A set of postulates for abstract geometry, expressed in terms of the simple relation of inclusion

Author:

Huntington Edward V.

Publisher

Springer Science and Business Media LLC

Subject

General Mathematics

Reference7 articles.

1. M. Pasch, Vorlesungen über neuere Geometrie, Leipzig 1882. G. Veronese, Fondamenti di Geometria a più dimensioni, 1891, translated into German by A. Schepp, Grundzüge der Geometrie, 1894. G. Peano, I Principii di Geometria, Turin 1889; also Sui fondamenti della geometria, in Rivista di Matematica 4, p. 51?90, 1894. M. Pieri, Della geometria elementare come sistema ipotetico deduttivo; monographia del punto e del moto, Memorie della Reale Accademia delle Scienze di Torino, (2) 49, p. 173?222, 1899; also Sur la géométrie envisagée comme un système purement logique, Bibliothèque du Congrès international de Philosophie, Paris 1900 3, p. 367?404. D. Hilbert, Grundlagen der Geometrie, Gauß-Weber Festschrift, 1899; translated into English by E. J. Townsend, The Foundations of Geometry, 1902; third German edition, as vol. 7 of the series called Wissenschaft und Hypothese, (Leipzig 1909). In this third edition, the numbering of the axioms is slightly altered, in view of an article by E. H. Moore, 1902; Axiom II 4 of the original list is now omitted, and what was originally Axiom II 5 is now numbered II 4. O. Veblen, A system of Axioms for Geometry, Trans. Am. Math. Soc. 5 (1904), p. 343?384. Also, The Foundations of Geometry, in a volume called Monographs on Topics of Modern Mathematics relevant to the Elementary Field, edited by J. W. A. Young, p. 1?51, 1911. Another set of postulates, based on concepts not so closely connected with the present work, has been recently given by A. R. Schweitzer, A theory of geometrical relations, Am. J. of Math., 31 (1909), p. 365?410.

2. E. V. Huntington, A complete set of postulates for the theory of absolute continuous magnitude, Trans. Am. Math. Soc., 3 (1902), p. 264?279, and later papers. Compare also the forthcoming Lehrbuch der Algebra by A. Loewy.

3. B. Russell, Principles of Mathematics, 1903; A. N. Whitehead and B. Russell, Principia Mathematica, 1, 1911. See also Whitehead's excellent popular Introduction to Mathematics, (?Home University Library?, London 1911).

4. F. Schur, Zur Proportionslehre, Math. Ann. 57 (1903), p. 205?208.

5. G. Vailati, Sui principi fondamentali della Geometria della retta, Rivista di Matematica, 2 (1892), p. 71?75; E. V. Huntington, The Continuum as a Type of Order, reprinted from the Annals of Mathematics, 1905 (Publication Office of Harvard University).

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