This is a preview of subscription content, log in via an institution to check access.
Bibliography
Beltrami, E., 1868: “Saggio di interpretazione della geometria non-Euclidea,“Giornale di Matematiche VI, 284–312.
Bonola, R., 1906:La geometria non-Euclidea, Zanichelli, Bologna.
Bonola, R., 1912:History of non-Euclidean geometry, tr, H.S. Carslaw, preface by F. Enriques, Open Court, Chicago.
Bottazzini, U., 1988: Fondamenti dell’arith- metica e della geometria, pp. 253-288 in vol. 3 ofStoria della scienza moderna e con-temporanea, Paolo Rossi editor. Unione Tipografico Editrice Torinese.
Courturat, L., 1905:Principes des mathématiques, Alcan, Paris.
Engel, F. and Stäckel, P., 1895:Theorie der Parallellinien von Euklid bis auf Gauss. Teubner, Leipzig.
Enriques, F., 1898:Lezioni di geometria proi- ettiva, Zanichelli, Bologna.
Enriques, F. (ed.), 1900:Questioni riguardanti la geometria elementare, Zanichelli, Bologna.
Fano, G., 1892: “Sui postulati fondamentali della geometria proiettiva,“Giornale di Matematiche 30, 106–131.
Field, J.V., and Gray, J.J., 1986:The Mathematical Work of Girard Desargues, Springer- Verlag, New York.
Freudenthal, H., 1957: “Zur Geschichte der Grundlagen der Geometrie,“Nieuw Archief voor Wiskunde (4) 5, 105–142.
Freudenthal, H, 1962: “The Main Trends in the Foundations of Geometry in the 19th Century,“ inLogic, Methodology and Philosophy of Sc/ence.Proceedingsofthe 1960 International Congress (E. Nagel, P. Suppes and A. Tarski, editors), Stanford University Press, 613-621.
Gray, J.J., 1986:Ideas of Space, Euclidean,non-Euclidean and Relativistic, Oxford University Press.
Helmholtz, H. von, 1870: “On the origin and significance of the axioms of geometry,” tr. M.F. Lowe, inHermann von Helmholtz, Epis-temological Writings, P. Hertz and M. Schlick, eds., Boston Studies in the physics of science 37, Reidel, Dordrecht and Boston, 1977.
Hilbert, D., 1899:Grundlagen der Geometrie, many subsequent editions.
Hubert, D., 1971:Foundations of geometry, 10th English edition, translation of the second German edition by L. Unger.
Hilbert, D., 1976: “Mathematical Problems,” inMathematical Developments arising from Hilbert Problems, Proceedings of Symposia in Pure Mathematics, American Mathematical Society, 2 vols, part 1.
Kline, M., 1972:Mathematical Thought from Ancient to Modern Times, Oxford University Press, Oxford.
Lobachetschefskij, N.I., 1899:Zwei geometrische Abhandlungen, tr. F. Engel. Teubner, Leipzig.
Moore, G.E., 1982:Zermelo’s Axiom of Choice, Springer-Verlag, New York.
Moulton, 1902: “A simple non-Desarguesian Plane Geometry,“Trans. American Mathematical Society, 3, 192–195.
Nagel, E., 1939: “The formation of modern concepts of formal logic in the development of geometry,“Osiris 7, 142–224.
Padoa, A., 1902: “Un nouveau système de définitions pour la géométrie euclidienne”Compte Rendu du Deuxième Congrès international des mathématiciens, Gauthier-Villars, Paris.
Pasch, M., 1882:Vorlesungen ü ber neuere Geometrie, Teubner, Leipzig.
Peano, G., 1889: /principii di geometria logicamente espositi, Turin, rep. inOpere scelte, 2, Rome, 1958, 56-91.
Peano, G., 1891:Die Grundzü ge des geometrischen Kalkü ls, tr. A. Schepp, Teubner, Leipzig.
Peano, G., 1894: “Sui fondamenti della Geometria,“Rivista di matematiche 4, 73.
Pieri, M., 1895: ‘Principii che reggiono la geometria di posizione’,Atti Accademia Torino, 30, 54–108.
Pieri, M., 1899: “I Principii della Geometria di Posizione, compositi in sistema logico de- duttivo,“Memorie della Reale Accademia delle Scienze di Torino (2) 48, 1–62.
Russell, B., 1903:Principles of Mathematics, Cambridge University Press, Cambridge.
Schur, F., 1899: “Über den Fundamentalsatz der projectiven Geometrie,”Mathematische Annalen 51, 401–409.
Segre, M., 1994: Peano’s Axioms in their Historical Context,Archive for History of Exact Sciences, 48, 201–342.
Steinitz, E. 1910 ’Algebraische Theorie der Körper’,Journal für Mathematik 137, reprinted as Steinitz, [1930].
Steinitz, E., 1930:Algebraische Theorie der Körper, R. Baer, H. Hasse (eds.), Walter de Gruyter, Leipzig.
Toepell, M.-M., 1986:Über die Entstehung von David Hilberts “Grundlagen der Geometrie”, Vandenhoeck & Ruprecht, Göttingen.
Vahlen.T., 1905:Abstrakte Geometrie, Leipzig.
Veblen, O., 1905:Princeton lectures “On the foundations of geometry,” University of Chicago Press.
Veblen, O. and J.W. Young, 1917:Protective Geometry, 2 vols, Ginn and Co., New York.
Whitehead, A.N., 1906:The Axioms of Projective Geometry, Cambridge University Press Tract nr. 4, Cambridge.
Wiener, H.L.G., 1890: “Ueber Grundlagen und Aufbau der Geometrie,”Jahresbericht der Deutschen Mathematiker-Vereinigung 1, 45–48.
Young, J.W., 1911:Lectures on Fundamental Concepts of Algebra and Geometry, Mac- millan, New York.
Zaitsev, E.A., 1994: “An Interpretation of Peano’s Logic,”Archive for History of Exact Sciences 46, 367–383.
Author information
Authors and Affiliations
Additional information
To David Fowler on the occasion of his 60th birthday.
Rights and permissions
About this article
Cite this article
Gray, J. Years ago. The Mathematical Intelligencer 20, 54–59 (1998). https://doi.org/10.1007/BF03025299
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF03025299