* Euclid's, Elements, IV. 4.Google Scholar

† Todhunter's, Elements of Euclid, p. 312 (1864).Google Scholar

‡ See the note on p. 32.

§ MrLemoine, E. in the Report (second part) of the 21st session of the Association Française pour l' avancement des sciences, p. 49 (1892).Google Scholar

This is established in the course of the proof of Heron' theorem regarding the area of a triangle. See § 8.

† The Bemiperimeter of a triangle is usually denoted, in this country and Korth America, by s; on the continent of Europe it is generally denoted p. Kuler, who was one of the first if not the first to introduce the notation a, b, c for the sides of ABC, denotes the semiperimeter ½(AB + BC + CA) by S. See an article by him entitled Varice demonstrationes geometrice printed in Novi Commentarii Academice Scientiarum Imperialis Petropolitance for the years 1747–1748, I. 53 (1750).Google Scholar

* Both (7) and (8) were proposed at a competitive examination in France in 1881. For the proofs see Vuibert's, Journal, VII. 121–3 (1883).Google Scholar

† See § 5, (34).