Linked bibliography for the SEP article "Nineteenth Century Geometry" by Roberto Torretti

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If everything goes well, this page should display the bibliography of the aforementioned article as it appears in the Stanford Encyclopedia of Philosophy, but with links added to PhilPapers records and Google Scholar for your convenience. Some bibliographies are not going to be represented correctly or fully up to date. In general, bibliographies of recent works are going to be much better linked than bibliographies of primary literature and older works. Entries with PhilPapers records have links on their titles. A green link indicates that the item is available online at least partially.

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Primary Sources

  • Bolyai, J., 1832. Scientia absoluta spatii. Appendix to Bolyai, F., Tentamen juventutem studiosam in elementa matheseos purae elementis ac sublimioris, methodo intuitiva, evidentiaque huic propria, introducendi, Tomus Primus. Maros Vasarhely: J. et S. Kali. (English translation by G. B. Halsted printed as a supplement to Bonola 1955.) (Scholar)
  • Cayley, Arthur, 1859. “A sixth memoir upon quantics,” Philosophical Transactions of the Royal Society of London, 149: 61–90.
  • Ehresmann, Ch., 1957. “Les connexions infinitésimales dans un espace fibré différentiable,” in Colloque de Topologie (Espaces Fibrés), Bruxelles 1950, Paris: Masson, pp. 29–55. (Scholar)
  • Einstein, A., 1915. “Die Feldgleichungen der Gravitation,” Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin (1915), pp. 844–847. (Scholar)
  • Einstein, A., 1916. “Die Grundlagen der allgemeinen Relativitätstheorie,” Annalen der Physik, 49: 769–822. (Scholar)
  • Euclides, Elementa, I. L. Heiberg (ed.), Leipzig: B. G. Teubner, 5 volumes., 1883–88. (For English translation, see below under Heath). (Scholar)
  • Gauss, C. F., 1828. Disquisitiones generales circa superficies curvas, Göttingen: Dieterich. (English translation by A. Hiltebietel and J. Morehead: Hewlett, NY, Raven Press, 1965.) (Scholar)
  • Hilbert, D., 1899. “Die Grundlagen der Geometrie,” in Festschrift zur Feier der Enthüllung des Gauss-Weber Denkmals, Leipzig: B.G. Teubner, pp. 3–92. (Scholar)
  • Hilbert, D., 1968. Grundlagen der Geometrie, mit Supplementen von P. Bernays. Zehnte Auflage. Stuttgart: Teubner. (Tenth, revised edition of Hilbert 1899.) (Scholar)
  • Klein, F., 1871. “Über die sogenannte Nicht-Euklidische Geometrie,” Mathematische Annalen, 4: 573–625. (Scholar)
  • Klein, F., 1872. Vergleichende Betrachtungen über neuere geometrische Forschungen, Erlangen: A. Duchert. (Scholar)
  • Klein, F., 1873. “Über die sogenannte Nicht-Euklidische Geometrie (Zweiter Aufsatz),” Mathematische Annalen, 6: 112–145. (Scholar)
  • Klein, F., 1893. “Vergleichende Betrachtungen über neuere geometrische Forschungen,” Mathematische Annalen, 43: 63–100. (Revised version of Klein 1872). (Scholar)
  • Klein, F., 1911. “Über die geometrischen Grundlagen der Lorentz-Gruppe,” Physikalische Zeitschrift, 12: 17–27. (Scholar)
  • Lie, S., 1888–1893. Theorie der Transformationsgruppen (3 volumes), Unter Mitwirkung von F. Engel, Leipzig: Teubner. (Scholar)
  • Lobachevsky, N. I., 1837. “Géométrie imaginaire,” Journal für die reine und angewandte Mathematik, 17: 295–320.
  • Lobachevsky, N. I., 1840. Geometrische Untersuchungen zur Theorie der Parallellinien, Berlin: F. Fincke. (English translation by G. B. Halsted printed as a supplement to Bonola 1955.) (Scholar)
  • Lobachevsky, N. I., 1856. Pangéométrie ou précis de géométrie fondée sur une théorie générale et rigoureuse des parallèles, Kazan: Universitet. (Scholar)
  • Locke, J., 1690. An Essay concerning Humane Understanding (in four books), London: Printed for Thomas Basset and sold by Edward Mory. (Published anonymously; the author's name was added in the second edition). (Scholar)
  • Minkowski, H., 1909. “Raum und Zeit,” Physikalische Zeitschrift, 10: 104–111. (Scholar)
  • Pasch, M., 1882. Vorlesungen über neueren Geometrie, Leipzig: Teubner. (Scholar)
  • Poincaré, H., 1887. “Sur les hipothèses fondamentales de la géométrie,” Bulletin de la Société mathématique de France, 15: 203–216. (Scholar)
  • Poncelet, J. V., 1822. Traité des propriétés projectives des figures, Paris: Bachelier. (Scholar)
  • Ricci, G. and T. Levi-Cività, 1901. “Méthodes de calcul différentiel absolu et leurs applications,” Mathematische Annalen, 54: 125–201.
  • Riemann, B., 1854. “Über die Hypothesen, welche der Geometrie zugrunde liegen,” Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen, 13 (1867): 133–152. (For English translation, see below under Spivak.) (Scholar)
  • Riemann, B., 1861. “Commentatio mathematica, qua respondere tentatur quaestioni ab illustrissima Acad. Parisiensi propositae,” in Bernhard Riemanns gesammelte mathematische Werke und wissenschaftlicher Nachlass, Leipzig: Teubner, 1876, pp. 391–404. (Scholar)
  • Russell, B., 1897. An Essay on the Foundations of Geometry, Cambridge: Cambridge University Press. (Unaltered reprint: New York, Dover, 1956.) (Scholar)
  • Saccheri, G. 1733. Euclides ab omni nævo vindicatus sive conatus geometricus quo stabiliuntur prima ipsa universæ geometriæ principia, Mediolani: Ex Typographia Pauli Antonii Montani. (Reprint, with facing English translation by G. B. Halsted: New York, Chelsea, 1986.) (Scholar)

Secondary Literature

  • Acuña, Pablo, 2016. “Minkowski spacetime and Lorentz invariance: The cart and the horse or two sides of a single coin?,” Studies in History and Philosophy of Science (Part B: Studies in History and Philosophy of Modern Physics), 55: 1–12. (Scholar)
  • Blumenthal, L. M., 1961. A Modern View of Geometry, San Francisco: Freeman. (Scholar)
  • Boi, Luciano, 1995. Le problème mathématique de l'espace: Une quête de l'intelligible, Berlin: Springer. (Scholar)
  • Bonola, R., 1955. Non-Euclidean Geometry: A critical and historical study of its development. English translation with additional appendices by H.S. Carslaw. New York: Dover. (Scholar)
  • Freudenthal, H., 1957. “Zur Geschichte der Grundlagen der Geometrie,” Nieuw Archief vor Wiskunde, 5: 105–142. (Scholar)
  • Freudenthal, H., 1960. “Die Grundlagen der Geometrie um die Wende des 19. Jahrhunderts,” Mathematisch-physikalische Semesterbericht, 7: 2–25. (Scholar)
  • Gallot, S., D. Hulin, and J. Lafontaine, 2004. Riemannian Geometry, Berlin: Springer, 3rd edition. (An up-to-date textbook, with solutions to odd-numbered exercises. A section is devoted to the “pseudo”-Riemannian geometry employed in Relativity Theory.) (Scholar)
  • Giedymin, J., 1982. Science and Convention: Essays on Henri Poincaré's Philosophy of Science and the Conventionalist Tradition, Oxford: Pergamon. (Scholar)
  • Greenberg, M. J., 2008. Euclidean & Non-Euclidean Geometry: Development and History, New York: Freeman, 4th edition. (An excellent tool for self-study at the high-school senior or college freshman level.) (Scholar)
  • Heath, T. L., 1956. The Thirteen Books of Euclid's Elements, translated from the text of Heiberg with introduction and commentary, New York: Dover, 3 volumes, 2nd edition, revised with additions. (Scholar)
  • Magnani, L., 2001. Philosophy and Geometry: Theoretical and Historical Issues, Dordrecht: Kluwer. (Scholar)
  • Nagel, E., 1939. “The formation of modern conceptions of formal logic in the development of geometry,” Osiris, 7: 142–224. (Scholar)
  • O'Neill, B., 1983. Semi-Riemannian Geometry with Applications to Relativity, New York: Academic Press. (Scholar)
  • Nomizu, K., 1956. Lie Groups and Differential Geometry, Tokyo: The Mathematical Society of Japan. (Scholar)
  • Ronan, M., 2008. “Lie Theory,” in T. Gowers (ed.), The Princeton Companion to Mathematics, Princeton, NJ: Princeton University Press, pp. 229–234. (Scholar)
  • Rosenfeld, B. A., 1988. A History of Non-Euclidean Geometry: Evolution of the Concept of a Geometric Space, translated by Abe Shenitzer, New York: Springer. (Scholar)
  • Spivak, M., 1979. A Comprehensive Introduction to Differential Geometry (5 volumes), Berkeley: Publish or Perish, 2nd edition. (Contains an excellent English translation, with mathematical commentary, of Riemann's lecture “On the hypotheses that lie at the foundation of geometry”; see Vol. 2, pp. 135ff.) (Scholar)
  • Torretti, R., 1978. Philosophy of Geometry from Riemann to Poincaré, Dordrecht: Reidel. (Corrected reprint: Dordrecht, Reidel, 1984). (Scholar)
  • Trudeau, R. J., 1987. The Non-Euclidean Revolution, Boston: Birkhäuser. (Scholar)
  • Winnie, J. W., 1986. “Invariants and objectivity: A theory with applications to relativity and geometry,” in R. G. Colodny (ed.), From Quarks to Quasars, Pittsburgh: Pittsburgh University Press, pp. 71–180. (Scholar)

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