[Of the following properties, some must have been long known, but I do not remember any early statement of them. The 1st, 10th, 15th, 16th, 19th, 20th, and 22nd are given, mostly without proof, in an article by Vecten in Gergonne's Annales de Matliématiques, vol. VII., p. 321 (1817); the first parts of the 3rd and 4th are proposed for proof by William Godward in The Gentleman's Diary for 1837, p. 48, and proved by him and others in the Diary for 1838, pp. 40-41; the first parts of the 5th, 6th, 12th, and 14th are given in M'Dowell's Exercises on Euclid and in Modern Geometry, §§ 27, 28, 29 (1863); the 9th in Milne's Weekly Problem Papers, p. 135 (1885); the first part of the 8th in Vuibert's Journal de Mathématiquts Elémentaires, 12° Année, p. 18 (1887); the 39th in the Journal de Mathématiques Elémentaires, edited by De Longchamps, 3° série,tome I.,p. 234 (1887). The others are believed to be new.