[33] Crelle's Journal, Vols. XIX. XX., 1839–40.

[34] Nicht-Euklid, I. p. 190.

[35] This article is more trigonometrical and analytical than the German book, and therefore makes the above interpretation peculiarly evident.

[36] Such surfaces are by no means particularly remote. One of them, for example, is formed by the revolution of the common Tractrix

x = a sin φ, y = a (log tan φ 2 + cos φ).

[37] "Teoria fondamentale degli spazii di curvatura costanta," Annali di Matematica, II. Vol. 2, 1868–9. Also translated by J. Hoüel, loc. cit.

[38] See Klein, Nicht-Euklid, I. p. 47 ff., and the references there given.

[39] See quotation below, from his British Association Address.

[40] Compare the opening sentence, due to Cayley, of Salmon's Higher Plane Curves.

[41] V. Nicht-Euklid, I. Chaps. I. and II.