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.

LEMIOINE'S, TUCKER'S, AND TAYLOR'S CIRCLES. i79
9. If through A [second Fig., Prop. 4] a line AF be drawn
parallel to BC, and meeting the circle AOC again in F; prove
that BF intersects the circle AOC in a Brocard point.
10. In the same Fig., if BC cutthe circle AOC in G, prove that
the triangles ABC, ABG have a common Brocard point.
SECTION III.
LEMOINE'S, TUCKER'S, AND TAYLOR'S CIRCLES.
Prop. 1.-The three parallels to the sides of a triangle
through its symmedian point meet the sides in six concyclic points.
Dem.-Let the parallels be DE', EF', FD'. Join
ED', DF', FE'. Now AFKE' is a parallelogram. AK

bisects FE'. Hence [Section I., Prop. 5, Cor. 2] FE'