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.

TWO FIGURES DIRECTLY SIMILAR.

177

CED will [III., Section r., Prop. 17] be a given point:
if this be 2, f2 will be the centre of similitude of the
triangle ABC, and an equiangular inscribed triangle,
such as DFE, whose vertex F, corresponding to A, is
on the line AB. In like manner, there is another point,
f', which is the centre of similitude of ABC, and similar
inscribed triangles such as E'F'D', having the vertex
corresponding to A on the line AC.

DrF. -Q, '2 are called the Brocard points of the triangle ABC.
CoR. 1.-The circumcircle of the triangle AgB touches
BC in B.
Dem.-Since 0 is the double point of the triangles
ABC, DEF, the triangles f2BD, f2FA are equiangular;.. the angle 13BD = OAF. Therefore the circle Af2B
touches BC in B. In like manner, the circumcircles
of the triangles BMOC, CQfA touch respectively CA in C,
and AB in A.