Note 7 — Chapter I · A SHORT HISTORY OF METAGEOMETRY.

Klein's first account of elliptic Geometry, as a result of Cayley's projective theory of distance, appeared in two articles entitled "Ueber die sogenannte Nicht-Euklidische Geometrie, I, II," Math. Annalen 4, 6 (1871–2). It was afterwards independently discovered by Newcomb, in an article entitled "Elementary Theorems relating to the geometry of a space of three dimensions, and of uniform positive curvature in the fourth dimension," Crelle's Journal für die reine und angewandte Mathematik, Vol. 83 (1877). For an account of the mathematical controversies concerning elliptic Geometry, see Klein's "Vorlesungen über Nicht-Euklidische Geometrie," Göttingen 1893, I. p. 284 ff. A bibliography of the relevant literature up to the year 1878 was given by Halsted in the American Journal of Mathematics, Vols. 1, 2.