Book Chapter

Galileo’s Mathematical Errors

  • Viktor Blåsjö

Galileo’s abilities as a mathematician were far below that of many of his contemporaries. He made numerous technical mistakes — including several high-profile, mathematically erroneous applications of his own law of fall — that were swiftly spotted and corrected by the leading mathematicians of the day. Many aspects of Galileo’s work can be viewed as consequences of this limited technical proficiency in mathematics. For example, he ignores Kepler’s work and dismisses comets as a chimerical atmospheric phenomena: decisions that are difficult to justify on scientific grounds but which make sense if we grant that Galileo wanted to avoid technical mathematics at all costs. Instead he drops rocks, looks through tubes, rails against Aristotelian philosophers, and expounds at length about basic principles of scientific method: all of which can be seen as dwelling on precisely those parts of the mathematician’s worldview that do not require any actual mathematics.

  • Keywords:
  • Galileo; cycloidal area; orbital speeds; extrusion by terrestrial whirling; atmospheric theory of comets,
+ Show More

Viktor Blåsjö

Utrecht University, Netherlands - ORCID: 0000-0001-8494-4567

  1. OGG: Le Opere di Galileo Galilei, Antonio Favaro (ed.), 20 volumes, Florence, 1890–1909, later reprinted with additions.
  2. Bertoloni Meli Domenico. 2006. Thinking with Objects: The Transformation of Mechanics in the Seventeenth Century. Baltimore, MA: Johns Hopkins University Press.
  3. Buchwald, Jed Z. & Robert Fox (eds.). 2013. The Oxford Handbook of the History of Physics,.. Oxford; Oxford University Press.
  4. Bukowski, John. 2008. “Christiaan Huygens and the Problem of the Hanging Chain.’ College Mathematics Journal 39/1: 2–11.
  5. Chalmers, Alan & Richard Nicholas. 1983. “Galileo on the Dissipative effect of a Rotating Earth.” Studies in History and Philosophy of Science Part A, 14/4: 315–340.
  6. Costabel, Pierre & Michel Pierre Lerner (eds.). 1973. “Introduction.” In Les nouvelles pensées de Galilée, 2 vols., Paris; J. Vrin.
  7. Damerow, Peter, Gideon Freudenthal, Peter McLaughlin, & Jürgen Renn. 2004. Exploring the Limits of Preclassical Mechanics: A Study of Conceptual Development in Early Modern Science: Free Fall and Compounded Motion in the Work of Descartes, Galileo, and Be
  8. Drake, Stillman & C. D. O’Malley. 1960. The Controversy on the Comets of 1618. Philadelphia: University of Pennsylvania Press.
  9. Drake, Stillman. 1964. “Galileo and the Law of Inertia.” American Journal of Physics 32/8: 601–608.
  10. Drake, Stillman. 1978. Galileo at Work. Chicago: University of Chicago Press.
  11. Drake, Stillman. 1999. Essays on Galileo and the History and Philosophy of Science. Volume 1. Selected and introduced by N. M. Swerdlow and T. H. Levere. Toronto: University of Toronto Press.
  12. Engelberg, Don & Michael Gertner. 1981. “A Marginal Note of Mersenne Concerning the Galileian Spiral.” Historia Mathematica 8/1: 1–14.
  13. Freguglia, Paolo & Mariano Giaquinta. 2016. The Early Period of the Calculus of Variations. Birkhäuser, 2016.
  14. Gaab, Hans & Pierre Leich (eds.). 2018. Simon Marius and His Research. Berlin: Springer.
  15. Galilei, Galileo. 1953. Dialogue Concerning the Two Chief World Systems, translated by Stillman Drake. Berkeley: University of California Press.
  16. Galilei, Galileo. 1957. Discoveries and Opinions of Galileo, translated with an introduction and notes by Stillman Drake. New York: Anchor Books.
  17. Galilei, Galileo. 1974. Two New Sciences, translated by Stillman Drake. Madison, WI: University of Wisconsin Press.
  18. Galilei, Galileo. 1989. Two New Sciences, translated by Stillman Drake, second edition, Wall & Emerson. Toronto, University of Toronto Press.
  19. Galilei, Galileo. 2001. Dialogue Concerning the Two Chief World Systems, translated by Stillman Drake. New York: Modern Library.
  20. Hall, A. Rupert. 1952. Ballistics in the Seventeenth Century. Cambridge: Cambridge University Press.
  21. Little Heath, Thomas (ed.). 2002. The Works of Archimedes. Mineola, NY: Dover Publications.
  22. Heilbron, J. L. 2010. Galileo. Oxford: Oxford University Press.
  23. Hill David K. 1984. “The Projection Argument in Galileo and Copernicus: Rhetorical Strategy in the Defence of the New System.” Annals of Science 41/2: 109–133.
  24. Jardine, Nicholas. 1984. The Birth of History and Philosophy of Science: Kepler’s A Defence of Tycho against Ursus with Essays on its Provenance and Significance. Cambridge: Cambridge University Press.
  25. Jullien, Vincent (ed.). 2015. Seventeenth-Century Indivisibles Revisited. Birkhäuser.
  26. Kline, Morris. 1972. Mathematical Thought from Ancient to Modern Times. Oxford: Oxford University Press.
  27. Koyré, Alexandre. 1955. “A Documentary History of the Problem of Fall from Kepler to Newton.” Transactions of the American Philosophical Society 45/4: 329–395.
  28. Koyré, Alexandre. 1978. Galileo Studies, translated by John Mepham. Hassocks: Harvester Press. [First published as Etudes Galiléennes, 1939].
  29. Magruder, Kerry V. 2009. “Jesuit Science After Galileo: The Cosmology of Gabriele Beati.” Centaurus 51/3: 189–212.
  30. Montesinos, José & Carlos Solis (eds.). 2001. Largo campo di filosofare: Eurosymposium Galileo 2001. La Orotava: Fundación Canaria Orotava de Historia de la Ciencia.
  31. Newton, Isaac. 1999. The Principia: Mathematical Principles of Natural Philosophy, translated by I. Bernard Cohen and Anne Whitman, preceded by “A guide to Newton’s Principia” by I. Bernard Cohen. Berkeley: University of California Press.
  32. Palmerino, Carla Rita & J.M.M.H. Thijssen (eds.). 2004. The Reception of the Galilean Science of Motion in Seventeenth-Century Europe. Berlin: Springer.
  33. Pasachoff, Jay M. 2015. “Simon Marius’s Mundus Iovialis: 400th Anniversary in Galileo’s Shadow.” Journal for the History of Astronomy 46/2: 218–234.
  34. Poupard, Paul C. (ed.) 1987. Galileo Galilei: Toward a Resolution of 350 Years of Debate. Pittsburg, PA: Duquesne University Press.
  35. Renn, Jürgen, Peter Damerow, & Simone Rieger. 2001. “Hunting the White Elephant: When and How did Galileo discover the law of fall?” In Jürgen Renn (ed.), Galileo in Context, 29-149. Cambridge: Cambridge University Press.
  36. de Santillana, Giorgio. 1955. The Crime of Galileo. Chicago: University of Chicago Press.
  37. Schemmel, Matthias. 2008. The English Galileo: Thomas Harriot’s Work on Motion as an Example of Preclassical Mechanics, Volume 1: Interpretation. Berlin: Springer.
  38. Schemmel, Matthias. 2012. “Thomas Harriot as an English Galileo: The Force of Shared Knowledge in Early Modern Mechanics.” In Robert Fox (ed.), Thomas Harriot and His World: Mathematics, Exploration, and Natural Philosophy on Early Modern England, 89-112.
  39. Shea, William. R. 1972. Galileo’s Intellectual Revolution. London: Macmillan.
  40. Shea, William R. 2009. Galileo’s Sidereus Nuncius or A Sidereal Message. Translated from the Latin by William R. Shea. Introduction and notes by William R. Shea and Tiziana Bascelli. Sagmore Beach MA: Science History Publications.
  41. Struik, Dirk Jan. 1969. A Source Book in Mathematics, 1200-1800. Cambridge, MA: Harvard University Press.
  42. Truesdell, Clifford. 1960. The rational mechanics of flexible or elastic bodies 1638–1788. In Leonhardi Euleri Opera Omnia, Series II, Volume XI, Part 2. Zürich: Füssli.
  43. Whitman, E. A. 1943. “Some Historical Notes on the Cycloid.” American Mathematical Monthly 50/5: 309–315.
  44. Wootton, David 2010. Galileo: Watcher of the Skies. New Haven: Yale University Press.
PDF
  • Publication Year: 2023
  • Pages: 87-103
  • Content License: CC BY 4.0
  • © 2023 Author(s)

XML
  • Publication Year: 2023
  • Content License: CC BY 4.0
  • © 2023 Author(s)

Chapter Information

Chapter Title

Galileo’s Mathematical Errors

Authors

Viktor Blåsjö

Language

Italian

DOI

10.36253/979-12-215-0266-4.07

Peer Reviewed

Publication Year

2023

Copyright Information

© 2023 Author(s)

Content License

CC BY 4.0

Metadata License

CC0 1.0

Bibliographic Information

Book Title

Errors, False Opinions and Defective Knowledge in Early Modern Europe

Authors

Marco Faini, Marco Sgarbi

Peer Reviewed

Number of Pages

145

Publication Year

2023

Copyright Information

© 2023 Author(s)

Content License

CC BY 4.0

Metadata License

CC0 1.0

Publisher Name

Firenze University Press

DOI

10.36253/979-12-215-0266-4

ISBN Print

979-12-215-0265-7

eISBN (pdf)

979-12-215-0266-4

eISBN (epub)

979-12-215-0267-1

Series Title

Knowledge and its Histories

184

Fulltext
downloads

741

Views

Export Citation

1,321

Open Access Books

in the Catalogue

2,008

Book Chapters

3,463,393

Fulltext
downloads

4,203

Authors

from 876 Research Institutions

of 64 Nations

64

scientific boards

from 343 Research Institutions

of 43 Nations

1,216

Referees

from 363 Research Institutions

of 38 Nations