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.

xvi

CONTENTS.

SECTION VIII.
PAGE
Miscellaneous Exercises,.. 148
In these Exercises will be found many remarkable
Propositions, some of which are of historical interest,
such as Miquel's Theorem, Malfatti's Problem, Bella.
vitis's Theorem, Weill's Theorem, and many others.
SUPPLEMENTARY CHAPTER.
SECTION I.
Theory of Isogonal and Isotomic Points, and of
Antiparallel and Symmedian Lines,.. 165
Isogonal conjugates with respect to an angle,.. 165, of concurrent lines,... 166,, with respect to a triangle,.. 167,, Exercises on,.... 167
Isotomic conjugates with respect to a side of a triangle, 168,, of concurrent lines,... 168,, with respect to a triangle,. 169,, Exercises on,. 169
Antiparallel lines,...... 169
Symmedian lines of a triangle,.170
Symmedian point of a triangle,.170,, properties of,.... 170
Brocard angle of triangle,..... 172
Symmedian point, Exercises on,.... 173
SECTION II.
Two Figures directly similar,. 173
Homothetic centre,..173
Homothetic figures, properties of,.... 174,, double points of,... 175,, properties of double points,. 176