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.

XVlll

CONTENTS.

SECTION V.
PAGE
Special Applications of the Theory of Figures
directly similar,.. 194
1~. The Brocard circle,...... 194
Brocard's first triangle,...... 195,,,, perspective properties of,. 196,,,, points, properties of,.. 196, second triangle,.... 197
Brocard's second triangle is the triangle of similitude of three figures described on the sides of
a triangle,... 197
Properties of symmedian lines of triangles formed
by three corresponding lines of three figures
directly similar,.... 197
Centres of similitude of triangles formed by corresponding lines,....... 199
2~. The nine-points circle,.. 199
New proof of Feuerbach's theorem,... 201
Exercises,....... 203
SECTION VI.
Theory of Harmonic Polygons,. 205
Harmonic polygons defined,.. 205,, symmedian point of,... 205,, symmedian lines of,.. 205,, Brocard circle of,.. 205,, Brocard angle of,... 205
Harmonic polygon, the inverse of a regular polygon,. 205
Re-entrant harmonic polygons,.... 206
Inversion of harmonic polygons into regular polygons, 207
Centres of inversion of harmonic polygons,. 208
Relation between Brocard angles of harmonic
polygons,.... 209
Properties of harmonic polygons,.... 209