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Beyond Stevin and Galileo: Seventeenth Century Hydrostatics in the Jesuit Class of the Sphere

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The History of Water Management in the Iberian Peninsula

Part of the book series: Trends in the History of Science ((TRENDSHISTORYSCIENCE))

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Abstract

In the first half of the seventeenth-century, philosophers and mathematicians were still trying to solve important questions on hydrostatics, like the existence of vacuum, the cohesion of matter, and pressure. Mathematicians like Simon Stevin and Galileo Galilei made contributions to these problems that became standard in the field. But Jesuit mathematicians in Portugal also provided solutions, albeit different ones. For instance, the Italian Jesuit Giovanni Paolo Lembo (1570–1618) explored the existence of vacuum and the Flemish Hendrick Uwens (1618–1667) mentioned the moment of speed in fluids to explain the hydrostatic paradox in the classes that they taught in Lisbon. This paper explores these answers to illustrate specific features of the Jesuit teaching of mathematics in early modern Lisbon. As the teaching of mathematics in seventeenth-century Portugal was centred in this school, this research is a much-needed survey of the teaching of hydrostatics in the country at that time.

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Notes

  1. 1.

    For recent discussions on the current state of research into early modern Iberian Science, see Portuondo (2017). For the historical disregard of religious institutions in the history of science, especially accentuated in the case of early modern Iberia, see Giurgevich (2016: 253–256).

  2. 2.

    For Portugal, see Leitão (2003); for Spain, see Navarro (2003). The contributions of Ugo Baldini, often quoted in this article, are also important, even while harder to find in English literature.

  3. 3.

    See, for example, Leitão (2001).

  4. 4.

    For a recent account, see Chalmers (2017).

  5. 5.

    For an introduction to Clavius and his role in the history of astronomy, see Lattis (1994).

  6. 6.

    For more on early-modern mixed mathematics and the role of the Jesuits, see Dear (1995).

  7. 7.

    See, for instance, Valleriani (2014: 137).

  8. 8.

    For a complete list of all of the professors in the Class of the Sphere, the years in which they taught, and their respective discussions, see Baldini (2000: 57–66; 2004: 382–465).

  9. 9.

    A survey and brief description of most of the extant manuscripts and printed books related to the Class of the Sphere can be found in Sphaera Mundi (2008).

  10. 10.

    For an initial study of Jesuits teaching astrology and other divinatory arts in the Class of the Sphere, see Leitão (2006).

  11. 11.

    This information is in a codex in the Biblioteca Cadaval, and was mentioned in Albuquerque (1972: 16, n35).

  12. 12.

    For an outline of Costa’s class notes, see Albuquerque (1972: 25–27).

  13. 13.

    The full codex has 140 folios, 30 cm in height.

  14. 14.

    Lembo mentions Hero and Commandino for the first time when he begins addressing recipients that contain water and wine, in Chapter 22 (Lembo 1615–17: fol. 103v).

  15. 15.

    Della Porta’s relationship with the inquisition is a little bit more complex. For a recent account, see Tarrant (2013).

  16. 16.

    For a more thorough explanation, see Grant (1981: 70–74).

  17. 17.

    “por todos os elementos e mixtos estão espalhados algumas partes do vaccuo, ainda que pequenas e delgadas, põem estas partes do vaccuo nos poros dos corpos” in Lembo (1615–17: fol. 95r).

  18. 18.

    See Aristotle, Physics, Book IV, Chap. 9.

  19. 19.

    Clavius planned to write on these topics so as to include them as part of the curriculum of the Jesuit Academy of Mathematics in Rome, but ended up not doing so (Baldini 2003: 62).

  20. 20.

    See, for example, Commentariorum (1594: 61–64).

  21. 21.

    This description comes from Albuquerque (1972: 37).

  22. 22.

    Materias mathematicas nas quais se contem astronometria, astrologia e outronometria, BNP, Cod. 2127.

  23. 23.

    There are two copies in the BNP: BNP, Res. 3140; BNP, S.A. 624 A.

  24. 24.

    BNP, Cod. 4333 (henceforth referred to as “Uwens”); BPE, CXXVI/2–7.

  25. 25.

    The BPE copy is entitled “Mathematical treatise of statics.”

  26. 26.

    See, for example, the scheme of the mathematical sciences by the Jesuit Paul Guldin in Guldin (1635: 21).

  27. 27.

    This sub-subdivision is also present in Guldin’s scheme of mathematics.

  28. 28.

    “Digamos logo que a natureza para sua conservação ata entre sy as couzas de sorte que não se podem separar sem succeder outra em seu lugar; esta atadura tem os corpos solidos de sua união da mesma a tenhão tambem os liquidos a qual seja examinem os Philosophos.” In Uwens (1645: fol. 130r).

  29. 29.

    Ibidem.

  30. 30.

    Uwens departed from Flanders for Lisbon in the spring of 1641, so there had been time for him to come across Galileo’s book, or at least to discuss some of its contents with other readers. For a short account of the circulation of Galileo’s Two New Sciences, see Raphael (2017: 15–19).

  31. 31.

    “a pouca agoa EF o que perde na cantidade ganha na preça do movimento,” in Uwens (1645: fol. 132v).

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Authors and Affiliations

  1. Department of History of Science and Technology, Johns Hopkins University, Baltimore, USA

    Nuno Castel-Branco

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Correspondence to Nuno Castel-Branco .

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  1. Centro Interuniversitário de História das Ciências e Tecnologia, Faculdade de Ciências, Universidade de Lisboa, Lisboa, Portugal

    Ana Duarte Rodrigues

  2. Escuela Técnica Superior de Arquitectura, Madrid, Spain

    Carmen Toribio Marín

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Castel-Branco, N. (2020). Beyond Stevin and Galileo: Seventeenth Century Hydrostatics in the Jesuit Class of the Sphere. In: Duarte Rodrigues, A., Toribio Marín, C. (eds) The History of Water Management in the Iberian Peninsula. Trends in the History of Science. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-34061-2_16

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