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An analysis of the Tabulae magistrales by Giovanni Bianchini

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Abstract

Bianchini called Tabulae magistrales a set of eight tables he compiled to solve problems in spherical astronomy. This set, which is the object of this paper, consists of auxiliary and trigonometric functions, including the sine and the tangent functions, for radii 10,000 and 60,000, and seems to be the first set of tables in Latin specifically devoted to mathematical tools for computational astronomy. Bianchini presented some of his tables in decimal form, which meant that for the first time one of the oldest astronomical tradition, the sexagesimal base (\(R = 60\)), was abandoned.

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Notes

  1. See Chabás and Goldstein (2009). For additional biographical information on Bianchini, see Federici Vescovini (1968).

  2. In a letter dated 1456 to Johann Nihil, court astrologer to Emperor Frederick III, Peurbach described the calculation of ephemerides he had computed together with Regiomontanus, for which they used Bianchini’s tables. While in Vienna in 1460 Regiomontanus made a copy of these tables for his own use and wrote abridged canons to them entitled, Canones breviati in tabulas Ioannis de Blanchinis. On Peurbach and Regiomontanus, see Swerdlow (forthcoming).

  3. On the trigonometrical tables of Bianchini, see Rosińska (1981). For a list of Bianchini’s various sets of tables extant in Cracow, see Rosińska (1984).

  4. This term refers to the outermost celestial sphere, responsible for diurnal rotation, and can be translated literally as “first movable.” The term was also used by John of Lignères and Regiomontanus, and eventually became standard, to characterize tables for spherical astronomy, most of which concern the diurnal rotation.

  5. See Magrini (1917), especially Letter II, pp. 24 and XIV. See also Gerl (1989).

  6. The two numbers sought are 13/5 and 13/8.

  7. See Jensen (1972), King (2004).

  8. See Chabás and Goldstein (2012).

  9. For another example, see Levi ben Gerson’s table of declination which is based on the same parameter used by Abraham Ibn Ezra, but the entries in their respective tables are all different: Goldstein (1974, p. 96).

  10. See, e.g., Chabás and Goldstein (2012) (ref. 7), p. 30.

  11. Excerpts of Tables 4 and 5 were published by Rosińska (1981) (ref. 3), pp. 49–50.

  12. See, for instance, Rosińska (1980) and Rosen (1975), especially p. 350.

References

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Authors and Affiliations

  1. Universitat Pompeu Fabra, Barcelona, Spain

    José Chabás

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  1. José Chabás
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Correspondence to José Chabás.

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Communicated by: Noel Swerdlow.

A preliminary version of this paper was presented in a workshop held in Paris (SYRTE-Observatoire de Paris) in June 2015, “Analysing and editing numerical tables from ancient astral sciences.” I thank all participants for their comments and suggestions. I am also grateful to Bernard R. Goldstein (Pittsburgh) for his helpful remarks on a draft of this paper.

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Chabás, J. An analysis of the Tabulae magistrales by Giovanni Bianchini. Arch. Hist. Exact Sci. 70, 543–552 (2016). https://doi.org/10.1007/s00407-016-0178-z

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