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.

CONTENTS.

XV

SECTION VI.
PAGE
Theory of Anharmonic Section,.... 126
Anharmonic ratio of four collinear points,.. 127
Anharmonic ratio of points of intersection of a transversal with a pencil of four rays,.... 128
Anharmonic ratio of a pencil defined,... 128
Anharmonic ratio of four concyclic points,.. 129
Pascal's Theorem,..129
Two equal pencils having a common ray,... 131
Desargues' Theorem,...... 131
Involution,..... 132
Examples of involution,...... 134
Homographic division,.. 136
To find the double points of Homographic division,. 136
Examples of Homographic division,.. 137
Exercises,....... 140
SECTION VII.
Theory of Poles and Polars, and Reciprocation,. 141
Anharmonic ratio of four collinear points is equal to
the anharmonic ratio of their four polars,.. 141
Applications,........ 141
Locus of pole of a line which joins corresponding
points on lines divided homographically,.. 143
For two homographic systems of points on two lines
there exist two points, at each of which the
several pairs of corresponding points subtend equal
angles,.... 143
Reciprocation,....... 144
Examples of reciprocation,..... 145
Brianchon's Theorem,...... 147
Homographic pencils,.. 148