Regimentos do Cosm\u00f3grafo-Mor,\u201d 257."},{"key":"5_CR21","unstructured":"See, especially, Baldini, \u201cThe Portuguese Assistancy of the Society of Jesus.\u201d"},{"key":"5_CR22","first-page":"399","volume":"19","author":"J Carvalho de","year":"1943","unstructured":"Joaquim de Carvalho, \u201cGalileu e a cultura Portuguesa sua contempor\u00e2nea,\u201d Biblos, 19 (1943), 399\u2013482.","journal-title":"Biblos"},{"key":"5_CR23","first-page":"117","volume":"3","author":"DMG Santos dos","year":"1951","unstructured":"Domingos Maur\u00edcio Gomes dos Santos, \u201cVicissitudes da obra do Pe. Crist\u00f3v\u00e3o Borri,\u201d Anais da Academia Portuguesa de Hist\u00f3ria, 3 (1951), 117\u2013150.","journal-title":"Anais da Academia Portuguesa de Hist\u00f3ria"},{"key":"5_CR24","unstructured":"As noted long ago by J. Pereira Gomes, and recently discussed in greater detail in Baldini\u2019s \u201cThe Portuguese Assistancy of the Society of Jesus.\u201d"},{"key":"5_CR25","unstructured":"\u201cA mesma obserua\u00e7\u00e3o fiz os meses passados estando i\u00e1 aqui em Lixboa e a mostrei n\u00e3o somente a meus ouuintes mas tambem a outras pessoas curiosas muitas que a vir\u00e3o com pontas do mesmo modo que a lua no princ\u00edpio menores, depois maiores cada vez mais. Falo com testemunhas de vista.\u201d Arquivo Nacional da Torre do Tombo, Manuscritos de Livraria, 1770, fol. 33v."},{"key":"5_CR26","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1080\/07341518708581702","volume":"4","author":"W Wallace","year":"1987","unstructured":"See William Wallace, \u201cThe Early Jesuits and the Heritage of Domingo de Soto,\u201d History and Technology, 4 (1987), 301\u2013320, reprinted in, Galileo, the Jesuits, and the Medieval Aristotle (Aldershot, 1991); Idem, \u201cLate Sixteenth-Century Portuguese Manuscripts Relating to Galileo\u2019s Early Notebooks,\u201d Revista Portuguesa de Filosofia, 51 (1995), 677\u2013698.","journal-title":"History and Technology"},{"key":"5_CR27","unstructured":"The venture proved short-lived since mathematical classes ceased by the late 1660s."},{"key":"5_CR28","first-page":"265","volume":"49","author":"O Vyver van de","year":"1980","unstructured":"Omer van de Vyver, \u201cL\u2019\u00c9cole de Math\u00e9matiques des J\u00e9suites de la Province Flandro-Belge au XVIIe si\u00e8cle,\u201d Archivum Romanum Societatis Iesu, 49 (1980), 265\u2013278; G. H. W. Vanpaemel, \u201cJesuit science in the Spanish Netherlands\u201d (forthcoming). I thank Professor Vanpaemel for allowing me to consult this work in manuscript.","journal-title":"Archivum Romanum Societatis Iesu"},{"key":"5_CR29","unstructured":"ARSI, Lus. 34, I, fol. 168."},{"key":"5_CR30","unstructured":"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, C\u00f3d. 2135, fols. 1r-14r."},{"key":"5_CR31","unstructured":"\u201cCum 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,\u201d Biblioteca Nacional, Lisbon, C\u00f3d. 2135, fol. 1 r."},{"key":"5_CR32","unstructured":"Ordinatio R. P. N. Thyrsi Gonzales Praepositi Generalis de forma et legibus examinis Mathematici in Provincia Lusitanorum (17 January 1693), Biblioteca Nacional, Lisbon, C\u00f3d. 2135, fols. 15v-19r."},{"key":"5_CR33","unstructured":"Confirmatio et extensio R. P. N. Thyrsi Gonzales cc.a ordinationem de forma et legibus examinis Mathematicae (1 August 1693). Biblioteca Nacional, Lisbon, C\u00f3d. 2135, fols. 21v-23r."},{"key":"5_CR34","unstructured":"Declarationes Praepositi Generalis circa studia Mathematicae (4 February 1702), Biblioteca Nacional, Lisbon, C\u00f3d. 2135, fols. 14v-15r."},{"key":"5_CR35","unstructured":"Michelangelo Tamburini, who succeed Gonzalez as General in 1706, continued his predecessor\u2019s 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."},{"key":"5_CR36","unstructured":"Baldini, \u201cThe Portuguese Assistancy of the Society of Jesus.\u201d"},{"key":"5_CR37","first-page":"299","volume-title":"The Last of the Aristotelians: The Transformation of Jesuit Physics in Germany, 1630\u20131773","author":"M Hellyer","year":"1998","unstructured":"Marcus Hellyer, The Last of the Aristotelians: The Transformation of Jesuit Physics in Germany, 1630\u20131773, unpublished Ph.D. Dissertation, University of California, San Diego (1998), 299."},{"key":"5_CR38","unstructured":"F. Rodrigues, Hist\u00f3ria da Companhia de Jesus na Assist\u00eancia de Portugal, III. i. 213\u2013219."},{"key":"5_CR39","first-page":"123","volume":"14","author":"M Lopes Almeida de","year":"1945","unstructured":"M. Lopes de Almeida, \u201cUma nota sobre o Pe. Jo\u00e3o K\u00f6nig (dos Reis) professor de Matem\u00e1tica na Universidade,\u201d Revista da Faculdade de Ci\u00eancias da Universidade de Coimbra, 14 (1945), 123\u2013135.","journal-title":"Revista da Faculdade de Ci\u00eancias da Universidade de Coimbra"},{"key":"5_CR40","unstructured":"Obediencias do padre provincial perpetuas, Biblioteca Nacional, Lisbon, C\u00f3d. 4458, fols. 267r, 273r. Similar instructions are also included in this volume."},{"key":"5_CR41","unstructured":"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\u20131698). For the history of this congregation in Portugal, see Eug\u00e9nio dos Santos, O Orat\u00f3rio no Norte de Portugal (Lisbon, 1982)."},{"key":"5_CR42","unstructured":"For a lucid analysis of the problems involved, see Francisco Contente Domingues, Ilustra\u00e7do e Catolicismo: Teodoro de Almeida (Lisbon, 1994)."},{"key":"5_CR43","first-page":"229","volume":"29","author":"LC Silva","year":"1973","unstructured":"See, for example, L\u00facio Craveiro da Silva, \u201cIn\u00e1cio Monteiro. Significado da sua vida e da sua obra,\u201d Revista Portuguesa de Filosofia, 29 (1973), 229\u2013266;","journal-title":"Revista Portuguesa de Filosofia"},{"key":"5_CR44","first-page":"289","volume":"29","author":"AB Andrade de","year":"1973","unstructured":"Ant\u00f3nio Banha de Andrade, \u201cIn\u00e1cio Monteiro e a evolu\u00e7\u00e3o dos estudos nas aulas dos Jesu\u00edtas de setecentos,\u201d Revista Portuguesa de Filosofia, 29 (1973), 289\u2013304;","journal-title":"Revista Portuguesa de Filosofia"},{"key":"5_CR45","doi-asserted-by":"crossref","first-page":"319","DOI":"10.17990\/RPF\/1998_54_2_0319","volume":"54","author":"AI Rosendo","year":"1998","unstructured":"Ana Isabel Rosendo, \u201cO Compendio dos Elementos de Mathematica do P. In\u00e1cio Monteiro,\u201d Revista Portuguesa de Filosofia. 54 (1998), 319\u2013353","journal-title":"Revista Portuguesa de Filosofia"},{"key":"5_CR46","volume-title":"Jesu\u00edtas Portugueses astr\u00f3nomos na China","author":"F Rodrigues","year":"1990","unstructured":"The scientific activities of the Portuguese Jesuits in China have never been carefully studied, despite the abundance of documentation in Portuguese archives. Francisco Rodrigues, Jesu\u00edtas Portugueses astr\u00f3nomos na China (Macau, 1990), is still the best survey, but it is incomplete. Several contributions in Hist\u00f3ria das Ci\u00eancias Matem\u00e1ticas: Portugal e o Oriente add important new information."},{"key":"5_CR47","first-page":"58","volume":"4","author":"AD Costa da","year":"1932","unstructured":"A. Delduque da Costa, \u201cOs padres matem\u00e1ticos no observat\u00f3rio de Jaipur,\u201d Oriente Portugu\u00eas, 4 (1932), 58\u201364;","journal-title":"Oriente Portugu\u00eas"},{"key":"5_CR48","first-page":"187","volume":"21","author":"A Gracias","year":"1938","unstructured":"Am\u00e2ncio Gracias, \u201cUma embaixada cient\u00edfica portuguesa \u00e0 corte dum rei indiano no s\u00e9culo XVIII,\u201d Oriente Portugu\u00eas, 19\u201321 (1938), 187\u2013202","journal-title":"Oriente Portugu\u00eas"},{"key":"5_CR49","unstructured":"F. Rodrigues, Hist\u00f3ria da Companhia de Jesus na Assist\u00eancia de Portugal, IV. i. 413\u2013418."},{"key":"5_CR50","unstructured":"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 Magn\u00e2nimo. Subs\u00eddios para uma hist\u00f3ria diplom\u00e1tica do reinado deD.Jodo V, unpublished Ph.D. dissertation, University of Lisbon (1956)."},{"key":"5_CR51","volume-title":"Marqu\u00eas de Pombal e a Companhia de Jesus. Correspond\u00eancia in\u00e9dita ao longo de 115 cartas","year":"1999","unstructured":"Ant\u00f3nio Lopes (ed.), Marqu\u00eas de Pombal e a Companhia de Jesus. Correspond\u00eancia in\u00e9dita ao longo de 115 cartas (Lisbon, 1999)."},{"key":"5_CR52","first-page":"123","volume":"1","author":"J Cortes\u00e3o","year":"1958","unstructured":"Jaime Cortes\u00e3o, \u201cA miss\u00e3o dos padres matem\u00e1ticos no Brasil,\u201d Studia, 1 (1958), 123\u2013150;","journal-title":"Studia"},{"key":"5_CR53","first-page":"596","volume":"45","author":"S Leite","year":"1947","unstructured":"Serafim Leite, \u201cDiogo Soares, S.I., matem\u00e1tico, astr\u00f3nomo e ge\u00f3grafo de Sua Majestade no Estado do Brasil (1684\u20131744),\u201d Brot\u00e9ria, 45 (1947), 596\u2013604.","journal-title":"Brot\u00e9ria"},{"key":"5_CR54","volume-title":"A astronomia em Portugal no s\u00e9culo XVIII","author":"R Carvalho de","year":"1983","unstructured":"R\u00f3mulo de Carvalho, A astronomia em Portugal no s\u00e9culo XVIII (Lisbon, 1983)."},{"key":"5_CR55","unstructured":"Mostly due to G. B. Carbone. See R\u00f3mulo de Carvalho, \u201cPortugal nos Philosophical Transactions, nos s\u00e9culos XVII e XVIII,\u201d Revista Filos\u00f3fica, 15\u201316 (1955\u201356)."}],"container-title":["Archimedes","The New Science and Jesuit Science: Seventeenth Century Perspectives"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-94-017-0361-1_5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,11]],"date-time":"2019-05-11T07:16:23Z","timestamp":1557558983000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-94-017-0361-1_5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003]]},"ISBN":["9789048161157","9789401703611"],"references-count":55,"URL":"https:\/\/doi.org\/10.1007\/978-94-017-0361-1_5","relation":{},"ISSN":["1385-0180"],"issn-type":[{"value":"1385-0180","type":"print"}],"subject":[],"published":{"date-parts":[[2003]]}}}