[42] See p. 9 of Cayley's address to the Brit. Ass. 1883. Also a quotation from Klein in Erdmann's Axiome der Geometrie, p. 124 note.

[43] Nature, Vol. XLV. p. 407.

[44] Nicht-Euklid, I. p. 200.

[45] I.e. the equation AB + BC = AC, for three points in one straight line.

[46] The formula substituted by Klein for Cayley's inverse sine or cosine. The two are equivalent, but Klein's is mathematically much the more convenient.

[47] Elements of Projective Geometry, Second Edition, Oxford, 1893, Chap. IX.

[48] Chap. III. Section B.

[49] See Nicht-Euklid, I. p. 338 ff.

[50] See his Geometrie der Lage, § 8, Harmonische Gebilde.

[51] The anharmonic ratio of four numbers, p, q, r, s, is defined as