# Oswald Veblen's Publications

A list of Oswald Veblen's publications appeared in Royal Society of Edinburgh Year Book 1962, 52-59. We give a version of the list below:
 1902 "Hilbert's Foundation of Geometry", Monist, 13, 303-309. 1904 (a) "The Heine-Borel Theorem", Bull. Amer. Math Soc., 10, 436-439. (b) "Polar-coordinate Proofs of Trigonometric Formulae", Amer. Math. Mon., 11, 6-12. (c) "The Transcendence of π and $e$", Amer. Math. Mon., 11, 219-223. (d) "A System of Axioms for Geometry", Trans. Amer. Math. Soc., 5, 343-384. 1905 (a) "Theory of Plane Curves in Non-metrical Analysis Situs", Trans. Amer. Math. Soc., 6, 83-98. (b) "Definitions in Terms of Order Alone in the Linear Continuum and well-ordered Sets", Trans. Amer. Math. Soc., 6, 165-171. 1906 (a) "The Square Root and the Relations of Order", Trans. Amer. Math. Soc., 7, 197-199. (b) (With W H Bussey) "Finite Projective Geometries", Trans. Amer. Math. Soc., 7, 241-259. 1907 (a) "On Magic Squares", Messeng. Math., 37, 116-118. (b) "Collineations in a Finite Projective Geometry", Trans. Amer. Math. Soc., 8, 366-368. (c) (With J H Maclagan-Wedderburn), "Non-Desarguesian and Non-Pascalian Geometries", Trans. Amer. Math. Soc., 8, 379-388. (d) (With N J Lennes) Introduction to Infinitesimal Analysis : Functions of One Real Variable. London, Chapman and Hall; New York, Wiley. 1908 (a) "Continuous Increasing Functions of Finite and Transfinite Ordinals", Trans. Amer. Math. Soc., 9, 280-292. (b) "On the well-ordered Subsets of the Continuum", R. C. Circ. Mat., Palermo, 25, 235-236, 397. (c) (With J W Young) "A set of Assumptions for Projective Geometry", Amer. J. Math., 30, 347-380. 1910 (a) Letter to the editor of the Jber. Dtsch. MatVer., 19, 263. (b) (With J W Young) Projective Geometry. Vol. I. Ginn and Co., Boston and London. 1912 (a) "On the Definition of Multiplication of Irrational Numbers", Amer. J. Math., 34, 211-214. (b) "An application of Modular Equations in Analysis Situs", Ann. Math., Princeton, 14, 86-94. 1913 (a) "Decomposition of an N-space by a Polyhedron", Trans. Amer. Math. Soc., 14, 65-72. (b) (With J W Alexander) "Manifolds of n Dimensions", Ann. Math., Princeton, 14, 163-178. 1917 (a) "On the Deformation of an n-cell", Proc. Nat. Acad. Sci., Wash., 3, 654-656. (b) "Doubly Oriented Lines", Bull. Amer. Math. Soc., 23, 444. 1918 (With J W Young) Projective Geometry. Vol. II. Ginn and Co., Boston and London. 1921 (With P H Franklin) "On Matrices whose Elements are Integers", Ann. Math., Princeton, 23, 1-15. 1922 (a) (with L P Eisenhart) "The Riemann Geometry and its Generalization, Proc. Nat. Acad. Sci., Wash., 8, 19-23. (b) "Normal Coordinates for the Geometry of Paths", Proc. Nal. Acad. Sci., Wash., 8, 192-197. (c) "Projective and Affine Geometry of Paths", Proc. Nat. Acad. Sci., Wash., 8, 347-350. (d) Analysis situs. Colloq. Lect. Amer. Math. Soc., 5. 1923 (a) Equiaffine Geometry of Paths", Proc. Nat. Acad. Sci., Wash., 9, 3-4. (b) "Projective and Affine Geometry of Paths", Bull. Amer. Math. Soc., 29,3-4. (c) (With T Y Thomas) "Geometries of Paths Admitting First Integrals", Bull. Amer. Math. Soc., 29, 218. 1924 (a) "The Intersection Numbers", Trans. Amer. Math. Soc., 25, 540-550. (b) "Invariance of the Poincaré Numbers of a Discrete Group", Bull. Amer. Math. Soc., 30, 405-406. (c) (With T Y Thomas) "Extensions of Relative Tensors", Trans. Amer. Math. Soc., 26, 373-377. (d) (With T Y Thomas) "The Geometry of Paths", Trans. Amer. Math. Soc., 25, 551-608. 1925 (a) "Remarks on the Foundations of Geometry", Bull. Amer. Math. Soc., 31, 121-141. (b) (With J M Thomas) "Projective Normal Coordinates for the Geometry of Paths", Proc. Nat. Acad. Sci., Wash., 11, 204-207. 1926 (With J M Thomas) "Projective Invariants of Affine Geometry of Paths", Ann. Math., Princeton, 27, 279-296. 1927 Invariants of Quadratic Differential Forms. Camb. Tracts Math., 24. 1928 (a) "Projective Tensors and Connections", Proc. Nat. Acad. Sci., Wash., 14, 154-166. (b) "Conformal Tensors and Connections", Proc. Nat. Acad. Sci., Wash., 14, 735-745. 1929 (a) "Henry Burchard Fine - In Memoriam", Bull. Amer. Math. Soc., 35, 726-730. (b) "Generalized Projective Geometry", J. Lond. Math. Soc., 4, 140-160. (c) "Differential Invariants and Geometry", Int. Congr. Math., 1, 181-189. 1930 (a) "A Generalization of the Quadratic Differential Form", Quart. J. Math., 1, 60-76. (b) (With B Hoffmann) "Projective Relativity", Phys. Rev., 36, 810-822. 1931 (With J H C Whitehead) "A Set of Axioms for Differential Geometry", Proc. Nat. Acad. Sci., Wash., 17, 551-561. (Erratum, p. 660.) 1932 (With J H C Whitehead) The Foundations of Differential Geometry, Camb. Tracts Math., 29. 1933 (a) "Geometry of Two-component Spinors", Proc. Nat. Acad. Sci., Wash., 19, 462-474. (b) "Geometry of Four-component Spinors", Proc. Nat. Acad. Sci., Wash., 19, 503-517. (c) "Spinors in Projective Relativity", Proc. Nat. Acad. Sci., Wash., 19, 979-989. (d) Projeklive Relativitätstheorie, Ergebn. Math., 2. 1934 (a) (With A H Taub) "Projective Differentiation of Spinors", Proc. Nat. Acad. Sci., Wash., 20, 85-92. (b) (With A H Taub and J von Neumann) "The Dirac Equation in Projective Relativity", Proc. Nat. Acad. Sci., Wash., 20, 383-388. (c) "Certain Aspects of Modern Geometry." (Three lectures delivered at the Rice Institute): I. The Modern Approach to Elementary Geometry. II. Analysis Situs. III. Modern Differential Geometry. Rice Inst. Pamthl., 21, 209-222, 223-236, 237-255. (d) "Spinors", J. Wash. Acad. Sci., 24, 281-290. 1935 (a) "Formalism for Conformal Geometry", Proc. Nat. Acad. Sci., Wash., 21, 168-173. (b) "A Conformal Wave Equation", Proc. Nat. Acad. Sci., Wash., 21, 484-487. 1936 (With J von Neumann) Geometry of Complex Domains. Mimeographed notes of lectures by 0 Veblen and J W Givens (notes by A H Taub and J W Givens). Institute for Advanced Study, Princeton. Revised edition, 1955. 1937 "Spinors and Projective Geometry", Int. Congr. Math., 1936,1, 111-127. 1954 (With D Montgomery): Obituary N J Lennes, Bull. Amer. Math. Soc., 60, 264-265.

Last Updated November 2007