A sequel to the first six books of the Elements of Euclid, containing an easy introduction to modern geometry, with numerous examples. By John Casey.

THEORY OF FIGURES DIRECTLY SIMILAR. 195
The Brocard circle is called after M. HI. ]3ROOARD, Chef de
JBataillen, who first studied its properties in the Nouvelle Correspondance, Mathematique, tomes urI., IV., V., VI. (1876, '77, '78,
'79); and subsequently in two Papers read before the Association
Frangaise pour l'avancement des Sciences, Congre's d'Alger, 1881,
and Congr's de Rouen, 1883. Several Geometers have since
studied its properties, especially Neuberg, M'Oay, and Tucker.
Prop. I.-Brocard's first triangle is inversely similar
to ABC.

Dem.-Since OA' is perpendicular to BC, and OB'
to AC, the angle A'OB' is equal to ACB; but [Tue.. III.
xxi.]I A'OB' is equal to A'C'B'. ilence A'C'' is equal