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.

vi

PREFACE.

most elegant Propositions in' Geometry. The
Supplement to Book VI. is the most important;
it embraces more than half the work, and consists
of eight Sections, as follows:-I., Additional Propositions; II., Centres of Similitude; III., Theory
of Harmonic Section; IV., Theory of Inversion;
V., Coaxal Circles; VI., Theory of Anharmonic
Section; VII., Theory of Poles and Polars, and
Reciprocation; VIII., Miscellaneous Exercises.
Some of the Propositions in these Sections have
first appeared in Papers published by myself; but
the greater number have been selected from the
writings of CHASLES, SALMON, and TOWNSEND.
For the proofs given by these authors, in some
instances others have been substituted, but in
no case except where by doing so they could be
made more simple and elementary.
The present edition is greatly enlarged: the
new matter, consisting of recent discoveries in Geometry, is contained in a Supplemental Chapter.
Several of the Demonstrations, and some of the
Propositions in this Chapter, are original, in particular the Theory of Harmonic Polygons, in Section VI. A large number of the Miscellaneous
Exercises are also original.
In collecting and arranging these additions
I have received valuable assistance from Professor
NEUBERG, of the University of Liege, and from
M. BROCARD (after whom the Brocard Circle is