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Traditional Cavalieri principles applied to the modern notion of area

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References

  • Barnard, Mark: Translation by Mark Barnard with the assistance of the author.

  • BondiH. & T.Gold: ‘The Steady-State Theory of the Expanding Universe,’ Mon. Not. R. Astron. Soc. 108 (1948), 252–270.

    Google Scholar 

  • BoyerCarl B.: A History of Mathematics, John Wiley & Sons, Inc., New York, New York, 1968.

    Google Scholar 

  • Brunner, Norbert: ‘Mathematische Intuition, Kontinuumshypothese und Auswahlaxiom’, Jahrbuch 1988 der Kurt-Gödel-Gesellschaft, 96–101.

  • Cavalieri, Francesco Bonaventura: Geometria indivisibilibus continuorum nova quadam ratione promota, Bologna, Italy, 1635, 2nd ed. 1653.

  • DaviesRoy O.: ‘Covering the Plane with Denumerably Many Curves,’ Journal of the London Mathematical Society 38 (1963) 433–438.

    Google Scholar 

  • DijksterhuisEduard Jan: Archimedes, Princeton University Press, Princeton, New Jersey, 1987. Translated by C. Dikshoorn. (Reprint of original 1956 edition.).

    Google Scholar 

  • EvesHoward: An Introduction to the History of Mathematics, 5th ed., Saunders College Publishing, Philadelphia, Pennsylvania, 1983.

    Google Scholar 

  • FreilingChris: ‘Axioms of Symmetry: Throwing Darts at the Real Number Line,’ The Journal of Symbolic Logic 51(1) (March 1986), 190–200.

    Google Scholar 

  • Freiling, Chris: personal communication.

  • GödelKurt: ‘What Is Cantor's Continuum Problem?,’ The American Mathematical Monthly 54 (November 1947), 515–525.

    Google Scholar 

  • HawkingStephen: A Brief History of Time: From the Big Bang to Black Holes, Bantam Books, New York, New York, 1988.

    Google Scholar 

  • HeathT. L.: The Method of Archimedes Recently Discovered by Heiberg, Cambridge University Press, New York, New York, 1912. Reprinted along with (Heath, 1897) by Dover.

    Google Scholar 

  • HeathT. L.: The Works of Archimedes, Cambridge University Press, New York, New York, 1897. Reprinted along with (Heath, 1912) by Dover.

    Google Scholar 

  • HewittEdwin & KarlStromberg: Real and Abstract Analysis, Springer-Verlag New York, Inc., New York, 1965.

    Google Scholar 

  • HoyleF.: ‘A New Model for the Expanding Universe,’ Mon. Not. R. Astron. Soc. 108(1948), 372–382.

    Google Scholar 

  • JechThomas: Set Theory, Academic Press, New York, 1978.

    Google Scholar 

  • Knorr, Wilbur R.: ‘Archimedes after Dijksterhuis: A Guide to Recent Studies,’ 1987. In (Dijksterhuis, 1987, pp. 419–451).

  • LamLay-Yong & ShenKangsheng: ‘The Chinese Concept of Cavalieri's Principle and Its Applications,’ Historia Mathematica 12 (1985), 219–228.

    Google Scholar 

  • MaddyPenelope: ‘Believing the Axioms. I,’ The Journal of Symbolic Logic 53 (2) (June 1988), 481–511.

    Google Scholar 

  • MisnerCharles W., Kip S.Thorne, & John ArchibaldWheeler: Gravitation, W. H. Freeman and Company, San Francisco, California, 1973.

    Google Scholar 

  • ReichenbachHans. The Theory of Probability, 2nd ed., University of California Press, Berkeley, California, 1949.

    Google Scholar 

  • RoydenH. L., Real Analysis, 2nd ed., The Macmillan Company, New York, 1968.

    Google Scholar 

  • SierpińskiWacław: Hypothèse du Continu, 2nd ed., Chelsea Publishing Company, New York, 1956.

    Google Scholar 

  • SierpińskiWacław: ‘On the Congruence of Sets and Their Equivalence by Finite Decomposition,’ in Congruence of Sets and Other Monographs, Chelsea Publishing Company, the Bronx, New York, 1954.

    Google Scholar 

  • SierpińskiWacław: Leçons sur les nombres transfinis, Gauthier-Villars, Paris, 1928.

    Google Scholar 

  • SierpińskiWacław: Leçons sur les nombres transfinis, Nouveau tirage, Collection de Monographies sur la Théorie des fonctions, publiée sous la direction de M. Émile Borel, Gauthier-Villars, Paris, 1950. Reprint of (Sierpiński, 1928).

    Google Scholar 

  • SmithDavid Eugene: History of Mathematics, Ginn and Company, Boston, 1923.

    Google Scholar 

  • WagonStan: The Banach-Tarski Paradox, Cambridge University Press, Cambridge, England, 1985.

    Google Scholar 

  • Webster's New Biographical Dictionary, Rev. ed. of Webster's Biographical Dictionary, Merriam-Webster Inc., Springfield, Massachusetts, 1983.

  • WillardStephen: General Topology, Addison Welsey Publishing Company, Reading, Massachusetts, 1970.

    Google Scholar 

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Simms, J.C. Traditional Cavalieri principles applied to the modern notion of area. J Philos Logic 18, 275–314 (1989). https://doi.org/10.1007/BF00274068

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