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Lectures and Practices. The Variety of Mathematical and Mechanical Teaching at the University of Uppsala in the 17th Century

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  1. For an overview of 17th-century universities see J. Gascoigne, “A Reappraisal of the Role of the Universities in the Scientific Revolution”, in D. C. Lindberg and R. S. Westman (eds.), Reappraisals of the Scientific Revolution (Cambridge: Cambridge University Press, 1990). R. Tuck, “The Institutional Setting”, in D. Garber and M. Ayers (eds.), The Cambridge History of Seventeenth-Century Philosophy, Vol. I (Cambridge: Cambridge University Press, 1998), pp. 14–23.

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  2. M. Feingold, The Mathematicians’ Apprenticeship: Science, Universities and Society in England 1560–1640, passim. M. Feingold, “The Mathematical Sciences and New Philosophies”, in N. Tyacke (ed.), The History of the University of Oxford, Vol. IV (Oxford: Clarendon Press, 1997), pp. 363–369; L. W. B. Brockliss, French Higher Education in the Seventeenth and Eighteenth Centuries (Oxford: Clarendon Press, 1987), pp. 381–382; Gascoigne, 221–224.

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  3. S. Lindroth, Svensk Lärdomshistoria: Frihetstiden (Stockholm: Norstedts 1978, reprint Södertälje: Fingraf Tryckeri, 1989), pp. 48–66, 297–413.

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  4. S. Lindroth, Svensk Lärdomshistoria: Medeltiden, Reformationstiden (Stockholm: Norstedts, 1975, reprint Södertälje: Fingraf Tryckeri, 1989), pp. 127, 137, 340–346; S. Lindroth, Uppsala Universitet 1477–1977 (Uppsala: Almqvist & Wiksell, 1976), pp. 41–44.

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  5. Statutes for the University of Uppsala 1626, in C. Annerstedt, Upsala Universitets Historia: Bihang I: Handlingar, 1477–1654 (Upsala: W. Schultz, 1877), p. 277; Principio vult S.R.M: tas Mathematicam professionem, non qvod vulgus professorum existimat esse Arithmeticam quamcumque vulgarem et Geometriam Practicam cum sphaerula sex maiorum, quatuor minorum peripheriarum sed ad mathematicam cathedram bene beateque illustrandam opus esse Euclide, Archimede, Ptolemaeo, Copernico, Diophanto, Nicomacho, Jordano, Apollonio, Sereno, Theodosio Menelao, Eutochio, Pappo, Proclo, Theone, Herone, Regiomontano, Ramo, Schonero et id genus alijs authoribus probatissimis.

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  6. Statutes 1626, in Annerstedt, Bihang I, 277–278. I have not been able to identify the suggested “Itabius”. It probably is a misprint for J. Stabius, an Austrian Cosmographer from the early 16th century. The authority for music is Freigius, and Frederic Reisner is recommended for optics. See also S. Lindroth, Svensk lärdomshistoria: Stormaktstiden (Stockholm: Norsteds, 1975, reprint Södertälje: Fingraf Tryckeri, 1989), pp. 468–469.

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  7. Praelectiones publicae Upsaliensi (Uppsala, 1636–1700). On Nycopensis see the years 1636, 1639, and 1645.

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  8. A report by the Clergy on how the University should be organised 10.9.1617, in Annerstedt, Bihang I, 141–143.

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  9. Lindroth, Uppsala Universitet, 41; I. Mäntylä, “Suurvaltakausi”, in S. Zetterberg (ed.), Suomen historian pikkujättiläinen (Porvoo: WSOY, 1997), pp. 185–186.

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  10. Statutes 1626, in Annerstedt, Bihang I, 278: Praestat vero accommodare praecepta mathematica ad civilem usum in agrorum dimensione altitudinis, profunditatis, latitudinis, aedificiorum, montium, fossarum, camporum, castrorum, fluminum; ad usum judicum in divisione bonorum, architectonicae et militaris disciplinae; mercatorum quoque in navigationibus, in locorum distantiis et supputationibus rationum, qualis hodie in S.R.M:tis Camera in usu sunt.

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  11. Meeting of the Senate of the University and the Chancellor on 26.–28.5.1627, in Uppsala Universitet: Akademiska konsistoriets protokoll I, 1624–1636, Acta Universitatis Upsaliensis, Skrifter rörande Uppsala universitet C. Organisation och historia 18:1, H. Sallander (ed.), (Uppsala, 1968), pp. 15–16.

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  12. Gascoigne, The role of the universities, 221–222. On the Melanchthonian educational programme see also S. Kusukawa, The Transformation of Natural Philosophy: The case of Philip Melanchthon (Cambridge: Cambridge University Press, 1995), passim.

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  13. P. Ramus, Scholarum mathematicarum libri unus et triginta (Francofurti: Andreas Wecheli heredes, 1599), Liber II.

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  14. L. Schonerus, “Praefatio”, in P. Ramus (ed.), Arithmeticae libri duo: Geometriae septem et viginti (Francofurti, Andreae Wecheli heredes, 1599), br-v. Statutes 1626, in Annerstedt, Bihang I, p. 280.

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  15. J. Schroderus, Dissertatio Mathematica de Mechanicae Artis praestantia, nobilitate, emolumentis ac fundamentis, adversus Aristippos & Epicureos philosophastros (Lemgoviae, 1598) Skytte was called Schroderus before rising to nobility. See also Chesnecopherus’ congratulations to J.S., Ibidem, E3.

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  16. Brockliss, French Higher Education, p. 382. Gascoigne, The role of universities, p. 233.

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  17. An outline for the Statutes of the University of Uppsala written by Johan Skytte 1625, in Annerstedt, Bihang I, pp. 166–167.

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  18. Meeting of the Senate of the University 26.–28.5.1627. Akademiska protokoll I, p. 17.

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  19. M. Kallinen, Change and Stability: Natural philosophy at the Academy of Turku, 1640–1713 (Helsinki: Hakapaino, 1995), p. 67.

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  21. Queen Christina’s letter to the University of Uppsala 8.11.1651, in Annerstedt, Bihang I, p. 398.

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  23. J. H. Lidén, Catalogus disputationum in Academiis et Gymnasiis Sveciae (Upsala: Edman, 1778). On Bilberg, 67–73, Bureus, 88, Magnus Celsius, 93–94, Fontelius, 188–190, Fornelius, 194, Gestrinius, 207–210, Nycopensis, 371–373, Stenius, 441–442, Spole, 433–436, and Vallerius, 499–505.

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  25. The oldest surviving lecture announcement of the University of Uppsala 20.11.1636, in Annerstedt, Bihang I, p. 329. Praelectiones publicae Upsaliensi, 1639–1659.

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  26. Praelectiones publicae Upsaliensi, 1660–1700. Elenchus Praelectionum publicarum (Aboae 1659, 1665, 1667, 1673, 1688–1690, 1692). Two textbooks in chronology appeared in Uppsala at the end of the 17th century. Nils Celsius, Computus Ecclesiasticus (Upsala, 1688). Anders Spole, Computus Ecclesiasticus, Multoties postquam Praelectus publice, ad Multorum desideria typis exscriptus (Upsaliae, 1692).

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  27. Annerstedt, Bihang I, pp. 294, 341.

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  28. Lindroth, Stormaktstiden, pp. 472–473.

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  29. This term was used in the Praelectiones publicae Upsaliensi 1651.

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  30. B. Hedraeus, Nova et Accurata Astrolabii Geometrici Structura... nec non Quadrantis Astronomici Azimuthalis, Quo non solum prima, sed & singula minuta secunda distincté observari possunt. Una cum Utriusque usu, Claris & Perspicuis exemplis illustratio (Lugduni Batavorum: W.C. Boxius, 1643). In addition to this publication Hedraeus has left behind a manuscript De triangulis planis, Uppsala University Library manuscript A501.

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  31. Hedraeus, Nova Astrolabii Structura, “Ad Lectorem”: Ne dicat quispiam cum Platone Ideas me delineasse, expertum subindicabo Artificem, qui ad divisionem hanc meam accuratummihi confecit Astrolabium; Ultrajaceti est J Snee Wins, qui experientiâ in aliis instrumentis Mathem. fabricandis summè laudandâ, & in hoc, cujus hîc descriptionem exhibeo, industriâ singulari. See also E. Zinner, Deutsche und Niederländische Astronomische Instrumente des 11.–18. Jahrhunderts (Munich: C.H.Beck’sche Verlagsbucchandlung, 1956), pp. 224, 537.

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  32. A. Losman, “Hedraeus, Benedictus Christierni”, Svenskt Biografiskt Lexikon, Band 18 (Stockholm: Kungliga Boktryckeriet P.A. Nordstedt & Söner, 1971), pp. 501–502.

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  33. Meetings of the Senate of the University, 18.7.1660, 16.1.1661, in Akademiska protokoll V, 1656–1660 (Uppsala, 1970), pp. 240–241 and Akademiska protokoll VI, 1661–1663 (Uppsala, 1971), p. 15. Nordenmark, Astronomins historia, p. 47.

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  34. Meetings of the Senate of the University, 17.1.1661, 6.9.1671, in Akademiska protokoll VI, 21–22. Akademiska protokoll IX, 1671–1672, (Uppsala, 1972), 141. The latter meeting suggests that one Olof Erson should get the salary which was earlier paid to Johannes Hoffwenius. See also Nordenmark, Astronomins historia, 47–48.

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  35. Lindroth, Stormaktstiden, 473. Praelectiones publicae Upsaliensi, 1671.

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  36. Meetings of the Senate of the Academy 16.2.1667, 20.4.1672, 12.3.1673, 26.10.1673, 5.11.1673, 28.3.1677, 18.11.1677, Akademiska protokoll VIII, 23. Akademiska protokoll IX, 245. Akademiska protokoll X, 1673 (Uppsala, 1972), 62, 215, 223. Akademiska protokoll XI, 1674–1675 (Uppsala, 1973), pp. 278, 362.

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  37. This chapter is indebted to Per Dahl’s and Sten Lindroth’s studies on Rudbeck. Per Dahl, Svensk ingenjörskonst under stormaktstiden: Olof Rudbecks tekniska undervisning och prak-tiska verksamhet (Uppsala: TK-tryck, 1995). Lindroth, Stormaktstiden, pp. 284–305, 413–446.

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  38. Herdin, Olof Rudbecks födelse och ungdom, 14. Rudbeck’s letter to the committee of in-spection on the economic state of the University 1.3.1685, in Bref af Olof Rudbeck d.ä.rörande Upsala universitet III, C. Annerstedt (ed.), Upsala universitets årsskrift 1905, 215. “I did never get the 30 ducats which had been promised for me for designing the Botanical Garden, nor the 750 thalers for being a master builder, although I had to make the capitals and plane the laths for the greenhouses with my own hands, because there was no carpenter available”.

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  39. Dahl, Svensk ingenjöorskonst, 169, 178. Rudbeck, who campaigned for fire protection for the University, nevertheless kept his own library, correspondence and other collections in the wooden part of his residence, not in the more fireproof stone buildings.

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  40. A. Spole, Hans självbiografiska anteckningar, in P. Wilstadius (ed.), Småländska hem-bygdsböcker XII (Tidaholm: Tidaholms tryckeri aktiebolag, 1946), pp. 13–17. Praelectiones publicae Upsaliensi 1661–1700. Lindroth, Stormaktstiden, pp. 501–506.

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  48. Ibid., pp. 169–170.

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  1. University of Oulu, Oulu

    Maija Kallinen (professor of history of science)

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  1. California Institute of Technology, USA

    Mordechai Feingold

  2. University of Valencia — CSIC, Spain

    Victor Navarro-Brotons

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Kallinen, M. (2006). Lectures and Practices. The Variety of Mathematical and Mechanical Teaching at the University of Uppsala in the 17th Century. In: Feingold, M., Navarro-Brotons, V. (eds) Universities and Science in the Early Modern Period. Archimedes, vol 12. Springer, Dordrecht . https://doi.org/10.1007/1-4020-3975-1_8

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