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James Gregory and the Impossibility of Squaring the Central Conic Sections

  • Davide Crippa
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Part of the Frontiers in the History of Science book series (FRHIS)

Abstract

The Vera Circuli et Hyperbolae Quadratura in sua propria proportionis specie inventa (Gregory 1667, hereinafter VCHQ) was James Gregory’s debut work in the domain of quadrature problems. It was published in Padua in 1667 and reprinted a few months later, in the spring of 1668, as an appendix to another treatise, the Geometriae Pars Universalis (Gregory 1668, hereinafter GPU).

References

  1. Beeley Philip and Scriba, Christoph. 2008. Disputed Glory. John Wallis and some questions of precedence in seventeenth-century mathematics. In Kosmos und Zahl. Beiträge zur Mathematik- und Astronomiegeschichte, zur Alexander von Humboldt und Leibniz. 275–299. Ed. H. Hacht, R. Mikosch, I. Schwarz et. al, 275–299. Stuttgart: Franz Steiner Verlag.Google Scholar
  2. Borwein, Jonathan and Borwein, Peter. 1998. πand the AGM: A Study in Analytic Number Theory and Computational Complexity. New York: Wiley-Interscience.zbMATHGoogle Scholar
  3. Bos, Henk. 2001. Redefining geometrical exactness. Dordrecht Heidelberg New York London: Springer.CrossRefGoogle Scholar
  4. Dehn, Max and Hellinger, Ernst. 1939. On James Gregory’s “Vera quadratura”. In The James Gregory tercentenary memorial volume. Ed. Herbert W. Turnbull, 468–478. Edinburgh: Royal Society of Edinburgh.Google Scholar
  5. Dehn, Max and Hellinger Ernerst. 1943. Certain mathematical achievements of James Gregory. In The American Mathematical Monthly. 50(3): 149–163.MathSciNetCrossRefGoogle Scholar
  6. Descartes, René. 1897–1913. Oeuvres de Descartes. Eds. Charles Adam and Paul Tannery. 12 vols. Paris: Cerf.Google Scholar
  7. Descartes, René. 1659-1661. Renati Descartes Geometria. Editio Secunda. Multis accessionibus exornata, et plus altera sua parte adaucta. Ed. Frans Van Schooten. Amsterdam: Apud Ludovicum et Danielem Elzevirios.Google Scholar
  8. Dijksterhuis, E. Jan. 1939. James Gregory and Christiaan Huygens. In The James Gregory Tercentenary Memorial Volume. Ed. Herbert W. Turnbull, 478–486. Edinburgh: Bell and Sons.Google Scholar
  9. Feingold, Mordechai. 1996. Huygens and the Royal Society. De Zeventiende Eeuw. 12: 22–36.Google Scholar
  10. Gregory, James. 1667. Vera circuli et hyperbolae quadratura, in sua propria specie inventa. Padua: ex typographia Iacobi de Cadorinis.Google Scholar
  11. Gregory, James. 1668. Geometriae pars universalis. Padua: Paolo Frambotti.Google Scholar
  12. Gregory, James. 1668a. Mr. Gregories answer to the animadversions of Mr. Hugenius upon his book, De vera Circuli & Hyperbolae Quadratura; as they were publish’d in the Journal des Scavans of July 2. 1668. Philosophical Transactions of the Royal Society. 3, 37: 732–735.CrossRefGoogle Scholar
  13. Gregory James. 1668b. Exercitationes geometricae. London: William Godbid.Google Scholar
  14. Gregory, James. 1668c. An Extract of a Letter of Mr. James Gregory to the Publisher, Containing Some Considerations of His, upon M. Hugens His Letter, Printed in Vindication of His Examen of the Book, Entitled Vera Circuli & Hyperbola Quadratura. Philosophical Transactions of the Royal Society. 3, 44: 882–886.CrossRefGoogle Scholar
  15. Heath, Thomas. 1896. Apollonius of Perga treatise on conic sections (edited in modern notation). Cambridge: Cambridge University Press.Google Scholar
  16. Hofmann, Joseph. 1974. Leibniz in Paris (1672-1676). His growth to mathematical maturity. Trans. A. Prag and D. T. Whiteside. Cambridge: Cambridge University Press.zbMATHGoogle Scholar
  17. Huygens, Christiaan. 1668. Extrait d’une lettre de M. Huigens à l’auteur du Journal, touchant la réponse que M. Gregory a faite à l’examen du livre intitulé Vera Circuli et Hyperboles Quadratura, dont on a parlé dans le V. Journal de cette anée. Journal des Sçavans. 12 November 1668: 109–112.Google Scholar
  18. Huygens, Christiaan. 1724. Christiani Hugenii Zulichemii, Dum viveret Zelemii Toparchae, Opera Varia. Volumen primum. Lugduni Batavorum: apud Janssonios vander Aa.Google Scholar
  19. Huygens, Christiaan. 1888–1950. Oeuvres complètes publiées par la Société hollandaise des sciences, 22 vol. Ed. Bierens de Haan. The Hague: M. Nijhoff.zbMATHGoogle Scholar
  20. Jesseph, Douglas. 1999. Squaring the Circle: the War between Hobbers and Wallis. Chicago and London: University of Chicago Press.zbMATHGoogle Scholar
  21. Journal. 1668. Vera Circuli et Hyperboles Quadratura, in propria sua proportionis specie inventa et demonstrata a Jacobo Gregorio Scoto. In 4 Patavii (anonymous review). Le Journal des Sçavans de l’an 1668: 74.Google Scholar
  22. Lützen, Jesper. 2014. 17th century arguments for the impossibility of the indefinite and the definite quadrature of the circle. Revue d’histoire des mathématiques. 20: 211–251.zbMATHGoogle Scholar
  23. Malet, Antoni. 1989a. Studies on James Gregorie. Phd Dissertation: Princeton University.Google Scholar
  24. Panza, Marco. 2005. Newton et les origines de l’analyse. Paris: Blanchard.zbMATHGoogle Scholar
  25. Pappus. 1986. Book 7 of the Collection, edited by A. Jones. ed., transl. Alexander Jones. Dordrecht Heidelberg New York London: Springer.Google Scholar
  26. Sasaki, Chihara. 2003. Descartes’s mathematical thought. Dordrecht Heidelberg New York London: Springer.CrossRefGoogle Scholar
  27. Scriba, Christoph. 1957. James Gregorys frühe Schriften zur Infinitesimalrechnung. Giessen: Selbstverlag des Mathematischen Seminars.Google Scholar
  28. Scriba, Christoph. 1983. Gregory’s converging double sequence. A New look at the controversy between Huygens and Gregory over the “analytical” quadrature of the circle. Historia Mathematica. 10: 274–285.MathSciNetCrossRefGoogle Scholar
  29. Stedall, Jacqueline. 2002. A Discourse Concerning Algebra: English Algebra to 1685. Oxford: Oxford University Press.zbMATHGoogle Scholar
  30. Transactions. 1668. An account of some Books (anonymous review). Philosophical Transactions of the Royal Society. 3: 685–688.CrossRefGoogle Scholar
  31. Turnbull, Herbert W. 1939. The James Gregory Tercentenary Memorial Volume. Edinburgh: Bell and Sons.Google Scholar
  32. Euclid. 1990. Les Eléments: traduction et notes de Bernard Vitrac. Volume III. Ed. Bernard Vitrac. Paris: Presses Universitaires de France (PUF).zbMATHGoogle Scholar
  33. Youkshevitch A. P. 1976. The Concept of Function up to the Middle of 19th Century. Archive for History of Exact Sciences. 16(1): 37–85.MathSciNetGoogle Scholar
  34. Wallis, John. 2004. The arithmetic of infinitesimals. Ed., transl. Jacqueline Stedall. Dordrecht Heidelberg New York London: Springer.Google Scholar
  35. Wallis, John. 2012. The Correspondence of John Wallis (1616-1703). Volume III. October 1668-1671. Eds. Philip Beeley, Cristoph Scriba. Oxford: Oxford University Press.Google Scholar
  36. Whiteside, Derek, Thomas. 1961. Patterns of mathematical thought in later 17th century mathematics. Archive for History of Exact Sciences. 1: 179–388.MathSciNetCrossRefGoogle Scholar

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Authors and Affiliations

  • Davide Crippa
    • 1
  1. 1.Université Paris Diderot, SPHèreParisFrance

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