Skip to main navigation menu Skip to main content Skip to site footer
Galilæana. Studies in Renaissance and Early Modern Science

Text and Documents

Vol. 21 No. 2 (2024)

The Olympic Competition of Thomas Digges: The measurement of parallax and the development of observational methods in astronomy

DOI
https://doi.org/10.57617/gal-43
Submitted
6 February 2024
Published
2024-10-29

Abstract

A few months after the appearance of the supernova SN1572, Thomas Digges wrote a Latin book entitled Alae seu Scalae Mathematicae… in which he presented new methods for measuring small parallax angles like those expected for planets and other objects at similar distances. On the basis of our new translation into English of some sections of this book, we point out several relevant innovations developed by Digges. These concern the accuracy of astronomical measurements and a discussion on the origin of observational and computational errors. Furthermore, Digges introduced a simple but effective method for the falsification of observational results, which was useful for disproving some incorrect claims reported by other observers. It is also clear that Digges is completely disinterested in the astrological implications of this unexpected celestial phenomenon.

References

  1. Bakker, Arthur, Gravemeijer, Koeno. “An Historical Phenomenology of Mean and Median”. Educational Studies in Mathematics 62, 2 (2006), 149-168.
  2. Boas Hall, Marie. The Scientific Renaissance 1450-1630. New York: Dover, 1962.
  3. Brahe, Tycho. De Nova stella…. In Tychonis Brahe Dani Scripta Astronomica, edited by John L.E. Dreyer, vol. 1, Hauniae in Libraria Gyldendaliana, 1573.
  4. Brahe, Tycho. Astronomiae Instaurate Progymnasmata…. In Tychonis Brahe Dani Scripta Astronomica, edited by John L.E. Dreyer, vol. 2, Hauniae in Libraria Gyldendaliana, 1602.
  5. Buchwald, Jed Z. “Discrepant measurements and experimental knowledge in the early modern era”. Archive for History of Exact Sciences 60, 6 (2006), 565-649.
  6. Cajori, Florian. A history of mathematical notations [1928, 1929]. New York: Dover, 1993.
  7. Chapman, Allan. “The accuracy of angular measuring instruments used in astronomy between 1500 and 1850”. Journal for History of Astronomy 14, 2 (1983), 133-137.
  8. Christianson, John R. “Tycho Brahe’s Earliest Instruments”. Nordic Journal of Renaissance Studies 12 (2017), 131-144.
  9. Dee, John. Parallaticae Commentationis Praxeosque Nucleus quidam. London: John Day, 1573.
  10. Digges, Leonard, Thomas Digges. Pantometria. London: Henrie Bynneman, 1571.
  11. Digges, Leonard, Thomas Digges. Stratioticos. London: Henrie Bynneman, 1579.
  12. Digges, Thomas. Alae seu Scalae Mathematicae….London: Thomas Marsh, 1573.
  13. Digges, Thomas. A perfit description of the caelestiall orbes. In A Prognostication Euerlastinge of Right Good Effecte …. Published by Leonard Digges … Corrected and Augmented by Thomas Digges his Sonne. London: Thomas Marsh, 1576.
  14. Gilbert, William. De Mundo Nostro Sublunari Philosophia Nova. Amsterdam: Apud Ludovicum Elzevirium, 1651.
  15. Goldstein, Bernard R. “Levi ben Gerson: On Instrumental Errors and the Transversal Scale”. Journal for the History of Astronomy 8, 2 (1977), 102-112.
  16. Goulding, Robert. “Wings (or Stairs) to the Heavens, The Parallactic Treatises of John Dee and Thomas Digges”. In John Dee: Interdisciplinary Studies in English Renaissance Thought, edited by Stephen Clucas, 41-64. Dordrecht: Springer, 2006.
  17. Granada, Miguel A. “Bruno, Digges, Palingenio: omogeneitá ed eterogeneitá nella concezione dell’universo infinito”. Rivista di storia della filosofia 47 (1992), 47-73.
  18. Granada, Miguel A. “Thomas Digges, Giordano Bruno y el desarollo del copernicanismo en Inglaterra”. Éndoxa: Series Filosóficas, (1994), Madrid: UNED, 7-42. doi: 10.5944/endoxa.4.1994.4817.
  19. Green, Daniel W. E. Assessment of early-modern observations of comets and supernovae: Focus on pre-telescopic European astrometric and physical data., Durham theses, Durham University, 2004. Available at Durham E-Theses Online: http://etheses.dur.ac.uk/3053/.
  20. Håkansson, Håkan. “Tycho the Apocalyptic: History, Prophecy and the Meaning of Natural Phenomena”. In Science in Contact at the Beginning of the Scientific Revolution, edited by Jitka Zamrzlová, 211-236, Prag: National Technical Museum, 2004.
  21. Helfricht, Jürgen. Astronomiegeschichte Dresdens. Dresden: Hellerau, 2001.
  22. Johnson, Francis R. “The influence of Thomas Digges on the progress of modern astronomy in Sixteenth-Century England”. Osiris 1 (1936), 390-410.
  23. Johnson, Francis R. Astronomical Thought in Renaissance England: A Study of English Scientific Writings from 1500 to 1645. Baltimore: The Johns Hopkins Press, 1937. Reprinted New York: Octagon Books, 1968.
  24. Johnston, Stephen A. “Making Mathematical Practice: Gentlemen, practitioners and artisans in Elizabethan England”- PhD diss. Cambridge University, St John’s College, 1994. https://doi.org/10.17863/CAM.19773.
  25. Koyré, Alexandre. From the Closed World to the Infinite Universe. Baltimore: Johns Hopkins Press, 1957.
  26. Krisciunas, Kevin. “Observatories”. arXiv:astro-ph/9902030 (1999).
  27. Lerner, Michel-Pierre. “The Origin and Meaning of “World System”. Journal for the History of Astronomy 36 (2005), 407-441.
  28. Marcellus Palingenius Stellatus. Zodiacus Vitae. Lyon: Jean de Tournes, 1503.
  29. Margetts, Andrew, Giles Dowkes, Damian Goodburn, et al. “What “incomparable Jewells Havens, and sure harbours are”: the remains of late 16th century Dover harbour and their wider significance”. Post-Medieval Archaeology 57 (2023), 177-198. doi: 10.1080/00794236.2023.2166442.
  30. Mosley, Adam. “Paul Wittich”. In Hockey, T., et al., The Biographical Encyclopedia of Astronomers, 1234-1235. New York: Springer, 2007. https://doi.org/10.1007/978-0-387-30400-7_1493.
  31. Palingenius: see Marcellus Palingenius Stellatus.
  32. Plackett, Robin L. “The principle of the arithmetic mean”. Biometrika 45, 1/2 (1958), 130-135.
  33. Roche, John J. “The Radius Astronomicus in England”. Annals of Science 38, 1 (1981), 1-32.
  34. Rogers, Leo. “Leonard and Thomas Digges: 16th Century Mathematical Practitioners”. Oral Presentation, University of Oxford, 669-678, 2004. https://hal.science/hal-01349243.
  35. Rudavsky, Tamar M. “Gersonides: Levi ben Gerson”. In Hockey, T., et al. Biographical Encyclopedia of Astronomers. Springer, New York, NY, 2014. https://doi.org/10.1007/978-1-4419-9917-7_512.
  36. Sanford, Vera. “La Disme of Simon Stevin ‒ The first Book on Decimals”. The Mathematical Teacher 14, 6 (1921), 321-333.
  37. Sheynin, Oscar. “The treatment of observation in early astronomy”. Archive for History of Exact Sciences 46, 2 (1993), 153-192.
  38. Taylor, Eva G.R. Mathematical Practitioners of Tudor and Stuart England. Cambridge: University Press, 1954.
  39. Usher, Peter D., Massaro, Enrico. “The sixteenth-century empirical disproof of Ptolemaic geocentrism”. Journal of Astronomical History and Heritage 26, 3 (2023), 659-666.
  40. Usher, Peter D., Massaro, Enrico. “The sixteenth-century empirical disproof of Ptolemaic geocentrism: Paper II”. Journal of Astronomical History and Heritage 27, 1 (2024), 63-72.
  41. Wallace, William A. Prelude to Galileo. Boston Studies in the Philosophy of Science, vol. 62, Dordrecht: D. Reidel Publishing Company, 1981.