[13] Frischauf, Absolute Geometrie, nach Johann Bolyai, Leipzig, 1872. Halsted, The Science Absolute of Space, translated from the Latin, 4th edition, Austin, Texas, U.S.A. 1896.
[14] Both Lobatchewsky and Bolyai, as Veronese remarks, start rather from the point-pair than from distance. See Frischauf, Absolute Geometrie, Anhang.
[15] Compare Stallo, Concepts of Modern Physics, p. 248.
[16] Gesammelte Werke, pp. 255–268.
[17] On the history of this word, see Stallo, Concepts of Modern Physics, p. 258. It was used by Kant, and adapted by Herbart to almost the same meaning as it bears in Riemann. Herbart, however, also uses the word Reihenform to express a similar idea. See Psychologie als Wissenschaft, I. § 100 and II. § 139, where Riemann's analogy with colours is also suggested.
[18] Compare Erdmann's "Grössenbegriff vom Raum."
[19] Compare Veronese, op. cit. p. 642: "Riemann ist in seiner Definition des Begriffs Grösse dunkel." See also Veronese's whole following criticism.
[20] Vorträge und Reden, Vol. II. p. 18.
[21] Cf. Klein, Nicht-Euklid, I. p. 160.
[22] Since we are considering the curvature at a point, we are only concerned with the first infinitesimal elements of the geodesics that start from such a point.