The Mathematical Intelligencer

, Volume 26, Issue 3, pp 32–42 | Cite as

Completing Book II of Archimedes’s On Floating Bodies



One need only glance at Archimedes’s Proposition 8 above to see thatOn Floating Bodies is several orders of magnitude more sophisticated than anything else found in ancient mathematics. It ranks with Newton’sPrincipia Mathematica as a work in which basic physical laws are both formulated and accompanied by superb applications.


Relative Density Tilt Angle Asymptotically Stable Mathematical Intelligencer Pitchfork Bifurcation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    D. M. Arrowsmith and C. M. Place,An Introduction to Dynamical Systems, Cambridge University Press, Cambridge, 1990, p. 79.MATHGoogle Scholar
  2. 2.
    R. C. Bailey, “Implications of iceberg dynamics for iceberg stability estimation,”Cold Regions Science and Technology 22 (1994), 197–203.CrossRefGoogle Scholar
  3. 3.
    D. W. Bass, “Stability of icebergs,”Annals of Glaciology 1 (1980), 43–47.Google Scholar
  4. 4.
    M. Clagett, “The impact of Archimedes on medieval science,”Isis 50 (1959), 419–429.CrossRefMATHGoogle Scholar
  5. 5.
    M. Clagett,Archimedes in the Middle Ages, Volume I, The Arabo-Latin Tradition, The University of Wisconsin Press, Madison, 1964, pp. 3–8.Google Scholar
  6. 6.
    M. Clagett,Biographical Dictionary of Mathematicians, (article on Archimedes) Charles Scribner’s Sons, New York, 1991, Vol. 1, p. 95.Google Scholar
  7. 7.
    R. Delbourgo, “The floating plank,”American Journal of Physics 55 (1987), 799–802.CrossRefGoogle Scholar
  8. 8.
    E. J. Dijksterhuis,Archimedes, (In Dutch: Chapters I-V, I. P. Noordhoff, Groningen, 1938: Chapters VI-XV,Euclides, VX-XVII, 1938-44). English translation by C. Dikshoom, Princeton University Press, NJ, 1987.MATHGoogle Scholar
  9. 9.
    B. R. Duffy, “A bifurcation problem in hydrostatics,”American Journal of Physics 61 (1993), 264–269.CrossRefGoogle Scholar
  10. 10.
    P. Erdős, G. Schibler, and R. C. Herndon, “Floating equilibrium of symmetrical objects and the breaking of symmetry. Part 1: Prisms,”American Journal of Physics 60 (1992), 335–345.CrossRefGoogle Scholar
  11. 11.
    P. Erdős, G. Schibler, and R. C. Herndon, “Floating equilibrium of symmetrical objects and the breaking of symmetry. Part 2: The cube, the octahedron, and the tetrahedron,”American Journal of Physics 60 (1992), 345–356.CrossRefGoogle Scholar
  12. 12.
    E. N. Gilbert, “How things float,”The American Mathematical Monthly 98 (1991), 201–216.CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    J. Hale and H. Koçak,Dynamics and Bifurcations, Springer-Verlag, New York, 1991, p. 19.CrossRefMATHGoogle Scholar
  14. 14.
    T. L. Heath,The Works of Archimedes, Dover Publications, New York, 2002. Unabridged republication ofThe Works of Archimedes (1897) andThe Method of Archimedes (1912), both published by The Cambridge University Press.Google Scholar
  15. 15.
    T. L. Heath,A History of Greek Mathematics, Dover Publications, New York, 1981, Vol. II, p. 95; Unabridged republication from Clarendon Press, Oxford, 1921.Google Scholar
  16. 16.
    J. L. Heiberg,Archimedis Opera Omnia, with corrections by E. S. Stamatis, B. G. Teubner, Stuttgart, 1972.Google Scholar
  17. 17.
    C. W. Keyes,Cicero: De Re Publica, Book I, Section 22, Loeb Classical Library, Harvard University Press, Cambridge, 1928.Google Scholar
  18. 18.
    H. Nowacki,Archimedes and Ship Stability, Max Planck Institute for the History of Science, Berlin, 2002.Google Scholar
  19. 19.
    H. Nowacki and L. D. Ferreiro,Historical Roots of the Theory of Hydrostatic Stability of Ships, Max Planck Institute for the History of Science, Berlin, 2003.Google Scholar
  20. 20.
    J. F. Nye and J. R. Potter, “The use of catastrophe theory to analyze the stability and toppling of icebergs,”Annals of Glaciology 1 (1980), 49–54.Google Scholar
  21. 21.
    J. Verne,20,000 Leagues Under the Sea, (translated by M. T. Brunetti), Penguin Putnam Inc., New York, 1969, p. 368.Google Scholar
  22. 22.
    E. S. Stamatis,The Complete Archimedes, (In Greek: E. Σ ΣTA-MATHΣ, AΠXIMH▵OEΣ AΠANTA) Volume B′, Athens, 1973.Google Scholar
  23. 23.
    S. Stein, “Archimedes and his Floating Paraboloids,” inMathematical Adventures for Students and Amateurs, Mathematical Association of America, Washington, D.C., 2004.Google Scholar
  24. 24.
    H. C. Williams, R. A. German, and C. R. Zarnke, “Solution of the Cattle Problem of Archimedes,”Mathematics of Computation 19 (1965), 671–674.CrossRefMATHGoogle Scholar
  25. 25.
    N. Wilson,The Archimedes Palimpsest, Christie’s Auction Catalog, New York, 1998.Google Scholar

Copyright information

© Springer-Verlag New York, LLC 2004

Authors and Affiliations

  1. 1.New Bolton CenterUniversity of PennsylvaniaKennett SquareUSA

Personalised recommendations